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Kubischta E, Teixeira I. Family of Quantum Codes with Exotic Transversal Gates. PHYSICAL REVIEW LETTERS 2023; 131:240601. [PMID: 38181144 DOI: 10.1103/physrevlett.131.240601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Revised: 10/13/2023] [Accepted: 11/16/2023] [Indexed: 01/07/2024]
Abstract
Recently, an algorithm has been constructed that shows that the binary icosahedral group 2I together with a T-like gate forms the most efficient single-qubit universal gate set. To carry out the algorithm fault tolerantly requires a code that implements 2I transversally. However, no such code has ever been demonstrated in the literature. We fill this void by constructing a family of distance d=3 codes that all implement 2I transversally. A surprising feature of this family is that the codes can be deduced entirely from symmetry considerations that only 2I affords.
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Affiliation(s)
- Eric Kubischta
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Ian Teixeira
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
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2
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Zheng X, Ma SQ, Zhang GF, Fan H, Liu WM. Unified and Exact Framework for Variance-Based Uncertainty Relations. Sci Rep 2020; 10:150. [PMID: 31924830 PMCID: PMC6954228 DOI: 10.1038/s41598-019-56803-2] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2019] [Accepted: 11/07/2019] [Indexed: 11/09/2022] Open
Abstract
We provide a unified and exact framework for the variance-based uncertainty relations. This unified framework not only recovers some well-known previous uncertainty relations, but also fixes the deficiencies of them. Utilizing the unified framework, we can construct the new uncertainty relations in both product and sum form for two and more incompatible observables with any tightness we require. Moreover, one can even construct uncertainty equalities to exactly express the uncertainty relation by the unified framework, and the framework is therefore exact in describing the uncertainty relation. Some applications have been provided to illustrate the importance of this unified and exact framework. Also, we show that the contradiction between uncertainty relation and non-Hermitian operator, i.e., most of uncertainty relations will be violated when applied to non-Hermitian operators, can be fixed by this unified and exact framework.
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Affiliation(s)
- Xiao Zheng
- School of Physics, Beihang University, Xueyuan Road No. 37, Beijing, 100191, China
| | - Shao-Qiang Ma
- School of Physics, Beihang University, Xueyuan Road No. 37, Beijing, 100191, China
| | - Guo-Feng Zhang
- School of Physics, Beihang University, Xueyuan Road No. 37, Beijing, 100191, China.
| | - Heng Fan
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.,School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China.,CAS Central of Excellence in Topological Quantum Computation, Beijing, 100190, China
| | - Wu-Ming Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.,School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China.,Songshan Lake Materials Laboratory, Dongguan, Guangdong, 523808, China
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3
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Long G. Physicists experimentally verify the multipartite generalized Hardy's paradox. Sci Bull (Beijing) 2018; 63:1597. [PMID: 36658846 DOI: 10.1016/j.scib.2018.12.011] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Affiliation(s)
- Guilu Long
- Department of Physics and State Key Laboratory of Low-dimensional Quantum Physics, Tsinghua University, Beijing 100084, China; Beijing National Research Center for Information Science and Technology, Beijing 100084, China; School of Information and Technology, Tsinghua University, Beijing 100084, China.
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De Chiara G, Sanpera A. Genuine quantum correlations in quantum many-body systems: a review of recent progress. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:074002. [PMID: 29671752 DOI: 10.1088/1361-6633/aabf61] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Quantum information theory has considerably helped in the understanding of quantum many-body systems. The role of quantum correlations and in particular, bipartite entanglement, has become crucial to characterise, classify and simulate quantum many body systems. Furthermore, the scaling of entanglement has inspired modifications to numerical techniques for the simulation of many-body systems leading to the, now established, area of tensor networks. However, the notions and methods brought by quantum information do not end with bipartite entanglement. There are other forms of correlations embedded in the ground, excited and thermal states of quantum many-body systems that also need to be explored and might be utilised as potential resources for quantum technologies. The aim of this work is to review the most recent developments regarding correlations in quantum many-body systems focussing on multipartite entanglement, quantum nonlocality, quantum discord, mutual information but also other non classical measures of correlations based on quantum coherence. Moreover, we also discuss applications of quantum metrology in quantum many-body systems.
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Affiliation(s)
- Gabriele De Chiara
- Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
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Jiang SH, Xu ZP, Su HY, Pati AK, Chen JL. Generalized Hardy's Paradox. PHYSICAL REVIEW LETTERS 2018; 120:050403. [PMID: 29481194 DOI: 10.1103/physrevlett.120.050403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2017] [Indexed: 06/08/2023]
Abstract
Here, we present the most general framework for n-particle Hardy's paradoxes, which include Hardy's original one and Cereceda's extension as special cases. Remarkably, for any n≥3, we demonstrate that there always exist generalized paradoxes (with the success probability as high as 1/2^{n-1}) that are stronger than the previous ones in showing the conflict of quantum mechanics with local realism. An experimental proposal to observe the stronger paradox is also presented for the case of three qubits. Furthermore, from these paradoxes we can construct the most general Hardy's inequalities, which enable us to detect Bell's nonlocality for more quantum states.
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Affiliation(s)
- Shu-Han Jiang
- Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, People's Republic of China
- School of Physics, Nankai University, Tianjin 300071, People's Republic of China
| | - Zhen-Peng Xu
- Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, People's Republic of China
- Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain
| | - Hong-Yi Su
- Graduate School of China Academy of Engineering Physics, Beijing 100193, People's Republic of China
| | - Arun Kumar Pati
- Quantum Information and Computation Group, Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - Jing-Ling Chen
- Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, People's Republic of China
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
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Bera A, Das T, Sadhukhan D, Singha Roy S, Sen De A, Sen U. Quantum discord and its allies: a review of recent progress. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:024001. [PMID: 28824014 DOI: 10.1088/1361-6633/aa872f] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We review concepts and methods associated with quantum discord and related topics. We also describe their possible connections with other aspects of quantum information and beyond, including quantum communication, quantum computation, many-body physics, and open quantum dynamics. Quantum discord in the multiparty regime and its applications are also discussed.
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Affiliation(s)
- Anindita Bera
- Department of Applied Mathematics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700 009, India. Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhunsi, Allahabad 211019, India
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Li M, Qin H, Wang J, Fei SM, Sun CP. Maximal violation of Bell inequalities under local filtering. Sci Rep 2017; 7:46505. [PMID: 28418036 PMCID: PMC5394482 DOI: 10.1038/srep46505] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2017] [Accepted: 03/16/2017] [Indexed: 11/16/2022] Open
Abstract
We investigate the behavior of the maximal violations of the CHSH inequality and Vèrtesi's inequality under the local filtering operations. An analytical method has been presented for general two-qubit systems to compute the maximal violation of the CHSH inequality and the lower bound of the maximal violation of Vértesi's inequality over the local filtering operations. We show by examples that there exist quantum states whose non-locality can be revealed after local filtering operation by the Vértesi's inequality instead of the CHSH inequality.
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Affiliation(s)
- Ming Li
- College of the Science, China University of Petroleum, Qingdao 266580, P. R. China
| | - Huihui Qin
- School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, P. R. China
- Max-Planck-Institute for Mathematics in the Sciences, Leipzig 04103, Germany
| | - Jing Wang
- College of the Science, China University of Petroleum, Qingdao 266580, P. R. China
| | - Shao-Ming Fei
- Max-Planck-Institute for Mathematics in the Sciences, Leipzig 04103, Germany
- School of Mathematical Sciences, Capital Normal University, Beijing 100048, P. R. China
| | - Chang-Pu Sun
- Beijing Computational Science Research Center, Beijing 100048, P. R. China
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Li M, Zhang T, Hua B, Fei SM, Li-Jost X. Quantum Nonlocality of Arbitrary Dimensional Bipartite States. Sci Rep 2015; 5:13358. [PMID: 26303075 PMCID: PMC4548185 DOI: 10.1038/srep13358] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2015] [Accepted: 07/23/2015] [Indexed: 11/18/2022] Open
Abstract
We study the nonlocality of arbitrary dimensional bipartite quantum states. By computing the maximal violation of a set of multi-setting Bell inequalities, an analytical and computable lower bound has been derived for general two-qubit states. This bound gives the necessary condition that a two-qubit state admits no local hidden variable models. The lower bound is shown to be better than that from the CHSH inequality in judging the nonlocality of some quantum states. The results are generalized to the case of high dimensional quantum states, and a sufficient condition for detecting the non-locality has been presented.
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Affiliation(s)
- Ming Li
- College of the Science, China University of Petroleum, Qingdao 266580, P. R. China
- Max-Planck-Institute for Mathematics in the Sciences, Leipzig 04103, Germany
| | - Tinggui Zhang
- College of Mathematics and Statistics, Hainan Normal University, Haikou 571158, P. R. China
- Max-Planck-Institute for Mathematics in the Sciences, Leipzig 04103, Germany
| | - Bobo Hua
- School of Mathematical Sciences, LMNS, Fudan University, Shanghai 200433, P. R. China
- Max-Planck-Institute for Mathematics in the Sciences, Leipzig 04103, Germany
| | - Shao-Ming Fei
- School of Mathematical Sciences, Capital Normal University, Beijing 100048, P. R. China
- Max-Planck-Institute for Mathematics in the Sciences, Leipzig 04103, Germany
| | - Xianqing Li-Jost
- College of Mathematics and Statistics, Hainan Normal University, Haikou 571158, P. R. China
- Max-Planck-Institute for Mathematics in the Sciences, Leipzig 04103, Germany
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Chen JL, Su HY, Xu ZP, Wu YC, Wu C, Ye XJ, Żukowski M, Kwek LC. Beyond Gisin's Theorem and its Applications: Violation of Local Realism by Two-Party Einstein-Podolsky-Rosen Steering. Sci Rep 2015; 5:11624. [PMID: 26108704 PMCID: PMC4479990 DOI: 10.1038/srep11624] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2015] [Accepted: 06/01/2015] [Indexed: 12/02/2022] Open
Abstract
We demonstrate here that for a given mixed multi-qubit state if there are at least two observers for whom mutual Einstein-Podolsky-Rosen steering is possible, i.e. each observer is able to steer the other qubits into two different pure states by spontaneous collapses due to von Neumann type measurements on his/her qubit, then nonexistence of local realistic models is fully equivalent to quantum entanglement (this is not so without this condition). This result leads to an enhanced version of Gisin's theorem (originally: all pure entangled states violate local realism). Local realism is violated by all mixed states with the above steering property. The new class of states allows one e.g. to perform three party secret sharing with just pairs of entangled qubits, instead of three qubit entanglements (which are currently available with low fidelity). This significantly increases the feasibility of having high performance versions of such protocols. Finally, we discuss some possible applications.
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Affiliation(s)
- Jing-Ling Chen
- Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, People’s Republic of China
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543
| | - Hong-Yi Su
- Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, People’s Republic of China
| | - Zhen-Peng Xu
- Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, People’s Republic of China
| | - Yu-Chun Wu
- Key Laboratory of Quantum Information, University of Science and Technology of China, 230026 Hefei, People’s Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, 230026 Hefei, Anhui, China
| | - Chunfeng Wu
- Pillar of Engineering Product Development, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372
| | - Xiang-Jun Ye
- Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, People’s Republic of China
| | - Marek Żukowski
- Institute of Theoretical Physics and Astrophysics, University of Gdańsk, PL-80-952 Gdańsk, Poland
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, 230026 Hefei, China
| | - L. C. Kwek
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543
- National Institute of Education,1 Nanyang Walk, Singapore 637616
- Institute of Advanced Studies, Nanyang Technological University, 60 Nanyang View, Singapore 639673
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10
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Demonstrating quantum contextuality of indistinguishable particles by a single family of noncontextuality inequalities. Sci Rep 2015; 5:11637. [PMID: 26109325 PMCID: PMC4480019 DOI: 10.1038/srep11637] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2014] [Accepted: 03/26/2015] [Indexed: 11/17/2022] Open
Abstract
Quantum theory has the intriguing feature that is inconsistent with noncontextual hidden variable models, for which the outcome of a measurement does not depend on which other compatible measurements are being performed concurrently. While various proofs of such contextual behavior of quantum systems have been established, relatively little is known concerning the possibility to demonstrate this intriguing feature for indistinguishable particles. Here, we show in a simple and systematic manner that with projective measurements alone, it is possible to demonstrate quantum contextuality for such systems of arbitrary Hilbert space dimensions, including those corresponding to a qubit. Our demonstration is applicable to a single fermion as well as multiple fermions, and thus also a composite boson formed from an even number of fermions. In addition, our approach gives a clear demonstration of the intimate connection between complementarity and contextuality, two seemingly unrelated aspects of quantum theory.
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Liang YC, Rosset D, Bancal JD, Pütz G, Barnea TJ, Gisin N. Family of Bell-like Inequalities as Device-Independent Witnesses for Entanglement Depth. PHYSICAL REVIEW LETTERS 2015; 114:190401. [PMID: 26024153 DOI: 10.1103/physrevlett.114.190401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2014] [Indexed: 06/04/2023]
Abstract
We present a simple family of Bell inequalities applicable to a scenario involving arbitrarily many parties, each of which performs two binary-outcome measurements. We show that these inequalities are members of the complete set of full-correlation Bell inequalities discovered by Werner-Wolf-Żukowski-Brukner. For scenarios involving a small number of parties, we further verify that these inequalities are facet defining for the convex set of Bell-local correlations. Moreover, we show that the amount of quantum violation of these inequalities naturally manifests the extent to which the underlying system is genuinely many-body entangled. In other words, our Bell inequalities, when supplemented with the appropriate quantum bounds, naturally serve as device-independent witnesses for entanglement depth, allowing one to certify genuine k-partite entanglement in an arbitrary n≥k-partite scenario without relying on any assumption about the measurements being performed, or the dimension of the underlying physical system. A brief comparison is made between our witnesses and those based on some other Bell inequalities, as well as quantum Fisher information. A family of witnesses for genuine k-partite nonlocality applicable to an arbitrary n≥k-partite scenario based on our Bell inequalities is also presented.
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Affiliation(s)
- Yeong-Cherng Liang
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
- Department of Physics, National Cheng Kung University, Tainan 701, Taiwan
| | - Denis Rosset
- Group of Applied Physics, University of Geneva, CH-1211 Geneva 4, Switzerland
| | - Jean-Daniel Bancal
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - Gilles Pütz
- Group of Applied Physics, University of Geneva, CH-1211 Geneva 4, Switzerland
| | - Tomer Jack Barnea
- Group of Applied Physics, University of Geneva, CH-1211 Geneva 4, Switzerland
| | - Nicolas Gisin
- Group of Applied Physics, University of Geneva, CH-1211 Geneva 4, Switzerland
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12
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Chen Q, Yu S, Zhang C, Lai CH, Oh CH. Test of genuine multipartite nonlocality without inequalities. PHYSICAL REVIEW LETTERS 2014; 112:140404. [PMID: 24765926 DOI: 10.1103/physrevlett.112.140404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2013] [Indexed: 06/03/2023]
Abstract
In this Letter we propose a set of conditions on the joint probabilities as a test of genuine multipartite nonlocality without inequality. Our test is failed by all nonsignaling local models in which even nonlocal correlations among some observables (not all) are allowed as long as these correlations respect the nonsignaling principle. A pass of our test by a state therefore indicates that this state cannot be simulated by any nonsignaling local models; i.e., the state exhibits genuine multipartite nonlocality. It turns out that all entangled symmetric n-qubit (n≥3) states pass our test and therefore are n-way nonlocal. Also we construct two Bell-type inequalities from our proposed test whose violations indicate genuine multipartite nonlocal correlations.
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Affiliation(s)
- Qing Chen
- Centre for quantum technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - Sixia Yu
- Centre for quantum technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore and Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Chengjie Zhang
- Centre for quantum technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - C H Lai
- Centre for quantum technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore and Physics department, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - C H Oh
- Centre for quantum technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore and Physics department, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
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