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Amaral B, Terra Cunha M. On geometrical aspects of the graph approach to contextuality. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2024; 382:20230008. [PMID: 38281724 DOI: 10.1098/rsta.2023.0008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2023] [Accepted: 12/23/2023] [Indexed: 01/30/2024]
Abstract
The connection between contextuality and graph theory has paved the way for numerous advancements in the field. One notable development is the realization that sets of probability distributions in many contextuality scenarios can be effectively described using well-established convex sets from graph theory. This geometric approach allows for a beautiful characterization of these sets. The application of geometry is not limited to the description of contextuality sets alone; it also plays a crucial role in defining contextuality quantifiers based on geometric distances. These quantifiers are particularly significant in the context of the resource theory of contextuality, which emerged following the recognition of contextuality as a valuable resource for quantum computation. In this paper, we provide a comprehensive review of the geometric aspects of contextuality. Additionally, we use this geometry to define several quantifiers, offering the advantage of applicability to other approaches to contextuality where previously defined quantifiers may not be suitable. This article is part of the theme issue 'Quantum contextuality, causality and freedom of choice'.
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Affiliation(s)
- Barbara Amaral
- Departamento de Matemática, Universidade Federal de Minas Gerais, Caixa Postal 702, 30123-970, Belo Horizonte, Minas Gerais, Brazil
- Departamento de Matemática, Universidade Federal de Ouro Preto, Ouro Preto, Minas Gerais, Brazil
- Departamento de Física e Matemática, CAP - Universidade Federal de São João del-Rei, 36.420-000, Ouro Branco, Minas Gerais, Brazil
- International Institute of Physics, Federal University of Rio Grande do Norte, 59078-970, PO Box 1613, Natal, Brazil
- Department of Mathematical Physics, Institute of Physics, University of São Paulo, R. do Matão 1371, São Paulo 05508-090, Brazil
| | - Marcelo Terra Cunha
- Departamento de Matemática, Universidade Federal de Minas Gerais, Caixa Postal 702, 30123-970, Belo Horizonte, Minas Gerais, Brazil
- Departamento de Matemática Aplicada, IMECC-Unicamp, 13084-970, Campinas, São Paulo, Brazil
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Fan X, Xiao Y, Gu Y. Demonstration of universal contextuality through communication games free of both operational inequivalence and compatibility loopholes. OPTICS EXPRESS 2023; 31:42764-42784. [PMID: 38178388 DOI: 10.1364/oe.502723] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2023] [Accepted: 11/18/2023] [Indexed: 01/06/2024]
Abstract
Universal contextuality is the leading notion of non-classicality even for single systems, showing its advantage as a more general quantum correlation than Bell non-locality, as well as preparation contextuality. However, a loophole-free experimental demonstration of universal contextuality at least requires that both operational inequivalence and compatibility loopholes are closed, which have never been simultaneously achieved to date. In our work, we experimentally test universal contextuality through (3,3) and (4,3) communication games, simultaneously restoring operational equivalence and circumventing the compatibility loophole. Our result exhibits the violation of universal non-contextuality bound by 97 standard deviations in (3,3) scenario, and 107 deviations in (4,3) scenario. Notably there are states which exhibit locality but reveal universal contextuality in both two scenarios. In addition, our result shows that universal contextuality is more general than preparation contextuality in (3,3) scenario, while equivalent to preparation contextuality in (4,3) scenario.
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Pavičić M. Non-Kochen-Specker Contextuality. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1117. [PMID: 37628147 PMCID: PMC10453090 DOI: 10.3390/e25081117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2023] [Revised: 07/21/2023] [Accepted: 07/24/2023] [Indexed: 08/27/2023]
Abstract
Quantum contextuality supports quantum computation and communication. One of its main vehicles is hypergraphs. The most elaborated are the Kochen-Specker ones, but there is also another class of contextual sets that are not of this kind. Their representation has been mostly operator-based and limited to special constructs in three- to six-dim spaces, a notable example of which is the Yu-Oh set. Previously, we showed that hypergraphs underlie all of them, and in this paper, we give general methods-whose complexity does not scale up with the dimension-for generating such non-Kochen-Specker hypergraphs in any dimension and give examples in up to 16-dim spaces. Our automated generation is probabilistic and random, but the statistics of accumulated data enable one to filter out sets with the required size and structure.
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Affiliation(s)
- Mladen Pavičić
- Center of Excellence for Advanced Materials and Sensors, Research Unit Photonics and Quantum Optics, Institute Ruđer Bošković, 10000 Zagreb, Croatia;
- Institute of Physics, 10000 Zagreb, Croatia
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Booth RI, Chabaud U, Emeriau PE. Contextuality and Wigner Negativity Are Equivalent for Continuous-Variable Quantum Measurements. PHYSICAL REVIEW LETTERS 2022; 129:230401. [PMID: 36563212 DOI: 10.1103/physrevlett.129.230401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2022] [Accepted: 10/24/2022] [Indexed: 06/17/2023]
Abstract
Quantum computers promise considerable speedups with respect to their classical counterparts. However, the identification of the innately quantum features that enable these speedups is challenging. In the continuous-variable setting-a promising paradigm for the realization of universal, scalable, and fault-tolerant quantum computing-contextuality and Wigner negativity have been perceived as two such distinct resources. Here we show that they are in fact equivalent for the standard models of continuous-variable quantum computing. While our results provide a unifying picture of continuous-variable resources for quantum speedup, they also pave the way toward practical demonstrations of continuous-variable contextuality and shed light on the significance of negative probabilities in phase-space descriptions of quantum mechanics.
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Affiliation(s)
- Robert I Booth
- School of Informatics, University of Edinburgh, Edinburgh EH8 9AB, United Kingdom
- LORIA CNRS, Inria-MOCQUA, Université de Lorraine, F-54000 Nancy, France
- Sorbonne Université, CNRS, LIP6, F-75005 Paris, France
| | - Ulysse Chabaud
- Institute for Quantum Information and Matter, Caltech, Pasadena, California 91125, USA
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What Is So Special about Quantum Clicks? ENTROPY 2020; 22:e22060602. [PMID: 33286374 PMCID: PMC7517140 DOI: 10.3390/e22060602] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/30/2020] [Revised: 05/19/2020] [Accepted: 05/20/2020] [Indexed: 11/17/2022]
Abstract
This is an elaboration of the "extra" advantage of the performance of quantized physical systems over classical ones, both in terms of single outcomes as well as probabilistic predictions. From a formal point of view, it is based on entities related to (dual) vectors in (dual) Hilbert spaces, as compared to the Boolean algebra of subsets of a set and the additive measures they support.
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Abstract
State-independent contextuality is a fundamental phenomenon in quantum mechanics, which has been demonstrated experimentally in different systems in recent years. Here we show that such contextuality can also be simulated in classical optical systems. Using path and polarization degrees of freedom of classical optics fields, we have constructed the classical trit (cetrit), here the term ‘cetrit’ is the classical counterpart of a qutrit in quantum systems. Furthermore, in classical optical systems we have simulated the violations of several Yu-Oh-like noncontextual inequalities in a state-independent manner by implementing the projection measurements. Our results not only provide new physical insights into the contextuality and also show the application prospects of the concepts developed recently in quantum information science to classical optical systems and optical information processes.
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Abstract
Quantum contextuality is a source of quantum computational power and a theoretical delimiter between classical and quantum structures. It has been substantiated by numerous experiments and prompted generation of state independent contextual sets, that is, sets of quantum observables capable of revealing quantum contextuality for any quantum state of a given dimension. There are two major classes of state-independent contextual sets—the Kochen-Specker ones and the operator-based ones. In this paper, we present a third, hypergraph-based class of contextual sets. Hypergraph inequalities serve as a measure of contextuality. We limit ourselves to qutrits and obtain thousands of 3-dim contextual sets. The simplest of them involves only 5 quantum observables, thus enabling a straightforward implementation. They also enable establishing new entropic contextualities.
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Pavičić M, Waegell M, Megill ND, Aravind PK. Automated generation of Kochen-Specker sets. Sci Rep 2019; 9:6765. [PMID: 31043624 PMCID: PMC6494998 DOI: 10.1038/s41598-019-43009-9] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2018] [Accepted: 04/08/2019] [Indexed: 11/28/2022] Open
Abstract
Quantum contextuality turns out to be a necessary resource for universal quantum computation and also has applications in quantum communication. Thus it becomes important to generate contextual sets of arbitrary structure and complexity to enable a variety of implementations. In recent years, such generation has been done for contextual sets known as Kochen-Specker sets. Up to now, two approaches have been used for massive generation of non-isomorphic Kochen-Specker sets: exhaustive generation up to a given size and downward generation from master sets and their associated coordinatizations. Master sets were obtained earlier from serendipitous or intuitive connections with polytopes or Pauli operators, and more recently from arbitrary vector components using an algorithm that generates orthogonal vector groupings from them. However, both upward and downward generation face an inherent exponential complexity barrier. In contrast, in this paper we present methods and algorithms that we apply to downward generation that can overcome the exponential barrier in many cases of interest. These involve tailoring and manipulating Kochen-Specker master sets obtained from a small number of simple vector components, filtered by the features of the sets we aim to obtain. Some of the classes of Kochen-Specker sets we generate contain all previously known ones, and others are completely novel. We provide examples of both kinds in 4- and 6-dim Hilbert spaces. We also give a brief introduction for a wider audience and a novice reader.
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Affiliation(s)
- Mladen Pavičić
- Department of Physics-Nanooptics, Faculty of Math. and Natural Sci. I, Humboldt University of Berlin, Berlin, Germany.
- Center of Excellence CEMS, Photonics and Quantum Optics Unit, Ruder Bošković Institute, Zagreb, Croatia.
| | - Mordecai Waegell
- Institute for Quantum Studies, Chapman University, Orange, CA, 92866, USA
| | | | - P K Aravind
- Physics Department, Worcester Polytechnic Institute, Worcester, MA, 01609, USA
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Pavičić M, Megill ND. Vector generation of contextual sets. EPJ WEB OF CONFERENCES 2019. [DOI: 10.1051/epjconf/201919800009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
As quantum contextuality proves to be a necessary resource for universal quantum computation, we present a general method for vector generation of Kochen-Specker (KS) contextual sets in the form of hypergraphs. The method supersedes all three previous methods: (i) fortuitous discoveries of smallest KS sets, (ii) exhaustive upward hypergraph-generation of sets, and (iii) random downward generation of sets from fortuitously obtained big master sets. In contrast to previous works, we can generate master sets which contain all possible KS sets starting with nothing but a few simple vector components. From them we can readily generate all KS sets obtained in the last half a century and any specified new KS sets. Herewith we can generate sufficiently large sets as well as sets with definite required features and structures to enable varieties of different implementations in quantum computation and communication.
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Pavičić M, Megill ND. Vector Generation of Quantum Contextual Sets in Even Dimensional Hilbert Spaces. ENTROPY 2018; 20:e20120928. [PMID: 33266652 PMCID: PMC7512515 DOI: 10.3390/e20120928] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/29/2018] [Revised: 11/21/2018] [Accepted: 11/24/2018] [Indexed: 11/16/2022]
Abstract
Recently, quantum contextuality has been proved to be the source of quantum computation's power. That, together with multiple recent contextual experiments, prompts improving the methods of generation of contextual sets and finding their features. The most elaborated contextual sets, which offer blueprints for contextual experiments and computational gates, are the Kochen-Specker (KS) sets. In this paper, we show a method of vector generation that supersedes previous methods. It is implemented by means of algorithms and programs that generate hypergraphs embodying the Kochen-Specker property and that are designed to be carried out on supercomputers. We show that vector component generation of KS hypergraphs exhausts all possible vectors that can be constructed from chosen vector components, in contrast to previous studies that used incomplete lists of vectors and therefore missed a majority of hypergraphs. Consequently, this unified method is far more efficient for generations of KS sets and their implementation in quantum computation and quantum communication. Several new KS classes and their features have been found and are elaborated on in the paper. Greechie diagrams are discussed.
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Affiliation(s)
- Mladen Pavičić
- Nano Optics, Department of Physics, Humboldt University, 12489 Berlin, Germany
- Center of Excellence for Advanced Materials and Sensors, Research Unit Photonics and Quantum Optics, Institute Ruder Bošković, 10000 Zagreb, Croatia
- Correspondence:
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Li T, Zhang X, Zeng Q, Wang B, Zhang X. Experimental simulation of monogamy relation between contextuality and nonlocality in classical light. OPTICS EXPRESS 2018; 26:11959-11975. [PMID: 29716113 DOI: 10.1364/oe.26.011959] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2018] [Accepted: 04/14/2018] [Indexed: 06/08/2023]
Abstract
The Clauser-Horne-Shimony-Holt (CHSH) inequality and the Klyachko-Can-Binicioglu-Shumovski (KCBS) inequality present a tradeoff on the no-disturbance (ND) principle. Recently, the fundamental monogamy relation between contextuality and nonlocality in quantum theory has been demonstrated experimentally. Here we show that such a relation and tradeoff can also be simulated in classical optical systems. Using polarization, path and orbital angular momentum of the classical optical beam, in classical optical experiment we have observed the stringent monogamy relation between the two inequalities by implementing the projection measurement. Our results show the application prospect of the concepts developed recently in quantum information science to classical optical system and optical information processing.
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Amaral B, Cabello A, Cunha MT, Aolita L. Noncontextual Wirings. PHYSICAL REVIEW LETTERS 2018; 120:130403. [PMID: 29694169 DOI: 10.1103/physrevlett.120.130403] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2017] [Revised: 12/05/2017] [Indexed: 06/08/2023]
Abstract
Contextuality is a fundamental feature of quantum theory necessary for certain models of quantum computation and communication. Serious steps have therefore been taken towards a formal framework for contextuality as an operational resource. However, the main ingredient of a resource theory-a concrete, explicit form of free operations of contextuality-was still missing. Here we provide such a component by introducing noncontextual wirings: a class of contextuality-free operations with a clear operational interpretation and a friendly parametrization. We characterize them completely for general black-box measurement devices with arbitrarily many inputs and outputs. As applications, we show that the relative entropy of contextuality is a contextuality monotone and that maximally contextual boxes that serve as contextuality bits exist for a broad class of scenarios. Our results complete a unified resource-theoretic framework for contextuality and Bell nonlocality.
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Affiliation(s)
- Barbara Amaral
- Departamento de Matemática, Universidade Federal de Ouro Preto, 35400-000 Ouro Preto, Minas Gerais, Brazil
- Departamento de Física e Matemática, CAP-Universidade Federal de São João del-Rei, 36.420-000 Ouro Branco, Minas Gerais, Brazil
- International Institute of Physics, Federal University of Rio Grande do Norte, 59070-405 Natal, Brazil
| | - Adán Cabello
- Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain
| | - Marcelo Terra Cunha
- Departamento de Matemática Aplicada, IMECC-Unicamp, 13084-970 Campinas, São Paulo, Brazil
| | - Leandro Aolita
- International Institute of Physics, Federal University of Rio Grande do Norte, 59070-405 Natal, Brazil
- Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, Rio de Janeiro 21941-972, Brazil
- ICTP South American Institute for Fundamental Research, Instituto de Física Teórica, UNESP-Universidade Estadual Paulista R. Dr. Bento T. Ferraz 271, Bl. II, São Paulo 01140-070, São Paulo, Brazil
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Abstract
The Klyachko, Can, Binicioglu, and Shumovsky (KCBS) inequality is an important contextuality inequality in three-level system, which has been demonstrated experimentally by using quantum states. Using the path and polarization degrees of freedom of classical optics fields, we have constructed the classical trit (cetrit), tested the KCBS inequality and its geometrical form (Wright's inequality) in this work. The projection measurement has been implemented, the clear violations of the KCBS inequality and its geometrical form have been observed. This means that the contextuality inequality, which is commonly used in test of the conflict between quantum theory and noncontextual realism, may be used as a quantitative tool in classical optical coherence to describe correlation characteristics of the classical fields.
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An experimental test of noncontextuality without unphysical idealizations. Nat Commun 2016; 7:ncomms11780. [PMID: 27292369 PMCID: PMC4909951 DOI: 10.1038/ncomms11780] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2015] [Accepted: 04/27/2016] [Indexed: 11/09/2022] Open
Abstract
To make precise the sense in which nature fails to respect classical physics, one requires a formal notion of classicality. Ideally, such a notion should be defined operationally, so that it can be subject to direct experimental test, and it should be applicable in a wide variety of experimental scenarios so that it can cover the breadth of phenomena thought to defy classical understanding. Bell's notion of local causality fulfils the first criterion but not the second. The notion of noncontextuality fulfils the second criterion, but it is a long-standing question whether it can be made to fulfil the first. Previous attempts to test noncontextuality have all assumed idealizations that real experiments cannot achieve, namely noiseless measurements and exact operational equivalences. Here we show how to devise tests that are free of these idealizations. We perform a photonic implementation of one such test, ruling out noncontextual models with high confidence. No noncontextual hidden-variable model can be consistent with quantum theory, but proving such an inconsistency with nature itself is a long-standing problem. Here, the authors devise experimentally-achievable tests of noncontextuality and perform a photonic implementation that rules out such models.
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Fundamental Features of Quantum Dynamics Studied in Matter-Wave Interferometry—Spin Weak Values and the Quantum Cheshire-Cat. ATOMS 2016. [DOI: 10.3390/atoms4010011] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
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Geppert H, Denkmayr T, Sponar S, Lemmel H, Hasegawa Y. Improvement of the polarized neutron interferometer setup demonstrating violation of a Bell-like inequality. NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH. SECTION A, ACCELERATORS, SPECTROMETERS, DETECTORS AND ASSOCIATED EQUIPMENT 2014; 763:417-423. [PMID: 26089579 PMCID: PMC4375610 DOI: 10.1016/j.nima.2014.06.080] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/30/2014] [Revised: 06/06/2014] [Accepted: 06/27/2014] [Indexed: 06/04/2023]
Abstract
For precise measurements with polarised neutrons high efficient spin-manipulation is required. We developed several neutron optical elements suitable for a new sophisticated setup, i.e., DC spin-turners and Larmor-accelerators which diminish thermal disturbances and depolarisation considerably. The gain in performance is exploited demonstrating violation of a Bell-like inequality for a spin-path entangled single-neutron state. The obtained value of [Formula: see text], which is much higher than previous measurements by neutron interferometry, is [Formula: see text] above the limit of S=2 predicted by contextual hidden variable theories. The new setup is more flexible referring to state preparation and analysis, therefore new, more precise measurements can be carried out.
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Affiliation(s)
- H. Geppert
- Atominstitut, Vienna University of Technology, Stadionallee 2, 1020 Vienna, Austria
| | - T. Denkmayr
- Atominstitut, Vienna University of Technology, Stadionallee 2, 1020 Vienna, Austria
| | - S. Sponar
- Atominstitut, Vienna University of Technology, Stadionallee 2, 1020 Vienna, Austria
| | - H. Lemmel
- Atominstitut, Vienna University of Technology, Stadionallee 2, 1020 Vienna, Austria
- Institut Laue Langevin, 38000 Grenoble, France
| | - Y. Hasegawa
- Atominstitut, Vienna University of Technology, Stadionallee 2, 1020 Vienna, Austria
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Yu S, Oh CH. State-independent proof of Kochen-Specker theorem with 13 rays. PHYSICAL REVIEW LETTERS 2012; 108:030402. [PMID: 22400719 DOI: 10.1103/physrevlett.108.030402] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2011] [Indexed: 05/31/2023]
Abstract
Quantum contextuality, as proved by Kochen and Specker, and also by Bell, should manifest itself in any state in any system with more than two distinguishable states and recently has been experimentally verified. However, for the simplest system capable of exhibiting contextuality, a qutrit, the quantum contextuality is verified only state dependently in experiment because too many (at least 31) observables are involved in all the known state-independent tests. Here we report an experimentally testable inequality involving only 13 observables that is satisfied by all noncontextual realistic models while being violated by all qutrit states. Thus our inequality facilitates a state-independent test of the quantum contextuality for an indivisible quantum system. We also provide a record-breaking state-independent proof of the Kochen-Specker theorem with 13 directions determined by 26 points on the surface of a magic cube.
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Affiliation(s)
- Sixia Yu
- Centre for quantum technologies and Physics department, National University of Singapore, 3 Science Drive 2, Singapore 117543
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Hasegawa Y, Durstberger-Rennhofer K, Sponar S, Rauch H. Kochen-Specker theorem studied with neutron interferometer. NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH. SECTION A, ACCELERATORS, SPECTROMETERS, DETECTORS AND ASSOCIATED EQUIPMENT 2011; 634:S21-S24. [PMID: 21731154 PMCID: PMC3120060 DOI: 10.1016/j.nima.2010.06.234] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291±0.008≰1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.
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Affiliation(s)
- Yuji Hasegawa
- Atominstitut, Technische Universität Wien, Stadionallee 2, A-1020
Wien, Austria
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Bartosik H, Klepp J, Schmitzer C, Sponar S, Cabello A, Rauch H, Hasegawa Y. Experimental test of quantum contextuality in neutron interferometry. PHYSICAL REVIEW LETTERS 2009; 103:040403. [PMID: 19659333 DOI: 10.1103/physrevlett.103.040403] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2009] [Indexed: 05/28/2023]
Abstract
We performed an experimental test of the Kochen-Specker theorem based on an inequality derived from the Peres-Mermin proof, using spin-path (momentum) entanglement in a single neutron system. Following the strategy proposed by Cabello et al. [Phys. Rev. Lett. 100, 130404 (2008)10.1103/PhysRevLett.100.130404], a Bell-like state was generated, and three expectation values were determined. The observed violation 2.291 +/- 0.008 not less, dbl equals1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden-variable theories.
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Affiliation(s)
- H Bartosik
- Atominstitut der Osterreichischen Universitäten, A-1020 Wien, Austria
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Quantum scholasticism: On quantum contexts, counterfactuals, and the absurdities of quantum omniscience. Inf Sci (N Y) 2009. [DOI: 10.1016/j.ins.2008.06.012] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Cabello A, Filipp S, Rauch H, Hasegawa Y. Proposed experiment for testing quantum contextuality with neutrons. PHYSICAL REVIEW LETTERS 2008; 100:130404. [PMID: 18517923 DOI: 10.1103/physrevlett.100.130404] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2007] [Indexed: 05/26/2023]
Abstract
We show that an experimental demonstration of quantum contextuality using 2 degrees of freedom of single neutrons based on a violation of an inequality derived from the Peres-Mermin proof of the Kochen-Specker theorem would be more conclusive than those obtained from previous experiments involving pairs of ions [M. A. Rowe, Nature (London) 409, 791 (2001)10.1038/35057215] and single neutrons [Y. Hasegawa, Nature (London) 425, 45 (2003)10.1038/nature01881] based on violations of Clauser-Horne-Shimony-Holt-like inequalities.
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Affiliation(s)
- Adán Cabello
- Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain.
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