1
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Guo Y, Liu Z, Tang H, Hu XM, Liu BH, Huang YF, Li CF, Guo GC, Chiribella G. Experimental Demonstration of Input-Output Indefiniteness in a Single Quantum Device. Phys Rev Lett 2024; 132:160201. [PMID: 38701466 DOI: 10.1103/physrevlett.132.160201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2023] [Accepted: 03/20/2024] [Indexed: 05/05/2024]
Abstract
Quantum theory allows information to flow through a single device in a coherent superposition of two opposite directions, resulting into situations where the input-output direction is indefinite. Here we introduce a theoretical method to witness input-output indefiniteness in a single quantum device, and we experimentally demonstrate it by constructing a photonic setup that exhibits input-output indefiniteness with a statistical significance exceeding 69 standard deviations. Our results provide a way to characterize input-output indefiniteness as a resource for quantum information and photonic quantum technologies and enable tabletop simulations of hypothetical scenarios exhibiting quantum indefiniteness in the direction of time.
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Affiliation(s)
- Yu Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China
| | - Zixuan Liu
- QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong
- HKU-Oxford Joint Laboratory for Quantum Information and Computation
| | - Hao Tang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China
| | - Xiao-Min Hu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China
| | - Bi-Heng Liu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China
| | - Yun-Feng Huang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China
| | - Giulio Chiribella
- QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong
- HKU-Oxford Joint Laboratory for Quantum Information and Computation
- Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, United Kingdom
- Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, Canada
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2
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Parzygnat AJ, Fullwood J, Buscemi F, Chiribella G. Virtual Quantum Broadcasting. Phys Rev Lett 2024; 132:110203. [PMID: 38563923 DOI: 10.1103/physrevlett.132.110203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2023] [Accepted: 02/02/2024] [Indexed: 04/04/2024]
Abstract
The quantum no-broadcasting theorem states that it is impossible to produce perfect copies of an arbitrary quantum state, even if the copies are allowed to be correlated. Here we show that, although quantum broadcasting cannot be achieved by any physical process, it can be achieved by a virtual process, described by a Hermitian-preserving trace-preserving map. This virtual process is canonical: it is the only map that broadcasts all quantum states, is covariant under unitary evolution, is invariant under permutations of the copies, and reduces to the classical broadcasting map when subjected to decoherence. We show that the optimal physical approximation to the canonical broadcasting map is the optimal universal quantum cloning, and we also show that virtual broadcasting can be achieved by a virtual measure-and-prepare protocol, where a virtual measurement is performed, and, depending on the outcomes, two copies of a virtual quantum state are generated. Finally, we use canonical virtual broadcasting to prove a uniqueness result for quantum states over time.
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Affiliation(s)
- Arthur J Parzygnat
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Experimental Study Group, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - James Fullwood
- School of Mathematics and Statistics, Hainan University, Haikou, Hainan, 570228, China
- School of Mathematical Sciences, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, China
| | - Francesco Buscemi
- Graduate School of Informatics, Nagoya University, Chikusa-ku, 464-8601 Nagoya, Japan
| | - Giulio Chiribella
- QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pok Fu Lam Road, Hong Kong
- Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, United Kingdom
- Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, Canada
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3
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van der Lugt T, Barrett J, Chiribella G. Device-independent certification of indefinite causal order in the quantum switch. Nat Commun 2023; 14:5811. [PMID: 37726274 PMCID: PMC10509257 DOI: 10.1038/s41467-023-40162-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2022] [Accepted: 07/14/2023] [Indexed: 09/21/2023] Open
Abstract
Quantum theory is compatible with scenarios in which the order of operations is indefinite. Experimental investigations of such scenarios, all of which have been based on a process known as the quantum switch, have provided demonstrations of indefinite causal order conditioned on assumptions on the devices used in the laboratory. But is a device-independent certification possible, similar to the certification of Bell nonlocality through the violation of Bell inequalities? Previous results have shown that the answer is negative if the switch is considered in isolation. Here, however, we present an inequality that can be used to device-independently certify indefinite causal order in the quantum switch in the presence of an additional spacelike-separated observer under an assumption asserting the impossibility of superluminal and retrocausal influences.
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Affiliation(s)
- Tein van der Lugt
- Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, United Kingdom.
| | - Jonathan Barrett
- Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, United Kingdom
- Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5, Canada
| | - Giulio Chiribella
- Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, United Kingdom.
- Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5, Canada.
- QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong, Hong Kong.
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4
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Wu YD, Zhu Y, Bai G, Wang Y, Chiribella G. Quantum Similarity Testing with Convolutional Neural Networks. Phys Rev Lett 2023; 130:210601. [PMID: 37295121 DOI: 10.1103/physrevlett.130.210601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Revised: 04/08/2023] [Accepted: 04/25/2023] [Indexed: 06/12/2023]
Abstract
The task of testing whether two uncharacterized quantum devices behave in the same way is crucial for benchmarking near-term quantum computers and quantum simulators, but has so far remained open for continuous variable quantum systems. In this Letter, we develop a machine learning algorithm for comparing unknown continuous variable states using limited and noisy data. The algorithm works on non-Gaussian quantum states for which similarity testing could not be achieved with previous techniques. Our approach is based on a convolutional neural network that assesses the similarity of quantum states based on a lower-dimensional state representation built from measurement data. The network can be trained off-line with classically simulated data from a fiducial set of states sharing structural similarities with the states to be tested, with experimental data generated by measurements on the fiducial states, or with a combination of simulated and experimental data. We test the performance of the model on noisy cat states and states generated by arbitrary selective number-dependent phase gates. Our network can also be applied to the problem of comparing continuous variable states across different experimental platforms, with different sets of achievable measurements, and to the problem of experimentally testing whether two states are equivalent up to Gaussian unitary transformations.
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Affiliation(s)
- Ya-Dong Wu
- Department of Computer Science, QICI Quantum Information and Computation Initiative, The University of Hong Kong, Pokfulam Road, Hong Kong
| | - Yan Zhu
- Department of Computer Science, QICI Quantum Information and Computation Initiative, The University of Hong Kong, Pokfulam Road, Hong Kong
| | - Ge Bai
- Centre for Quantum Technologies, National University of Singapore, Block S15, 3 Science Drive 2, 117543, Singapore
| | - Yuexuan Wang
- Department of Computer Science, AI Technology Laboratory, The University of Hong Kong, Pokfulam Road, Hong Kong
- College of Computer Science and Technology, Zhejiang University, Zhejiang Province 310058, China
| | - Giulio Chiribella
- Department of Computer Science, QICI Quantum Information and Computation Initiative, The University of Hong Kong, Pokfulam Road, Hong Kong
- Department of Computer Science, Parks Road, Oxford OX1 3QD, United Kingdom
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
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5
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Gao N, Li D, Mishra A, Yan J, Simonov K, Chiribella G. Measuring Incompatibility and Clustering Quantum Observables with a Quantum Switch. Phys Rev Lett 2023; 130:170201. [PMID: 37172250 DOI: 10.1103/physrevlett.130.170201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2022] [Revised: 02/20/2023] [Accepted: 03/21/2023] [Indexed: 05/14/2023]
Abstract
The existence of incompatible observables is a cornerstone of quantum mechanics and a valuable resource in quantum technologies. Here we introduce a measure of incompatibility, called the mutual eigenspace disturbance (MED), which quantifies the amount of disturbance induced by the measurement of a sharp observable on the eigenspaces of another. The MED provides a metric on the space of von Neumann measurements, and can be efficiently estimated by letting the measurement processes act in an indefinite order, using a setup known as the quantum switch, which also allows one to quantify the noncommutativity of arbitrary quantum processes. Thanks to these features, the MED can be used in quantum machine learning tasks. We demonstrate this application by providing an unsupervised algorithm that clusters unknown von Neumann measurements. Our algorithm is robust to noise and can be used to identify groups of observers that share approximately the same measurement context.
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Affiliation(s)
- Ning Gao
- QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong
| | - Dantong Li
- QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong
| | - Anchit Mishra
- QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong
| | - Junchen Yan
- QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong
| | - Kyrylo Simonov
- Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
| | - Giulio Chiribella
- QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong
- Quantum Group, Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, United Kingdom
- Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, N2L 2Y5 Ontario, Canada
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6
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Zhu Y, Wu YD, Bai G, Wang DS, Wang Y, Chiribella G. Flexible learning of quantum states with generative query neural networks. Nat Commun 2022; 13:6222. [PMID: 36266334 PMCID: PMC9584912 DOI: 10.1038/s41467-022-33928-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2022] [Accepted: 10/07/2022] [Indexed: 12/24/2022] Open
Abstract
Deep neural networks are a powerful tool for characterizing quantum states. Existing networks are typically trained with experimental data gathered from the quantum state that needs to be characterized. But is it possible to train a neural network offline, on a different set of states? Here we introduce a network that can be trained with classically simulated data from a fiducial set of states and measurements, and can later be used to characterize quantum states that share structural similarities with the fiducial states. With little guidance of quantum physics, the network builds its own data-driven representation of a quantum state, and then uses it to predict the outcome statistics of quantum measurements that have not been performed yet. The state representations produced by the network can also be used for tasks beyond the prediction of outcome statistics, including clustering of quantum states and identification of different phases of matter.
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Affiliation(s)
- Yan Zhu
- grid.194645.b0000000121742757QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam, Hong Kong
| | - Ya-Dong Wu
- grid.194645.b0000000121742757QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam, Hong Kong
| | - Ge Bai
- grid.194645.b0000000121742757QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam, Hong Kong
| | - Dong-Sheng Wang
- grid.9227.e0000000119573309CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190 P.R. China
| | - Yuexuan Wang
- grid.194645.b0000000121742757QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam, Hong Kong ,grid.13402.340000 0004 1759 700XCollege of Computer Science and Technology, Zhejiang University, Hangzhou, China
| | - Giulio Chiribella
- grid.194645.b0000000121742757QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam, Hong Kong ,grid.4991.50000 0004 1936 8948Department of Computer Science, Oxford, OX1 3QD UK ,grid.420198.60000 0000 8658 0851Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5 Canada
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7
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Chiribella G, Wilson M, Chau HF. Quantum and Classical Data Transmission through Completely Depolarizing Channels in a Superposition of Cyclic Orders. Phys Rev Lett 2021; 127:190502. [PMID: 34797135 DOI: 10.1103/physrevlett.127.190502] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2020] [Revised: 07/20/2021] [Accepted: 09/15/2021] [Indexed: 06/13/2023]
Abstract
Completely depolarizing channels are often regarded as the prototype of physical processes that are useless for communication: any message that passes through them along a well-defined trajectory is completely erased. When two such channels are used in a quantum superposition of two alternative orders, they become able to transmit some amount of classical information, but still no quantum information can pass through them. Here, we show that the ability to place N completely depolarizing channels in a superposition of N alternative causal orders enables a high-fidelity heralded transmission of quantum information with error vanishing as 1/N. This phenomenon highlights a fundamental difference with the N=2 case, where completely depolarizing channels are unable to transmit quantum data, even when placed in a superposition of causal orders. The ability to place quantum channels in a superposition of orders also leads to an increase of the classical communication capacity with N, which we rigorously prove by deriving an exact single-letter expression. Our results highlight the more complex patterns of correlations arising from multiple causal orders, which are similar to the more complex patterns of entanglement arising in multipartite quantum systems.
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Affiliation(s)
- Giulio Chiribella
- QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam Road 999077, Hong Kong; Department of Physics, The University of Hong Kong, Pokfulam Road 999077, Hong Kong; Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, United Kingdom;HKU-Oxford Joint Laboratory for Quantum Information and Computation; Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada
| | - Matt Wilson
- Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, United Kingdom and HKU-Oxford Joint Laboratory for Quantum Information and Computation
| | - H F Chau
- Department of Physics, The University of Hong Kong, Pokfulam Road 999077, Hong Kong
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8
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Wu YD, Bai G, Chiribella G, Liu N. Efficient Verification of Continuous-Variable Quantum States and Devices without Assuming Identical and Independent Operations. Phys Rev Lett 2021; 126:240503. [PMID: 34213942 DOI: 10.1103/physrevlett.126.240503] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2020] [Accepted: 05/18/2021] [Indexed: 06/13/2023]
Abstract
Continuous-variable quantum information, encoded into infinite-dimensional quantum systems, is a promising platform for the realization of many quantum information protocols, including quantum computation, quantum metrology, quantum cryptography, and quantum communication. To successfully demonstrate these protocols, an essential step is the certification of multimode continuous-variable quantum states and quantum devices. This problem is well studied under the assumption that multiple uses of the same device result in identical and independently distributed (i.i.d.) operations. However, in realistic scenarios, identical and independent state preparation and calls to the quantum devices cannot be generally guaranteed. Important instances include adversarial scenarios and instances of time-dependent and correlated noise. In this Letter, we propose the first set of reliable protocols for verifying multimode continuous-variable entangled states and devices in these non-i.i.d scenarios. Although not fully universal, these protocols are applicable to Gaussian quantum states, non-Gaussian hypergraph states, as well as amplification, attenuation, and purification of noisy coherent states.
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Affiliation(s)
- Ya-Dong Wu
- QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong
| | - Ge Bai
- QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong
| | - Giulio Chiribella
- QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong
- The University of Hong Kong Shenzhen Institute of Research and Innovation, 5/F, Key Laboratory Platform Building, No. 6, Yuexing 2nd Road, Nanshan, Shenzhen 518057, China
- Department of Computer Science, Parks Road, Oxford OX1 3QD, United Kingdom
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
| | - Nana Liu
- Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
- Ministry of Education, Key Laboratory in Scientific and Engineering Computing, Shanghai Jiao Tong University, Shanghai 200240, China
- University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai 200240, China
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9
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Yang Y, Renner R, Chiribella G. Optimal Universal Programming of Unitary Gates. Phys Rev Lett 2020; 125:210501. [PMID: 33274974 DOI: 10.1103/physrevlett.125.210501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2020] [Accepted: 09/17/2020] [Indexed: 06/12/2023]
Abstract
A universal quantum processor is a device that takes as input a (quantum) program, containing an encoding of an arbitrary unitary gate, and a (quantum) data register, on which the encoded gate is applied. While no perfect universal quantum processor can exist, approximate processors have been proposed in the past two decades. A fundamental open question is how the size of the smallest quantum program scales with the approximation error. Here we answer the question, by proving a bound on the size of the program and designing a concrete protocol that attains the bound in the asymptotic limit. Our result is based on a connection between optimal programming and the Heisenberg limit of quantum metrology, and establishes an asymptotic equivalence between the tasks of programming, learning, and estimating unitary gates.
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Affiliation(s)
- Yuxiang Yang
- Institute for Theoretical Physics, Wolfgang-Pauli-Strasse 27, 8093, ETH Zürich
| | - Renato Renner
- Institute for Theoretical Physics, Wolfgang-Pauli-Strasse 27, 8093, ETH Zürich
| | - Giulio Chiribella
- QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong 999077, China
- Department of Computer Science, University of Oxford, Parks Road, Oxford, OX1 3QD, United Kingdom
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
- The University of Hong Kong Shenzhen Institute of Research and Innovation, 5/F, Key Laboratory Platform Building, No.6, Yuexing 2nd Road, Nanshan, Shenzhen 518057, China
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10
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Abstract
We address the study of quantum metrology enhanced by indefinite causal order, demonstrating a quadratic advantage in the estimation of the product of two average displacements in a continuous variable system. We prove that no setup where the displacements are used in a fixed order can have root-mean-square error vanishing faster than the Heisenberg limit 1/N, where N is the number of displacements contributing to the average. In stark contrast, we show that a setup that probes the displacements in a superposition of two alternative orders yields a root-mean-square error vanishing with super-Heisenberg scaling 1/N^{2}, which we prove to be optimal among all superpositions of setups with definite causal order. Our result opens up the study of new measurement setups where quantum processes are probed in an indefinite order, and suggests enhanced tests of the canonical commutation relations, with potential applications to quantum gravity.
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Affiliation(s)
- Xiaobin Zhao
- QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pok Fu Lam Road, Hong Kong 999077, China
- The University of Hong Kong Shenzhen Institute of Research and Innovation, Yuexing 2nd Rd Nanshan, Shenzhen 518057, China
| | - Yuxiang Yang
- Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland
| | - Giulio Chiribella
- QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pok Fu Lam Road, Hong Kong 999077, China
- The University of Hong Kong Shenzhen Institute of Research and Innovation, Yuexing 2nd Rd Nanshan, Shenzhen 518057, China
- Department of Computer Science, University of Oxford, Parks Road, Oxford OX1 3QD, United Kingdom
- Perimeter Institute for Theoretical Physics, Caroline Street, Waterloo, Ontario N2L 2Y5, Canada
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11
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Burniston J, Grabowecky M, Scandolo CM, Chiribella G, Gour G. Necessary and sufficient conditions on measurements of quantum channels. Proc Math Phys Eng Sci 2020; 476:20190832. [PMID: 32398940 PMCID: PMC7209144 DOI: 10.1098/rspa.2019.0832] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2019] [Accepted: 03/24/2020] [Indexed: 11/12/2022] Open
Abstract
Quantum supermaps are a higher-order genera- lization of quantum maps, taking quantum maps to quantum maps. It is known that any completely positive and trace non-increasing (CPTNI) map can be performed as part of a quantum measurement. By providing an explicit counterexample we show that, instead, not every quantum supermap sending a quantum channel to a CPTNI map can be realized in a measurement on quantum channels. We find that the supermaps that can be implemented in this way are exactly those transforming quantum channels into CPTNI maps even when tensored with the identity supermap. We link this result to the fact that the principle of causality fails in the theory of quantum supermaps.
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Affiliation(s)
- John Burniston
- Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada
- Institute for Quantum Science and Technology, University of Calgary, Calgary, Alberta, Canada
| | - Michael Grabowecky
- Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada
- Institute for Quantum Science and Technology, University of Calgary, Calgary, Alberta, Canada
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada
| | - Carlo Maria Scandolo
- Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada
- Institute for Quantum Science and Technology, University of Calgary, Calgary, Alberta, Canada
| | - Giulio Chiribella
- Department of Computer Science, The University of Hong Kong, Hong Kong, People’s Republic of China
- Department of Computer Science, University of Oxford, Oxford, UK
| | - Gilad Gour
- Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada
- Institute for Quantum Science and Technology, University of Calgary, Calgary, Alberta, Canada
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12
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Guo Y, Hu XM, Hou ZB, Cao H, Cui JM, Liu BH, Huang YF, Li CF, Guo GC, Chiribella G. Experimental Transmission of Quantum Information Using a Superposition of Causal Orders. Phys Rev Lett 2020; 124:030502. [PMID: 32031864 DOI: 10.1103/physrevlett.124.030502] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2018] [Revised: 03/27/2019] [Indexed: 06/10/2023]
Abstract
Communication in a network generally takes place through a sequence of intermediate nodes connected by communication channels. In the standard theory of communication, it is assumed that the communication network is embedded in a classical spacetime, where the relative order of different nodes is well defined. In principle, a quantum theory of spacetime could allow the order of the intermediate points between sender and receiver to be in a coherent superposition. Here we experimentally realize a tabletop simulation of this exotic possibility on a photonic system, demonstrating high-fidelity transmission of quantum information over two noisy channels arranged in a superposition of two alternative causal orders.
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Affiliation(s)
- Yu Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Xiao-Min Hu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Zhi-Bo Hou
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Huan Cao
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Jin-Ming Cui
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Bi-Heng Liu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Yun-Feng Huang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Giulio Chiribella
- Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong 999077, People's Republic of China
- Department of Computer Science, University of Oxford, Parks Road, Oxford OX1 3QD, United Kingdom
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13
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Chiribella G, Kristjánsson H. Quantum Shannon theory with superpositions of trajectories. Proc Math Phys Eng Sci 2019; 475:20180903. [PMID: 31236050 PMCID: PMC6545039 DOI: 10.1098/rspa.2018.0903] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2018] [Accepted: 03/29/2019] [Indexed: 11/12/2022] Open
Abstract
Shannon's theory of information was built on the assumption that the information carriers were classical systems. Its quantum counterpart, quantum Shannon theory, explores the new possibilities arising when the information carriers are quantum systems. Traditionally, quantum Shannon theory has focused on scenarios where the internal state of the information carriers is quantum, while their trajectory is classical. Here we propose a second level of quantization where both the information and its propagation in space-time is treated quantum mechanically. The framework is illustrated with a number of examples, showcasing some of the counterintuitive phenomena taking place when information travels simultaneously through multiple transmission lines.
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Affiliation(s)
- Giulio Chiribella
- Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong, People's Republic of China
- Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, UK
| | - Hlér Kristjánsson
- Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, UK
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14
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Abstract
The ability to identify cause-effect relations is an essential component of the scientific method. The identification of causal relations is generally accomplished through statistical trials where alternative hypotheses are tested against each other. Traditionally, such trials have been based on classical statistics. However, classical statistics becomes inadequate at the quantum scale, where a richer spectrum of causal relations is accessible. Here we show that quantum strategies can greatly speed up the identification of causal relations. We analyse the task of identifying the effect of a given variable, and we show that the optimal quantum strategy beats all classical strategies by running multiple equivalent tests in a quantum superposition. The same working principle leads to advantages in the detection of a causal link between two variables, and in the identification of the cause of a given variable.
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Affiliation(s)
- Giulio Chiribella
- Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong.
- Department of Computer Science, University of Oxford, Oxford, OX1 3QD, UK.
- Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5, Canada.
| | - Daniel Ebler
- Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong
- Department of Physics, Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China
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15
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Yang Y, Chiribella G, Hayashi M. Correction to ‘Quantum stopwatch: how to store time in a quantum memory’. Proc Math Phys Eng Sci 2019; 475:20190052. [DOI: 10.1098/rspa.2019.0052] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
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16
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Yang Y, Chiribella G, Hayashi M. Quantum stopwatch: how to store time in a quantum memory. Proc Math Phys Eng Sci 2018; 474:20170773. [PMID: 29887749 DOI: 10.1098/rspa.2017.0773] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2017] [Accepted: 04/24/2018] [Indexed: 11/12/2022] Open
Abstract
Quantum mechanics imposes a fundamental trade-off between the accuracy of time measurements and the size of the systems used as clocks. When the measurements of different time intervals are combined, the errors due to the finite clock size accumulate, resulting in an overall inaccuracy that grows with the complexity of the set-up. Here, we introduce a method that, in principle, eludes the accumulation of errors by coherently transferring information from a quantum clock to a quantum memory of the smallest possible size. Our method could be used to measure the total duration of a sequence of events with enhanced accuracy, and to reduce the amount of quantum communication needed to stabilize clocks in a quantum network.
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Affiliation(s)
- Yuxiang Yang
- Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong.,HKU Shenzhen Institute of Research and Innovation Yuexing 2nd Rd Nanshan, Shenzhen 518057, People's Republic of China
| | - Giulio Chiribella
- Department of Computer Science, The University of Oxford, Parks Road, Oxford, UK.,Canadian Institute for Advanced Research, CIFAR Program in Quantum Information Science, Toronto, ON, Canada M5G 1Z8
| | - Masahito Hayashi
- Graduate School of Mathematics, Nagoya University, Nagoya, Japan.,Centre for Quantum Technologies, National University of Singapore, Singapore
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17
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Abstract
Quantum benchmarks are routinely used to validate the experimental demonstration of quantum information protocols. Many relevant protocols, however, involve an infinite set of input states, of which only a finite subset can be used to test the quality of the implementation. This is a problem, because the benchmark for the finitely many states used in the test can be higher than the original benchmark calculated for infinitely many states. This situation arises in the teleportation and storage of coherent states, for which the benchmark of 50% fidelity is commonly used in experiments, although finite sets of coherent states normally lead to higher benchmarks. Here, we show that the average fidelity over all coherent states can be indirectly probed with a single setup, requiring only two-mode squeezing, a 50-50 beam splitter, and homodyne detection. Our setup enables a rigorous experimental validation of quantum teleportation, storage, amplification, attenuation, and purification of noisy coherent states. More generally, we prove that every quantum benchmark can be tested by preparing a single entangled state and measuring a single observable.
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Affiliation(s)
- Ge Bai
- Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong 999077, China and HKU Shenzhen Institute of Research and Innovation, Yuexing 2nd Rd Nanshan, Shenzhen 518057, China
| | - Giulio Chiribella
- Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom and CIFAR Program in Quantum Information Science, Canadian Institute for Advanced Research, Toronto, Ontario ON M5G 1Z8, Canada
- Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong 999077, China and HKU Shenzhen Institute of Research and Innovation, Yuexing 2nd Rd Nanshan, Shenzhen 518057, China
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18
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Abstract
In quantum Shannon theory, the way information is encoded and decoded takes advantage of the laws of quantum mechanics, while the way communication channels are interlinked is assumed to be classical. In this Letter, we relax the assumption that quantum channels are combined classically, showing that a quantum communication network where quantum channels are combined in a superposition of different orders can achieve tasks that are impossible in conventional quantum Shannon theory. In particular, we show that two identical copies of a completely depolarizing channel become able to transmit information when they are combined in a quantum superposition of two alternative orders. This finding runs counter to the intuition that if two communication channels are identical, using them in different orders should not make any difference. The failure of such intuition stems from the fact that a single noisy channel can be a random mixture of elementary, noncommuting processes, whose order (or lack thereof) can affect the ability to transmit information.
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Affiliation(s)
- Daniel Ebler
- Department of Computer Science, The University of Hong Kong, Pokfulam Road, Pokfulam 999077, Hong Kong
- HKU Shenzhen Institute of Research and Innovation, Kejizhong 2nd Road, Shenzhen 518057, China
| | - Sina Salek
- Department of Computer Science, The University of Hong Kong, Pokfulam Road, Pokfulam 999077, Hong Kong
| | - Giulio Chiribella
- Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom
- Canadian Institute for Advanced Research, CIFAR Program in Quantum Information Science, Toronto, Ontario M5G 1Z8, Canada
- HKU Shenzhen Institute of Research and Innovation, Kejizhong 2nd Road, Shenzhen 518057, China
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19
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Abstract
Sudden changes are ubiquitous in nature. Identifying them is crucial for a number of applications in biology, medicine, and social sciences. Here we take the problem of detecting sudden changes to the quantum domain. We consider a source that emits quantum particles in a default state, until a point where a mutation occurs that causes the source to switch to another state. The problem is then to find out where the change occurred. We determine the maximum probability of correctly identifying the change point, allowing for collective measurements on the whole sequence of particles emitted by the source. Then, we devise online strategies where the particles are measured individually and an answer is provided as soon as a new particle is received. We show that these online strategies substantially underperform the optimal quantum measurement, indicating that quantum sudden changes, although happening locally, are better detected globally.
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Affiliation(s)
- Gael Sentís
- Departamento de Física Teórica e Historia de la Ciencia, Universidad del País Vasco UPV/EHU, E-48080 Bilbao, Spain
| | - Emilio Bagan
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
| | - John Calsamiglia
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
| | - Giulio Chiribella
- Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong
- Canadian Institute for Advanced Research, CIFAR Program in Quantum Information Science, Toronto, Ontario M5G 1Z8
| | - Ramon Muñoz-Tapia
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
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20
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Abstract
We establish the ultimate limits to the compression of sequences of identically prepared qubits. The limits are determined by Holevo's information quantity and are attained through use of the optimal universal cloning machine, which finds here a novel application to quantum Shannon theory.
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Affiliation(s)
- Yuxiang Yang
- Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong
| | - Giulio Chiribella
- Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong
- Canadian Institute for Advanced Research, CIFAR Program in Quantum Information Science, Toronto, Ontario M5G 1Z8, Canada
| | - Masahito Hayashi
- Graduate School of Mathematics, Nagoya University, Nagoya, Japan
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
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21
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Yang Y, Chiribella G, Ebler D. Efficient Quantum Compression for Ensembles of Identically Prepared Mixed States. Phys Rev Lett 2016; 116:080501. [PMID: 26967400 DOI: 10.1103/physrevlett.116.080501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2015] [Indexed: 06/05/2023]
Abstract
We present one-shot compression protocols that optimally encode ensembles of N identically prepared mixed states into O(logN) qubits. In contrast to the case of pure-state ensembles, we find that the number of encoding qubits drops down discontinuously as soon as a nonzero error is tolerated and the spectrum of the states is known with sufficient precision. For qubit ensembles, this feature leads to a 25% saving of memory space. Our compression protocols can be implemented efficiently on a quantum computer.
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Affiliation(s)
- Yuxiang Yang
- Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong
| | - Giulio Chiribella
- Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong
| | - Daniel Ebler
- Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong
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22
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23
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Chiribella G, Yang Y, Huang C. Universal superreplication of unitary gates. Phys Rev Lett 2015; 114:120504. [PMID: 25860728 DOI: 10.1103/physrevlett.114.120504] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2014] [Indexed: 06/04/2023]
Abstract
Quantum states obey an asymptotic no-cloning theorem, stating that no deterministic machine can reliably replicate generic sequences of identically prepared pure states. In stark contrast, we show that generic sequences of unitary gates can be replicated deterministically at nearly quadratic rates, with an error vanishing on most inputs except for an exponentially small fraction. The result is not in contradiction with the no-cloning theorem, since the impossibility of deterministically transforming pure states into unitary gates prevents the application of the gate replication protocol to states. In addition to gate replication, we show that N parallel uses of a completely unknown unitary gate can be compressed into a single gate acting on O(log_{2}N) qubits, leading to an exponential reduction of the amount of quantum communication needed to implement the gate remotely.
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Affiliation(s)
- G Chiribella
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Y Yang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - C Huang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
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24
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Gendra B, Calsamiglia J, Muñoz-Tapia R, Bagan E, Chiribella G. Probabilistic metrology attains macroscopic cloning of quantum clocks. Phys Rev Lett 2014; 113:260402. [PMID: 25615289 DOI: 10.1103/physrevlett.113.260402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2014] [Indexed: 06/04/2023]
Abstract
It has recently been shown that probabilistic protocols based on postselection boost the performances of the replication of quantum clocks and phase estimation. Here we demonstrate that the improvements in these two tasks have to match exactly in the macroscopic limit where the number of clones grows to infinity, preserving the equivalence between asymptotic cloning and state estimation for arbitrary values of the success probability. Remarkably, the cloning fidelity depends critically on the number of rationally independent eigenvalues of the clock Hamiltonian. We also prove that probabilistic metrology can simulate cloning in the macroscopic limit for arbitrary sets of states when the performance of the simulation is measured by testing small groups of clones.
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Affiliation(s)
- B Gendra
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
| | - J Calsamiglia
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
| | - R Muñoz-Tapia
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
| | - E Bagan
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain and Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - G Chiribella
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
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25
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Chiribella G, Adesso G. Quantum benchmarks for pure single-mode Gaussian states. Phys Rev Lett 2014; 112:010501. [PMID: 24483875 DOI: 10.1103/physrevlett.112.010501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2013] [Indexed: 06/03/2023]
Abstract
Teleportation and storage of continuous variable states of light and atoms are essential building blocks for the realization of large-scale quantum networks. Rigorous validation of these implementations require identifying, and surpassing, benchmarks set by the most effective strategies attainable without the use of quantum resources. Such benchmarks have been established for special families of input states, like coherent states and particular subclasses of squeezed states. Here we solve the longstanding problem of defining quantum benchmarks for general pure Gaussian single-mode states with arbitrary phase, displacement, and squeezing, randomly sampled according to a realistic prior distribution. As a special case, we show that the fidelity benchmark for teleporting squeezed states with totally random phase and squeezing degree is 1/2, equal to the corresponding one for coherent states. We discuss the use of entangled resources to beat the benchmarks in experiments.
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Affiliation(s)
- Giulio Chiribella
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Gerardo Adesso
- School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
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26
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Chiribella G, Xie J. Optimal design and quantum benchmarks for coherent state amplifiers. Phys Rev Lett 2013; 110:213602. [PMID: 23745872 DOI: 10.1103/physrevlett.110.213602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2013] [Revised: 03/31/2013] [Indexed: 06/02/2023]
Abstract
We establish the ultimate quantum limits to the amplification of an unknown coherent state, both in the deterministic and probabilistic case, investigating the realistic scenario where the expected photon number is finite. In addition, we provide the benchmark that experimental realizations have to surpass in order to beat all classical amplification strategies and to demonstrate genuine quantum amplification. Our result guarantees that a successful demonstration is in principle possible for every finite value of the expected photon number.
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Affiliation(s)
- Giulio Chiribella
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China.
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27
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Bisio A, Chiribella G, D'Ariano GM, Facchini S, Perinotti P. Optimal quantum tomography of States, measurements, and transformations. Phys Rev Lett 2009; 102:010404. [PMID: 19257173 DOI: 10.1103/physrevlett.102.010404] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2008] [Indexed: 05/27/2023]
Abstract
We present the first complete optimization of quantum tomography, for states, positive operator value measures, and various classes of transformations, for arbitrary prior ensemble and arbitrary representation, giving corresponding feasible experimental schemes in terms of random Bell measurements.
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Affiliation(s)
- A Bisio
- Quit group, Dipartimento di Fisica A. Volta, and INFN Sezione di Pavia, via Bassi 6, I-27100 Pavia, Italy
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28
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Abstract
We consider quantum-memory assisted protocols for discriminating quantum channels. We show that for optimal discrimination of memory channels, memory assisted protocols are needed. This leads to a new notion of distance for channels with memory, based on the general theory of quantum testers. For discrimination and estimation of sets of independent unitary channels, we prove optimality of parallel protocols among all possible architectures.
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Affiliation(s)
- Giulio Chiribella
- QUIT-Quantum Information Theory Group, Dipartimento di Fisica "A. Volta" Università di Pavia, via A. Bassi 6, I-27100 Pavia, Italy
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29
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Chiribella G, D'Ariano GM, Perinotti P. Optimal cloning of unitary transformation. Phys Rev Lett 2008; 101:180504. [PMID: 18999806 DOI: 10.1103/physrevlett.101.180504] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2008] [Indexed: 05/27/2023]
Abstract
After proving a general no-cloning theorem for black boxes, we derive the optimal universal cloning of unitary transformations, from one to two copies. The optimal cloner is realized by quantum channels with memory, and greatly outperforms the optimal measure-and-reprepare cloning strategy. Applications are outlined, including two-way quantum cryptographic protocols.
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Affiliation(s)
- Giulio Chiribella
- QUIT Group, Dipartimento di Fisica "A. Volta" and INFN Sezione di Pavia, via Bassi 6, 27100 Pavia, Italy.
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30
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Abstract
We present a method for optimizing quantum circuits architecture, based on the notion of a quantum comb, which describes a circuit board where one can insert variable subcircuits. Unexplored quantum processing tasks, such as cloning and storing or retrieving of gates, can be optimized, along with setups for tomography and discrimination or estimation of quantum circuits.
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Affiliation(s)
- G Chiribella
- QUIT Group, Dipartimento di Fisica "A. Volta" and Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, via Bassi 6, I-27100 Pavia, Italy
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31
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Adesso G, Chiribella G. Quantum benchmark for teleportation and storage of squeezed states. Phys Rev Lett 2008; 100:170503. [PMID: 18518264 DOI: 10.1103/physrevlett.100.170503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2007] [Indexed: 05/26/2023]
Abstract
We provide a quantum benchmark for teleportation and storage of single-mode squeezed states with zero displacement and a completely unknown degree of squeezing along a given direction. For pure squeezed input states, a fidelity higher than 81.5% has to be attained in order to outperform any classical strategy based on an estimation of the unknown squeezing and repreparation of squeezed states. For squeezed thermal input states, we derive an upper and a lower bound on the classical average fidelity which tighten for moderate degree of mixedness. These results enable a critical discussion of recent experiments with squeezed light.
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Affiliation(s)
- Gerardo Adesso
- Dipartimento di Matematica e Informatica, Universitá degli Studi di Salerno, Via Ponte Don Melillo, 84084 Fisciano (SA), Italy
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32
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Chiribella G, D'Ariano GM, Schlingemann D. How continuous quantum measurements in finite dimensions are actually discrete. Phys Rev Lett 2007; 98:190403. [PMID: 17677608 DOI: 10.1103/physrevlett.98.190403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2007] [Indexed: 05/16/2023]
Abstract
We show that in finite dimensions a quantum measurement with a continuous set of outcomes can be always realized as a continuous random choice of measurements with a finite number of outcomes.
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Affiliation(s)
- Giulio Chiribella
- QUIT Group, Dipartimento di Fisica A. Volta and INFM, via Bassi 6, 27100 Pavia, Italy.
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33
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Chiribella G, Maccone L, Perinotti P. Secret quantum communication of a reference frame. Phys Rev Lett 2007; 98:120501. [PMID: 17501103 DOI: 10.1103/physrevlett.98.120501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2006] [Indexed: 05/15/2023]
Abstract
We propose quantum-cryptographic protocols to secretly communicate a reference frame--unspeakable information in the sense it cannot be encoded into a string of bits. Two distant parties can secretly align their Cartesian axes by exchanging N spin-1/2 particles, achieving the optimal accuracy 1/N. A possible eavesdropper cannot gain any information without being detected.
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Affiliation(s)
- Giulio Chiribella
- QUIT-Quantum Information Theory Group, Dipartimento di Fisica A. Volta Università di Pavia, via A. Bassi 6, I-27100 Pavia, Italy
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34
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Abstract
Any physical transformation that equally distributes quantum information over a large number M of users can be approximated by a classical broadcasting of measurement outcomes. The accuracy of the approximation is at least of the order O(M(-1)). In particular, quantum cloning of pure and mixed states can be approximated via quantum state estimation. As an example, for optimal qubit cloning with 10 output copies, a single user has an error probability p(err) > or = 0.45 in distinguishing classical from quantum output, a value close to the error probability of the random guess.
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Affiliation(s)
- Giulio Chiribella
- QUIT Group, Dipartimento di Fisica A. Volta and INFM, via Bassi 6, 27100 Pavia, Italy.
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35
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Buscemi F, Chiribella G, Mauro D'Ariano G. Inverting quantum decoherence by classical feedback from the environment. Phys Rev Lett 2005; 95:090501. [PMID: 16197194 DOI: 10.1103/physrevlett.95.090501] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2005] [Indexed: 05/04/2023]
Abstract
We show that for qubits and qutrits it is always possible to perfectly recover quantum coherence by performing a measurement only on the environment, whereas for dimension d >3 there are situations where recovery is impossible, even with complete access to the environment. For qubits, the minimal amount of classical information to be extracted from the environment equals the entropy exchange.
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Affiliation(s)
- Francesco Buscemi
- QUIT Group, Dipartimento di Fisica A. Volta, Università di Pavia, via A. Bassi 6, I-27100 Pavia, Italy
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36
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Chiribella G, D'Ariano GM, Perinotti P, Sacchi MF. Efficient use of quantum resources for the transmission of a reference frame. Phys Rev Lett 2004; 93:180503. [PMID: 15525143 DOI: 10.1103/physrevlett.93.180503] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2004] [Indexed: 05/24/2023]
Abstract
We propose a covariant protocol for transmitting reference frames encoded on N spins, achieving sensitivity N-2 without the need of a preestablished reference frame and without using entanglement between sender and receiver. The protocol exploits the use of equivalent representations that were overlooked in the previous literature.
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Affiliation(s)
- G Chiribella
- QUIT Quantum Information Theory Group of the INFM, unità di Pavia, Dipartimento di Fisica A. Volta, via Bassi 6, I-27100 Pavia, Italy
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