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Fanizza M, Hirche C, Calsamiglia J. Ultimate Limits for Quickest Quantum Change-Point Detection. PHYSICAL REVIEW LETTERS 2023; 131:020602. [PMID: 37505971 DOI: 10.1103/physrevlett.131.020602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2022] [Revised: 05/30/2023] [Accepted: 06/05/2023] [Indexed: 07/30/2023]
Abstract
Detecting abrupt changes in data streams is crucial because they are often triggered by events that have important consequences if left unattended. Quickest change-point detection has become a vital sequential analysis primitive that aims at designing procedures that minimize the expected detection delay of a change subject to a bounded expected false alarm time. We put forward the quantum counterpart of this fundamental primitive on streams of quantum data. We give a lower bound on the mean minimum delay when the expected time of a false alarm is asymptotically large, under the most general quantum detection strategy, which is given by a sequence of adaptive collective (potentially weak) measurements on the growing string of quantum data. In addition, we give particular strategies based on repeated measurements on independent blocks of samples that asymptotically attain the lower bound and thereby establish the ultimate quantum limit for quickest change-point detection. Finally, we discuss online change-point detection in quantum channels.
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Affiliation(s)
- Marco Fanizza
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, ES-08193 Bellaterra (Barcelona), Spain
| | - Christoph Hirche
- Center for Quantum Technologies, National University of Singapore Zentrum Mathematik, Technical University of Munich, 85748 Garching, Germany
| | - John Calsamiglia
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, ES-08193 Bellaterra (Barcelona), Spain
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Martínez Vargas E, Hirche C, Sentís G, Skotiniotis M, Carrizo M, Muñoz-Tapia R, Calsamiglia J. Quantum Sequential Hypothesis Testing. PHYSICAL REVIEW LETTERS 2021; 126:180502. [PMID: 34018787 DOI: 10.1103/physrevlett.126.180502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2020] [Accepted: 04/13/2021] [Indexed: 06/12/2023]
Abstract
We introduce sequential analysis in quantum information processing, by focusing on the fundamental task of quantum hypothesis testing. In particular, our goal is to discriminate between two arbitrary quantum states with a prescribed error threshold ε when copies of the states can be required on demand. We obtain ultimate lower bounds on the average number of copies needed to accomplish the task. We give a block-sampling strategy that allows us to achieve the lower bound for some classes of states. The bound is optimal in both the symmetric as well as the asymmetric setting in the sense that it requires the least mean number of copies out of all other procedures, including the ones that fix the number of copies ahead of time. For qubit states we derive explicit expressions for the minimum average number of copies and show that a sequential strategy based on fixed local measurements outperforms the best collective measurement on a predetermined number of copies. Whereas for general states the number of copies increases as log1/ε, for pure states sequential strategies require a finite average number of samples even in the case of perfect discrimination, i.e., ε=0.
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Affiliation(s)
- Esteban Martínez Vargas
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellatera (Barcelona) Spain
| | - Christoph Hirche
- QMATH, Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - Gael Sentís
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellatera (Barcelona) Spain
| | - Michalis Skotiniotis
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellatera (Barcelona) Spain
| | - Marta Carrizo
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellatera (Barcelona) Spain
| | - Ramon Muñoz-Tapia
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellatera (Barcelona) Spain
| | - John Calsamiglia
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellatera (Barcelona) Spain
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Deterministic realization of collective measurements via photonic quantum walks. Nat Commun 2018; 9:1414. [PMID: 29650977 PMCID: PMC5897416 DOI: 10.1038/s41467-018-03849-x] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2018] [Accepted: 03/13/2018] [Indexed: 11/08/2022] Open
Abstract
Collective measurements on identically prepared quantum systems can extract more information than local measurements, thereby enhancing information-processing efficiency. Although this nonclassical phenomenon has been known for two decades, it has remained a challenging task to demonstrate the advantage of collective measurements in experiments. Here, we introduce a general recipe for performing deterministic collective measurements on two identically prepared qubits based on quantum walks. Using photonic quantum walks, we realize experimentally an optimized collective measurement with fidelity 0.9946 without post selection. As an application, we achieve the highest tomographic efficiency in qubit state tomography to date. Our work offers an effective recipe for beating the precision limit of local measurements in quantum state tomography and metrology. In addition, our study opens an avenue for harvesting the power of collective measurements in quantum information-processing and for exploring the intriguing physics behind this power. Demonstrating the advantage of collective measurements in experiments remains a daunting task. Here the authors introduce a general recipe for performing deterministic collective measurements on two identically prepared qubits based on quantum walks.
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Bagan E, Calsamiglia J, Bergou JA, Hillery M. Duality Games and Operational Duality Relations. PHYSICAL REVIEW LETTERS 2018; 120:050402. [PMID: 29481158 DOI: 10.1103/physrevlett.120.050402] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2017] [Indexed: 06/08/2023]
Abstract
We give operational meaning to wave-particle duality in terms of discrimination games. Duality arises as a constraint on the probability of winning these games. The games are played with the aid of an n-port interferometer, and involve 3 parties, Alice and Bob, who cooperate, and the House, who supervises the game. In one game called ways they attempt to determine the path of a particle in the interferometer. In another, called phases, they attempt to determine which set of known phases have been applied to the different paths. The House determines which game is to be played by flipping a coin. We find a tight wave-particle duality relation that allows us to relate the probabilities of winning these games, and use it to find an upper bound on the probability of winning the combined game. This procedure allows us to express wave-particle duality in terms of discrimination probabilities.
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Affiliation(s)
- 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
| | - János A Bergou
- Department of Physics and Astronomy, Hunter College, City University of New York, 695 Park Avenue, New York, New York 10065, USA
- Graduate Center, City University of New York, 365 Fifth Avenue, New York, New York 10016, USA
| | - Mark Hillery
- Department of Physics and Astronomy, Hunter College, City University of New York, 695 Park Avenue, New York, New York 10065, USA
- Graduate Center, City University of New York, 365 Fifth Avenue, New York, New York 10016, USA
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Sentís G, Calsamiglia J, Muñoz-Tapia R. Exact Identification of a Quantum Change Point. PHYSICAL REVIEW LETTERS 2017; 119:140506. [PMID: 29053327 DOI: 10.1103/physrevlett.119.140506] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2017] [Indexed: 06/07/2023]
Abstract
The detection of change points is a pivotal task in statistical analysis. In the quantum realm, it is a new primitive where one aims at identifying the point where a source that supposedly prepares a sequence of particles in identical quantum states starts preparing a mutated one. We obtain the optimal procedure to identify the change point with certainty-naturally at the price of having a certain probability of getting an inconclusive answer. We obtain the analytical form of the optimal probability of successful identification for any length of the particle sequence. We show that the conditional success probabilities of identifying each possible change point show an unexpected oscillatory behavior. We also discuss local (online) protocols and compare them with the optimal procedure.
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Affiliation(s)
- Gael Sentís
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, 57068 Siegen, Germany
- Departamento de Física Teórica e Historia de la Ciencia, Universidad del País Vasco UPV/EHU, E-48080 Bilbao, Spain
| | - John Calsamiglia
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
| | - Ramon Muñoz-Tapia
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
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Biamonte J, Wittek P, Pancotti N, Rebentrost P, Wiebe N, Lloyd S. Quantum machine learning. Nature 2017; 549:195-202. [DOI: 10.1038/nature23474] [Citation(s) in RCA: 1159] [Impact Index Per Article: 165.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2017] [Accepted: 07/04/2017] [Indexed: 01/24/2023]
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Monràs A, Sentís G, Wittek P. Inductive Supervised Quantum Learning. PHYSICAL REVIEW LETTERS 2017; 118:190503. [PMID: 28548536 DOI: 10.1103/physrevlett.118.190503] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2016] [Indexed: 06/07/2023]
Abstract
In supervised learning, an inductive learning algorithm extracts general rules from observed training instances, then the rules are applied to test instances. We show that this splitting of training and application arises naturally, in the classical setting, from a simple independence requirement with a physical interpretation of being nonsignaling. Thus, two seemingly different definitions of inductive learning happen to coincide. This follows from the properties of classical information that break down in the quantum setup. We prove a quantum de Finetti theorem for quantum channels, which shows that in the quantum case, the equivalence holds in the asymptotic setting, that is, for large numbers of test instances. This reveals a natural analogy between classical learning protocols and their quantum counterparts, justifying a similar treatment, and allowing us to inquire about standard elements in computational learning theory, such as structural risk minimization and sample complexity.
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Affiliation(s)
- Alex Monràs
- Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona, ES-08193 Bellaterra (Barcelona), Spain
| | - Gael Sentís
- Departamento de Física Teórica e Historia de la Ciencia, Universidad del País Vasco UPV/EHU, E-48080 Bilbao, Spain
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, 57068 Siegen, Germany
| | - Peter Wittek
- ICFO-The Institute of Photonic Sciences, Castelldefels E-08860 Spain
- University of Borås, Borås S-50190 Sweden
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