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Kalaga JK, Kowalewska-Kudłaszyk A, Leoński W, Peřina J. Legget-Garg inequality for a two-mode entangled bosonic system. OPTICS EXPRESS 2024; 32:9946-9957. [PMID: 38571218 DOI: 10.1364/oe.513855] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2023] [Accepted: 02/08/2024] [Indexed: 04/05/2024]
Abstract
We discuss a model of two nonlinear quantum oscillators mutually coupled by linear interaction and continuously driven by external coherent excitation. For such a system, we analyze temporal correlations. We examine the violation of the Leggett-Garg inequality analysing various scenarios of measurements. These scenarios are based on the projection onto different Bell states. We show that the possibility of violation of the Leggett-Garg inequalities is associated with the use of different projectors.
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2
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Das D, Home D, Ulbricht H, Bose S. Mass-Independent Scheme to Test the Quantumness of a Massive Object. PHYSICAL REVIEW LETTERS 2024; 132:030202. [PMID: 38307064 DOI: 10.1103/physrevlett.132.030202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2023] [Accepted: 11/30/2023] [Indexed: 02/04/2024]
Abstract
The search for empirical schemes to evidence the nonclassicality of large masses is a central quest of current research. However, practical schemes to witness the irreducible quantumness of an arbitrarily large mass are still lacking. To this end, we incorporate crucial modifications to the standard tools for probing the quantum violation of the pivotal classical notion of macrorealism (MR): while usual tests use the same measurement arrangement at successive times, here we use two different measurement arrangements. This yields a striking result: a mass-independent violation of MR is possible for harmonic oscillator systems. In fact, our adaptation enables probing quantum violations for literally any mass, momentum, and frequency. Moreover, coarse-grained position measurements at an accuracy much worse than the standard quantum limit, as well as knowing the relevant parameters only to this precision, without requiring them to be tuned, suffice for our proposal. These should drastically simplify the experimental effort in testing the nonclassicality of massive objects ranging from atomic ions to macroscopic mirrors in LIGO.
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Affiliation(s)
- Debarshi Das
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, England, United Kingdom
| | - Dipankar Home
- Center for Astroparticle Physics and Space Science (CAPSS), Bose Institute, Kolkata 700 091, India
| | - Hendrik Ulbricht
- School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, England, United Kingdom
| | - Sougato Bose
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, England, United Kingdom
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3
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Fulton J, Thenabadu M, Teh RY, Reid MD. Weak versus Deterministic Macroscopic Realism, and Einstein-Podolsky-Rosen's Elements of Reality. ENTROPY (BASEL, SWITZERLAND) 2023; 26:11. [PMID: 38275490 DOI: 10.3390/e26010011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2023] [Revised: 10/25/2023] [Accepted: 11/13/2023] [Indexed: 01/27/2024]
Abstract
The violation of a Leggett-Garg inequality confirms the incompatibility between quantum mechanics and the combined premises (called macro-realism) of macroscopic realism (MR) and noninvasive measurability (NIM). Arguments can be given that the incompatibility arises because MR fails for systems in a superposition of macroscopically distinct states-or else, that NIM fails. In this paper, we consider a strong negation of macro-realism, involving superpositions of coherent states, where the NIM premise is replaced by Bell's locality premise. We follow recent work and propose the validity of a subset of Einstein-Podolsky-Rosen (EPR) and Leggett-Garg premises, referred to as weak macroscopic realism (wMR). In finding consistency with wMR, we identify that the Leggett-Garg inequalities are violated because of failure of both MR and NIM, but also that both are valid in a weaker (less restrictive) sense. Weak MR is distinguished from deterministic macroscopic realism (dMR) by recognizing that a measurement involves a reversible unitary interaction that establishes the measurement setting. Weak MR posits that a predetermined value for the outcome of a measurement can be attributed to the system after the interaction, when the measurement setting is experimentally specified. An extended definition of wMR considers the "element of reality" defined by EPR for system A, where one can predict with certainty the outcome of a measurement on A by performing a measurement on system B. Weak MR posits that this element of reality exists once the unitary interaction determining the measurement setting at B has occurred. We demonstrate compatibility of systems violating Leggett-Garg inequalities with wMR but point out that dMR has been shown to be falsifiable. Other tests of wMR are proposed, the predictions of wMR agreeing with quantum mechanics. Finally, we compare wMR with macro-realism models discussed elsewhere. An argument in favour of wMR is presented: wMR resolves a potential contradiction pointed out by Leggett and Garg between failure of macro-realism and assumptions intrinsic to quantum measurement theory.
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Affiliation(s)
- Jesse Fulton
- Centre for Quantum Science and Technology Theory, Swinburne University of Technology, Melbourne 3122, Australia
| | - Manushan Thenabadu
- Centre for Quantum Science and Technology Theory, Swinburne University of Technology, Melbourne 3122, Australia
| | - Run Yan Teh
- Centre for Quantum Science and Technology Theory, Swinburne University of Technology, Melbourne 3122, Australia
| | - Margaret D Reid
- Centre for Quantum Science and Technology Theory, Swinburne University of Technology, Melbourne 3122, Australia
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4
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Zhang Y, Tan X, Qiu T. Quantum violation of LGI under an energy constraint for different scenarios systems. Sci Rep 2023; 13:12530. [PMID: 37532739 PMCID: PMC10397236 DOI: 10.1038/s41598-023-39612-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2023] [Accepted: 07/27/2023] [Indexed: 08/04/2023] Open
Abstract
In this paper, we consider a qubit in four scenarios: with drive, without drive, and in the presence of dissipation and dephasing, to investigate the quantum violation of the Leggett-Garg inequality (LGI) in an energy constraint. In the case of the energy constraint, we find that under the coarsening measurement in reference and final resolution, the quantum violation of the LGI for the pure qubit is the most robust; on the other hand, the quantum violation of the LGI for the dephasing qubit is the most vulnerable, and the quantum violation of the LGI for driven qubit lies between that of pure qubit and dissipation qubit. Under the coarsening of measurement temporal reference, the quantum violation of the LGI for the pure qubit is more robust than that of the qubit with driven. Moreover, in the case of a qubit that is subjected to driving and is in the presence of dissipation and dephasing, the robustness of quantum violations of the LGI for these scenario systems will become vulnerable, with the driven intensity and the rate of spontaneous emission increasing, respectively, for coarsening measurement both in reference and in final resolution. In addition, in the energy constraint and the projective measurement, the LGI can attain its maximum violation value, 1.5, for the coherent dynamics; while for drive, dissipative and dephasing qubits, the LGI cannot attain the value of 1.5. For systems in the presence of dissipation and dephasing, we find that in the energy constraint, the robustness of the coarsening measurement in final resolution exhibits more vulnerable than that of the coarsening measurement in reference. And for systems with drive and without drive, the robustness of the coarsening measurement in temporal reference is the most robust, and the robustness of the coarsening of measurement final measurement resolution is the most vulnerable.
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Affiliation(s)
- Yuxia Zhang
- School of Science, Qingdao University of Technology, Qingdao, 266520, China.
| | - Xiangguan Tan
- College of Electronic and Information Engineering, Shandong University of Science and Technology, Qingdao, 266590, China
| | - Tianhui Qiu
- School of Science, Qingdao University of Technology, Qingdao, 266520, China
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5
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Optical experiment to test negative probability in context of quantum-measurement selection. Sci Rep 2019; 9:19021. [PMID: 31836724 PMCID: PMC6910950 DOI: 10.1038/s41598-019-53121-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2019] [Accepted: 10/24/2019] [Indexed: 12/01/2022] Open
Abstract
Negative probability values have been widely employed as an indicator of the nonclassicality of quantum systems. Known as a quasiprobability distribution, they are regarded as a useful tool that provides significant insight into the underlying fundamentals of quantum theory when compared to the classical statistics. However, in this approach, an operational interpretation of these negative values with respect to the definition of probability—the relative frequency of occurred event—is missing. An alternative approach is therefore considered where the quasiprobability operationally reveals the negativity of measured quantities. We here present an experimental realization of the operational quasiprobability, which consists of sequential measurements in time. To this end, we implement two sets of polarization measurements of single photons. We find that the measured negativity can be interpreted in the context of selecting measurements, and it reflects the nonclassical nature of photons. Our results suggest a new operational way to unravel the nonclassicality of photons in the context of measurement selection.
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Mendoza-Arenas JJ, Gómez-Ruiz FJ, Rodríguez FJ, Quiroga L. Enhancing violations of Leggett-Garg inequalities in nonequilibrium correlated many-body systems by interactions and decoherence. Sci Rep 2019; 9:17772. [PMID: 31780693 PMCID: PMC6882789 DOI: 10.1038/s41598-019-54121-1] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2019] [Accepted: 10/22/2019] [Indexed: 11/09/2022] Open
Abstract
We identify different schemes to enhance the violation of Leggett-Garg inequalities in open many-body systems. Considering a nonequilibrium archetypical setup of quantum transport, we show that particle interactions control the direction and amplitude of maximal violation, and that in the strongly-interacting and strongly-driven regime bulk dephasing enhances the violation. Through an analytical study of a minimal model we unravel the basic ingredients to explain this decoherence-enhanced quantumness, illustrating that such an effect emerges in a wide variety of systems.
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Affiliation(s)
- J J Mendoza-Arenas
- Departamento de Física, Universidad de los Andes, A.A. 4976, Bogotá, D. C., Colombia
| | - F J Gómez-Ruiz
- Departamento de Física, Universidad de los Andes, A.A. 4976, Bogotá, D. C., Colombia. .,Donostia International Physics Center, E-20018, San Sebastián, Spain.
| | - F J Rodríguez
- Departamento de Física, Universidad de los Andes, A.A. 4976, Bogotá, D. C., Colombia
| | - L Quiroga
- Departamento de Física, Universidad de los Andes, A.A. 4976, Bogotá, D. C., Colombia
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7
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Bose S, Home D, Mal S. Nonclassicality of the Harmonic-Oscillator Coherent State Persisting up to the Macroscopic Domain. PHYSICAL REVIEW LETTERS 2018; 120:210402. [PMID: 29883147 DOI: 10.1103/physrevlett.120.210402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2017] [Revised: 12/29/2017] [Indexed: 06/08/2023]
Abstract
Can the most "classical-like" of all quantum states, namely the Schrödinger coherent state of a harmonic oscillator, exhibit nonclassical behavior? We find that for an oscillating object initially in a coherent state, merely by observing at various instants which spatial region the object is in, the Leggett-Garg inequality (LGI) can be violated through a genuine negative result measurement, thereby repudiating the everyday notion of macrorealism. This violation thus reveals an unnoticed nonclassicality of the very state which epitomizes classicality within the quantum description. It is found that for any given mass and oscillator frequency, a significant quantum violation of LGI can be obtained by suitably choosing the initial peak momentum of the coherent state wave packet. It thus opens up potentially the simplest way (without coupling with any ancillary quantum system or using nonlinearity) for testing whether various recently engineered and sought after macroscopic oscillators, such as feedback cooled thermal trapped nanocrystals of ∼10^{6}-10^{9} amu mass, are indeed bona fide nonclassical objects.
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Affiliation(s)
- S Bose
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - D Home
- CAPSS, Physics Department, Bose Institute, Salt Lake, Sector V, Kolkata 700097, India
| | - S Mal
- S.N. Bose National Center for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700098, India
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8
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Miller HJD, Anders J. Leggett-Garg Inequalities for Quantum Fluctuating Work. ENTROPY (BASEL, SWITZERLAND) 2018; 20:E200. [PMID: 33265291 PMCID: PMC7845770 DOI: 10.3390/e20030200] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/01/2018] [Revised: 02/28/2018] [Accepted: 03/08/2018] [Indexed: 11/16/2022]
Abstract
The Leggett-Garg inequalities serve to test whether or not quantum correlations in time can be explained within a classical macrorealistic framework. We apply this test to thermodynamics and derive a set of Leggett-Garg inequalities for the statistics of fluctuating work done on a quantum system unitarily driven in time. It is shown that these inequalities can be violated in a driven two-level system, thereby demonstrating that there exists no general macrorealistic description of quantum work. These violations are shown to emerge within the standard Two-Projective-Measurement scheme as well as for alternative definitions of fluctuating work that are based on weak measurement. Our results elucidate the influences of temporal correlations on work extraction in the quantum regime and highlight a key difference between quantum and classical thermodynamics.
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Affiliation(s)
| | - Janet Anders
- Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, UK
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9
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Wang K, Emary C, Zhan X, Bian Z, Li J, Xue P. Enhanced violations of Leggett-Garg inequalities in an experimental three-level system. OPTICS EXPRESS 2017; 25:31462-31470. [PMID: 29245821 DOI: 10.1364/oe.25.031462] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2017] [Accepted: 11/22/2017] [Indexed: 06/07/2023]
Abstract
Leggett-Garg inequalities are tests of macroscopic realism that can be violated by quantum mechanics. In this letter, we realise photonic Leggett-Garg tests on a three-level system and implement measurements that admit three distinct measurement outcomes, rather than the usual two. In this way we obtain violations of three- and four-time Leggett-Garg inequalities that are significantly in excess of those obtainable in standard Leggett-Garg tests. We also report violations the quantum-witness equality up to the maximum permitted for a three-outcome measurement. Our results highlight differences between spatial and temporal correlations in quantum mechanics.
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10
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Venturelli OS, Tei M, Bauer S, Chan LJG, Petzold CJ, Arkin AP. Programming mRNA decay to modulate synthetic circuit resource allocation. Nat Commun 2017; 8:15128. [PMID: 28443619 PMCID: PMC5414051 DOI: 10.1038/ncomms15128] [Citation(s) in RCA: 45] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2016] [Accepted: 03/02/2017] [Indexed: 01/03/2023] Open
Abstract
Synthetic circuits embedded in host cells compete with cellular processes for limited intracellular resources. Here we show how funnelling of cellular resources, after global transcriptome degradation by the sequence-dependent endoribonuclease MazF, to a synthetic circuit can increase production. Target genes are protected from MazF activity by recoding the gene sequence to eliminate recognition sites, while preserving the amino acid sequence. The expression of a protected fluorescent reporter and flux of a high-value metabolite are significantly enhanced using this genome-scale control strategy. Proteomics measurements discover a host factor in need of protection to improve resource redistribution activity. A computational model demonstrates that the MazF mRNA-decay feedback loop enables proportional control of MazF in an optimal operating regime. Transcriptional profiling of MazF-induced cells elucidates the dynamic shifts in transcript abundance and discovers regulatory design elements. Altogether, our results suggest that manipulation of cellular resource allocation is a key control parameter for synthetic circuit design. Synthetic circuits in host cells compete with endogenous processes for limited resources. Here the authors use MazF to funnel cellular resources to a synthetic circuit to increase product production and demonstrate how resource allocation can be manipulated.
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Affiliation(s)
- Ophelia S Venturelli
- California Institute for Quantitative Biosciences, University of California Berkeley, Berkeley, California 94158, USA.,Department of Bioengineering, University of California Berkeley, Berkeley, California 94720, USA
| | - Mika Tei
- California Institute for Quantitative Biosciences, University of California Berkeley, Berkeley, California 94158, USA.,Department of Bioengineering, University of California Berkeley, Berkeley, California 94720, USA
| | - Stefan Bauer
- Energy Biosciences Institute, University of California Berkeley, Berkeley, California 94704, USA
| | - Leanne Jade G Chan
- Joint BioEnergy Institute and Biological Systems and Engineering Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Christopher J Petzold
- Joint BioEnergy Institute and Biological Systems and Engineering Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Adam P Arkin
- California Institute for Quantitative Biosciences, University of California Berkeley, Berkeley, California 94158, USA.,Department of Bioengineering, University of California Berkeley, Berkeley, California 94720, USA.,Energy Biosciences Institute, University of California Berkeley, Berkeley, California 94704, USA.,Environmental Genomics and Systems Biology, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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11
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Robens C, Alt W, Emary C, Meschede D, Alberti A. Atomic "bomb testing": the Elitzur-Vaidman experiment violates the Leggett-Garg inequality. APPLIED PHYSICS. B, LASERS AND OPTICS 2016; 123:12. [PMID: 32214686 PMCID: PMC7064022 DOI: 10.1007/s00340-016-6581-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2016] [Accepted: 11/04/2016] [Indexed: 06/07/2023]
Abstract
Elitzur and Vaidman have proposed a measurement scheme that, based on the quantum superposition principle, allows one to detect the presence of an object-in a dramatic scenario, a bomb-without interacting with it. It was pointed out by Ghirardi that this interaction-free measurement scheme can be put in direct relation with falsification tests of the macro-realistic worldview. Here we have implemented the "bomb test" with a single atom trapped in a spin-dependent optical lattice to show explicitly a violation of the Leggett-Garg inequality-a quantitative criterion fulfilled by macro-realistic physical theories. To perform interaction-free measurements, we have implemented a novel measurement method that correlates spin and position of the atom. This method, which quantum mechanically entangles spin and position, finds general application for spin measurements, thereby avoiding the shortcomings inherent in the widely used push-out technique. Allowing decoherence to dominate the evolution of our system causes a transition from quantum to classical behavior in fulfillment of the Leggett-Garg inequality.
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Affiliation(s)
- Carsten Robens
- Institut Für Angewandte Physik, Universität Bonn, Wegelerstr. 8, 53115 Bonn, Germany
| | - Wolfgang Alt
- Institut Für Angewandte Physik, Universität Bonn, Wegelerstr. 8, 53115 Bonn, Germany
| | - Clive Emary
- Joint Quantum Centre Durham-Newcastle, Newcastle University, Newcastle upon Tyne, NE1 7RU UK
| | - Dieter Meschede
- Institut Für Angewandte Physik, Universität Bonn, Wegelerstr. 8, 53115 Bonn, Germany
| | - Andrea Alberti
- Institut Für Angewandte Physik, Universität Bonn, Wegelerstr. 8, 53115 Bonn, Germany
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12
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Knee GC, Kakuyanagi K, Yeh MC, Matsuzaki Y, Toida H, Yamaguchi H, Saito S, Leggett AJ, Munro WJ. A strict experimental test of macroscopic realism in a superconducting flux qubit. Nat Commun 2016; 7:13253. [PMID: 27811844 PMCID: PMC5097155 DOI: 10.1038/ncomms13253] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2016] [Accepted: 09/15/2016] [Indexed: 11/15/2022] Open
Abstract
Macroscopic realism is the name for a class of modifications to quantum theory that allow macroscopic objects to be described in a measurement-independent manner, while largely preserving a fully quantum mechanical description of the microscopic world. Objective collapse theories are examples which aim to solve the quantum measurement problem through modified dynamical laws. Whether such theories describe nature, however, is not known. Here we describe and implement an experimental protocol capable of constraining theories of this class, that is more noise tolerant and conceptually transparent than the original Leggett–Garg test. We implement the protocol in a superconducting flux qubit, and rule out (by ∼84 s.d.) those theories which would deny coherent superpositions of 170 nA currents over a ∼10 ns timescale. Further, we address the ‘clumsiness loophole' by determining classical disturbance with control experiments. Our results constitute strong evidence for the superposition of states of nontrivial macroscopic distinctness. Objective collapse theories are formulations of quantum physics that attempt to solve the measurement problem through modified dynamical laws. Here, the authors constrain such theories by testing a generalization of the Leggett-Garg inequality in a superconducting flux qubit experiment.
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Affiliation(s)
- George C Knee
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Kosuke Kakuyanagi
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Mao-Chuang Yeh
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Yuichiro Matsuzaki
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Hiraku Toida
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Hiroshi Yamaguchi
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Shiro Saito
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Anthony J Leggett
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - William J Munro
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan
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13
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Bechtold A, Li F, Müller K, Simmet T, Ardelt PL, Finley JJ, Sinitsyn NA. Quantum Effects in Higher-Order Correlators of a Quantum-Dot Spin Qubit. PHYSICAL REVIEW LETTERS 2016; 117:027402. [PMID: 27447523 DOI: 10.1103/physrevlett.117.027402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2015] [Indexed: 06/06/2023]
Abstract
We measure time correlators of a spin qubit in an optically active quantum dot beyond the second order. Such higher-order correlators are shown to be directly sensitive to pure quantum effects that cannot be explained within the classical framework. They allow direct determination of ensemble and quantum dephasing times, T_{2}^{*} and T_{2}, using only repeated projective measurements and without the need for coherent spin control. Our method enables studies of purely quantum behavior in solid state systems, including tests of the Leggett-Garg type of inequalities that rule out local hidden variable interpretation of the quantum-dot spin dynamics.
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Affiliation(s)
- A Bechtold
- Walter Schottky Institut and Physik Department, Technische Universität München, 85748 Garching, Germany
| | - F Li
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 USA
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - K Müller
- Walter Schottky Institut and Physik Department, Technische Universität München, 85748 Garching, Germany
- E. L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
| | - T Simmet
- Walter Schottky Institut and Physik Department, Technische Universität München, 85748 Garching, Germany
| | - P-L Ardelt
- Walter Schottky Institut and Physik Department, Technische Universität München, 85748 Garching, Germany
| | - J J Finley
- Walter Schottky Institut and Physik Department, Technische Universität München, 85748 Garching, Germany
| | - N A Sinitsyn
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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14
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Clemente L, Kofler J. No Fine Theorem for Macrorealism: Limitations of the Leggett-Garg Inequality. PHYSICAL REVIEW LETTERS 2016; 116:150401. [PMID: 27127944 DOI: 10.1103/physrevlett.116.150401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2015] [Indexed: 06/05/2023]
Abstract
Tests of local realism and macrorealism have historically been discussed in very similar terms: Leggett-Garg inequalities follow Bell inequalities as necessary conditions for classical behavior. Here, we compare the probability polytopes spanned by all measurable probability distributions for both scenarios and show that their structure differs strongly between spatially and temporally separated measurements. We arrive at the conclusion that, in contrast to tests of local realism where Bell inequalities form a necessary and sufficient set of conditions, no set of inequalities can ever be necessary and sufficient for a macrorealistic description. Fine's famous proof that Bell inequalities are necessary and sufficient for the existence of a local realistic model, therefore, cannot be transferred to macrorealism. A recently proposed condition, no-signaling in time, fulfills this criterion, and we show why it is better suited for future experimental tests and theoretical studies of macrorealism. Our work thereby identifies a major difference between the mathematical structures of local realism and macrorealism.
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Affiliation(s)
- Lucas Clemente
- Max Planck Institute of Quantum Optics, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
| | - Johannes Kofler
- Max Planck Institute of Quantum Optics, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
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15
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Chen SL, Lambert N, Li CM, Miranowicz A, Chen YN, Nori F. Quantifying Non-Markovianity with Temporal Steering. PHYSICAL REVIEW LETTERS 2016; 116:020503. [PMID: 26824533 DOI: 10.1103/physrevlett.116.020503] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2015] [Indexed: 06/05/2023]
Abstract
Einstein-Podolsky-Rosen (EPR) steering is a type of quantum correlation which allows one to remotely prepare, or steer, the state of a distant quantum system. While EPR steering can be thought of as a purely spatial correlation, there does exist a temporal analogue, in the form of single-system temporal steering. However, a precise quantification of such temporal steering has been lacking. Here, we show that it can be measured, via semidefinite programing, with a temporal steerable weight, in direct analogy to the recently proposed EPR steerable weight. We find a useful property of the temporal steerable weight in that it is a nonincreasing function under completely positive trace-preserving maps and can be used to define a sufficient and practical measure of strong non-Markovianity.
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Affiliation(s)
- Shin-Liang Chen
- Department of Physics and National Center for Theoretical Sciences, National Cheng-Kung University, Tainan 701, Taiwan
| | | | - Che-Ming Li
- Department of Engineering Science, National Cheng-Kung University, Tainan City 701, Taiwan
| | - Adam Miranowicz
- CEMS, RIKEN, 351-0198 Wako-shi, Japan
- Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland
| | - Yueh-Nan Chen
- Department of Physics and National Center for Theoretical Sciences, National Cheng-Kung University, Tainan 701, Taiwan
- CEMS, RIKEN, 351-0198 Wako-shi, Japan
| | - Franco Nori
- CEMS, RIKEN, 351-0198 Wako-shi, Japan
- Department of Physics, The University of Michigan, Ann Arbor, Michigan 48109-1040, USA
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16
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Abstract
In ordinary, non-relativistic, quantum physics, time enters only as a parameter and not as an observable: a state of a physical system is specified at a given time and then evolved according to the prescribed dynamics. While the state can, and usually does, extend across all space, it is only defined at one instant of time. Here we ask what would happen if we defined the notion of the quantum density matrix for multiple spatial and temporal measurements. We introduce the concept of a pseudo-density matrix (PDM) which treats space and time indiscriminately. This matrix in general fails to be positive for measurement events which do not occur simultaneously, motivating us to define a measure of causality that discriminates between spatial and temporal correlations. Important properties of this measure, such as monotonicity under local operations, are proved. Two qubit NMR experiments are presented that illustrate how a temporal pseudo-density matrix approaches a genuinely allowed density matrix as the amount of decoherence is increased between two consecutive measurements.
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17
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Budroni C, Vitagliano G, Colangelo G, Sewell RJ, Gühne O, Tóth G, Mitchell MW. Quantum Nondemolition Measurement Enables Macroscopic Leggett-Garg Tests. PHYSICAL REVIEW LETTERS 2015; 115:200403. [PMID: 26613423 DOI: 10.1103/physrevlett.115.200403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2015] [Indexed: 06/05/2023]
Abstract
We show how a test of macroscopic realism based on Leggett-Garg inequalities (LGIs) can be performed in a macroscopic system. Using a continuous-variable approach, we consider quantum nondemolition (QND) measurements applied to atomic ensembles undergoing magnetically driven coherent oscillation. We identify measurement schemes requiring only Gaussian states as inputs and giving a significant LGI violation with realistic experimental parameters and imperfections. The predicted violation is shown to be due to true quantum effects rather than to a classical invasivity of the measurement. Using QND measurements to tighten the "clumsiness loophole" forces the stubborn macrorealist to recreate quantum backaction in his or her account of measurement.
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Affiliation(s)
- C Budroni
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Str. 3, D-57068 Siegen, Germany
| | - G Vitagliano
- Department of Theoretical Physics, University of the Basque Country UPV/EHU, P.O. Box 644, E-48080 Bilbao, Spain
| | - G Colangelo
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - R J Sewell
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - O Gühne
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Str. 3, D-57068 Siegen, Germany
| | - G Tóth
- Department of Theoretical Physics, University of the Basque Country UPV/EHU, P.O. Box 644, E-48080 Bilbao, Spain
- IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao, Spain
- Wigner Research Centre for Physics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary
| | - M W Mitchell
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
- ICREA-Institució Catalana de Recerca i Estudis Avançats, 08015 Barcelona, Spain
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18
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Zhou ZQ, Huelga SF, Li CF, Guo GC. Experimental detection of quantum coherent evolution through the violation of Leggett-Garg-type inequalities. PHYSICAL REVIEW LETTERS 2015; 115:113002. [PMID: 26406826 DOI: 10.1103/physrevlett.115.113002] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2014] [Indexed: 06/05/2023]
Abstract
We discuss the use of inequalities of the Leggett-Garg type (LGtI) to witness quantum coherence and present the first experimental violation of this type of inequalities using a light-matter interfaced system. By separately benchmarking the Markovian character of the evolution and the translational invariance of the conditional probabilities, the observed violation of a LGtI is attributed to the quantum coherent character of the process. These results provide a general method to benchmark "quantumness" when the absence of memory effects can be independently certified and confirm the persistence of quantum coherent features within systems of increasing complexity.
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Affiliation(s)
- Zong-Quan Zhou
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Susana F Huelga
- Institut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm, D-89069 Ulm, Germany
| | - Chuan-Feng Li
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Guang-Can Guo
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
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19
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Chen PW, Ali MM. Investigating Leggett-Garg inequality for a two level system under decoherence in a non-Markovian dephasing environment. Sci Rep 2014; 4:6165. [PMID: 25145508 PMCID: PMC4141272 DOI: 10.1038/srep06165] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2014] [Accepted: 08/04/2014] [Indexed: 11/09/2022] Open
Abstract
Leggett-Garg inequalities (LGI) test the correlations of a single system measured at different times. Violation of LGI implies either the absence of a realistic description of the system or the impossibility of measuring the system without disturbing it. We investigate the violation of the Leggett-Garg inequality for a two level system under decoherence in a non-Markovian dephasing environment. We discuss the non-Markovian dynamics of the violation of LGI at zero temperature and also at finite temperature for different structured environments. An enhanced quantum coherence is shown through the violation of Leggett-Garg inequality in the strong non-Markovian regime of the environment.
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Affiliation(s)
- Po-Wen Chen
- Physics Division, Institute of Nuclear Energy Research, Longtan, Taoyuan 32546, Taiwan
| | - Md Manirul Ali
- Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan
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20
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Asadian A, Brukner C, Rabl P. Probing macroscopic realism via Ramsey correlation measurements. PHYSICAL REVIEW LETTERS 2014; 112:190402. [PMID: 24877918 DOI: 10.1103/physrevlett.112.190402] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2013] [Indexed: 06/03/2023]
Abstract
We describe a new and experimentally feasible protocol for performing fundamental tests of quantum mechanics with massive objects. In our approach, a single two-level system is used to probe the motion of a nanomechanical resonator via multiple Ramsey interference measurements. This scheme enables the measurement of modular variables of macroscopic continuous-variable systems; we show that correlations thereof violate a Leggett-Garg inequality and can be applied for tests of quantum contextuality. Our method can be implemented with a variety of different solid-state or photonic qubit-resonator systems, and it provides a clear experimental signature to distinguish the predictions of quantum mechanics from those of other alternative theories at a macroscopic scale.
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Affiliation(s)
- A Asadian
- Institute of Atomic and Subatomic Physics, TU Wien, Stadionallee 2, 1020 Wien, Austria
| | - C Brukner
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria and Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - P Rabl
- Institute of Atomic and Subatomic Physics, TU Wien, Stadionallee 2, 1020 Wien, Austria
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21
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Briggs GAD, Butterfield JN, Zeilinger A. The Oxford Questions on the foundations of quantum physics. Proc Math Phys Eng Sci 2013; 469:20130299. [PMID: 24062626 PMCID: PMC3780811 DOI: 10.1098/rspa.2013.0299] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2013] [Accepted: 06/07/2013] [Indexed: 11/12/2022] Open
Abstract
The twentieth century saw two fundamental revolutions in physics—relativity and quantum. Daily use of these theories can numb the sense of wonder at their immense empirical success. Does their instrumental effectiveness stand on the rock of secure concepts or the sand of unresolved fundamentals? Does measuring a quantum system probe, or even create, reality or merely change belief? Must relativity and quantum theory just coexist or might we find a new theory which unifies the two? To bring such questions into sharper focus, we convened a conference on Quantum Physics and the Nature of Reality. Some issues remain as controversial as ever, but some are being nudged by theory's secret weapon of experiment.
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Affiliation(s)
- G A D Briggs
- Department of Materials , University of Oxford , Oxford OX1 3PH, UK
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22
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Groen JP, Ristè D, Tornberg L, Cramer J, de Groot PC, Picot T, Johansson G, DiCarlo L. Partial-measurement backaction and nonclassical weak values in a superconducting circuit. PHYSICAL REVIEW LETTERS 2013; 111:090506. [PMID: 24033014 DOI: 10.1103/physrevlett.111.090506] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2013] [Revised: 06/29/2013] [Indexed: 06/02/2023]
Abstract
We realize indirect partial measurement of a transmon qubit in circuit quantum electrodynamics by interaction with an ancilla qubit and projective ancilla measurement with a dedicated readout resonator. Accurate control of the interaction and ancilla measurement basis allows tailoring the measurement strength and operator. The tradeoff between measurement strength and qubit backaction is characterized through the distortion of a qubit Rabi oscillation imposed by ancilla measurement in different bases. Combining partial and projective qubit measurements, we provide the solid-state demonstration of the correspondence between a nonclassical weak value and the violation of a Leggett-Garg inequality.
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Affiliation(s)
- J P Groen
- Kavli Institute of Nanoscience, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands
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23
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Chen GY, Chen SL, Li CM, Chen YN. Examining non-locality and quantum coherent dynamics induced by a common reservoir. Sci Rep 2013; 3:2514. [PMID: 23979099 PMCID: PMC3753592 DOI: 10.1038/srep02514] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2013] [Accepted: 08/05/2013] [Indexed: 12/02/2022] Open
Abstract
If two identical emitters are coupled to a common reservoir, entanglement can be generated during the decay process. When using Bell's inequality to examine the non-locality, however, it is possible that the bound cannot be violated in some cases. Here, we propose to use the steering inequality to examine the non-locality induced by a common reservoir. Compared with the Bell inequality, we find that the steering inequality has a better tolerance for examining non-locality. In view of the dynamic nature of the entangling process, we also propose to observe the quantum coherent dynamics by using the Leggett-Garg inequalities. We also suggest a feasible scheme, which consists of two quantum dots coupled to nanowire surface plasmons, for possible experimental realization.
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Affiliation(s)
- Guang-Yin Chen
- Department of Physics, National Chung Hsing University, Taichung 402, Taiwan
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24
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George RE, Robledo LM, Maroney OJE, Blok MS, Bernien H, Markham ML, Twitchen DJ, Morton JJL, Briggs GAD, Hanson R. Opening up three quantum boxes causes classically undetectable wavefunction collapse. Proc Natl Acad Sci U S A 2013; 110:3777-81. [PMID: 23412336 PMCID: PMC3593868 DOI: 10.1073/pnas.1208374110] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
One of the most striking features of quantum mechanics is the profound effect exerted by measurements alone. Sophisticated quantum control is now available in several experimental systems, exposing discrepancies between quantum and classical mechanics whenever measurement induces disturbance of the interrogated system. In practice, such discrepancies may frequently be explained as the back-action required by quantum mechanics adding quantum noise to a classical signal. Here, we implement the "three-box" quantum game [Aharonov Y, et al. (1991) J Phys A Math Gen 24(10):2315-2328] by using state-of-the-art control and measurement of the nitrogen vacancy center in diamond. In this protocol, the back-action of quantum measurements adds no detectable disturbance to the classical description of the game. Quantum and classical mechanics then make contradictory predictions for the same experimental procedure; however, classical observers are unable to invoke measurement-induced disturbance to explain the discrepancy. We quantify the residual disturbance of our measurements and obtain data that rule out any classical model by ≳7.8 standard deviations, allowing us to exclude the property of macroscopic state definiteness from our system. Our experiment is then equivalent to the test of quantum noncontextuality [Kochen S, Specker E (1967) J Math Mech 17(1):59-87] that successfully addresses the measurement detectability loophole.
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Affiliation(s)
- Richard E George
- Department of Materials, University of Oxford, Oxford OX1 3PH, United Kingdom.
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25
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Abstract
Quantum coherence is one of the primary non-classical features of quantum systems. While protocols such as the Leggett-Garg inequality (LGI) and quantum tomography can be used to test for the existence of quantum coherence and dynamics in a given system, unambiguously detecting inherent "quantumness" still faces serious obstacles in terms of experimental feasibility and efficiency, particularly in complex systems. Here we introduce two "quantum witnesses" to efficiently verify quantum coherence and dynamics in the time domain, without the expense and burden of non-invasive measurements or full tomographic processes. Using several physical examples, including quantum transport in solid-state nanostructures and in biological organisms, we show that these quantum witnesses are robust and have a much finer resolution in their detection window than the LGI has. These robust quantum indicators may assist in reducing the experimental overhead in unambiguously verifying quantum coherence in complex systems.
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26
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Xu JS, Li CF, Zou XB, Guo GC. Experimental violation of the Leggett-Garg inequality under decoherence. Sci Rep 2012; 1:101. [PMID: 22355619 PMCID: PMC3216586 DOI: 10.1038/srep00101] [Citation(s) in RCA: 57] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2011] [Accepted: 09/09/2011] [Indexed: 11/09/2022] Open
Abstract
Despite the great success of quantum mechanics, questions regarding its application still exist and the boundary between quantum and classical mechanics remains unclear. Based on the philosophical assumptions of macrorealism and noninvasive measurability, Leggett and Garg devised a series of inequalities (LG inequalities) involving a single system with a set of measurements at different times. Introduced as the Bell inequalities in time, the violation of LG inequalities excludes the hidden-variable description based on the above two assumptions. We experimentally investigated the single photon LG inequalities under decoherence simulated by birefringent media. These generalized LG inequalities test the evolution trajectory of the photon and are shown to be maximally violated in a coherent evolution process. The violation of LG inequalities becomes weaker with the increase of interaction time in the environment. The ability to violate the LG inequalities can be used to set a boundary of the classical realistic description.
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Affiliation(s)
- Jin-Shi Xu
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS , Hefei. 230026, China
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