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Xu ZP, Saha D, Bharti K, Cabello A. Certifying Sets of Quantum Observables with Any Full-Rank State. PHYSICAL REVIEW LETTERS 2024; 132:140201. [PMID: 38640382 DOI: 10.1103/physrevlett.132.140201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2023] [Revised: 02/10/2024] [Accepted: 03/01/2024] [Indexed: 04/21/2024]
Abstract
We show that some sets of quantum observables are unique up to an isometry and have a contextuality witness that attains the same value for any initial state. We prove that these two properties make it possible to certify any of these sets by looking at the statistics of experiments with sequential measurements and using any initial state of full rank, including thermal and maximally mixed states. We prove that this "certification with any full-rank state" (CFR) is possible for any quantum system of finite dimension d≥3 and is robust and experimentally useful in dimensions 3 and 4. In addition, we prove that complete Kochen-Specker sets can be Bell self-tested if and only if they enable CFR. This establishes a fundamental connection between these two methods of certification, shows that both methods can be combined in the same experiment, and opens new possibilities for certifying quantum devices.
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Affiliation(s)
- Zhen-Peng Xu
- School of Physics and Optoelectronics Engineering, Anhui University, 230601 Hefei, People's Republic of China
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
| | - Debashis Saha
- School of Physics, Indian Institute of Science Education and Research Thiruvananthapuram, Kerala 695551, India
| | - Kishor Bharti
- Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Republic of Singapore
| | - Adán Cabello
- Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Sevilla, E-41012 Sevilla, Spain
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2
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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: 1] [Impact Index Per Article: 1.0] [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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3
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Xu JM, Zhen YZ, Yang YX, Cheng ZM, Ren ZC, Chen K, Wang XL, Wang HT. Experimental Demonstration of Quantum Pseudotelepathy. PHYSICAL REVIEW LETTERS 2022; 129:050402. [PMID: 35960591 DOI: 10.1103/physrevlett.129.050402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2021] [Revised: 04/29/2022] [Accepted: 06/23/2022] [Indexed: 06/15/2023]
Abstract
Quantum pseudotelepathy is a strong form of nonlocality. Different from the conventional nonlocal games where quantum strategies win statistically, e.g., the Clauser-Horne-Shimony-Holt game, quantum pseudotelepathy in principle allows quantum players to with probability 1. In this Letter, we report a faithful experimental demonstration of quantum pseudotelepathy via playing the nonlocal version of Mermin-Peres magic square game, where Alice and Bob cooperatively fill in a 3×3 magic square. We adopt the hyperentanglement scheme and prepare photon pairs entangled in both the polarization and the orbital angular momentum degrees of freedom, such that the experiment is carried out in a resource-efficient manner. Under the locality and fair-sampling assumption, our results show that quantum players can simultaneously win all the queries over any classical strategy.
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Affiliation(s)
- Jia-Min Xu
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Centre for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Yi-Zheng Zhen
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Centre for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Yu-Xiang Yang
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China
| | - Zi-Mo Cheng
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China
| | - Zhi-Cheng Ren
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China
| | - Kai Chen
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Centre for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Xi-Lin Wang
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China
| | - Hui-Tian Wang
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China
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4
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Wang P, Zhang J, Luan CY, Um M, Wang Y, Qiao M, Xie T, Zhang JN, Cabello A, Kim K. Significant loophole-free test of Kochen-Specker contextuality using two species of atomic ions. SCIENCE ADVANCES 2022; 8:eabk1660. [PMID: 35138888 PMCID: PMC8827658 DOI: 10.1126/sciadv.abk1660] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2021] [Accepted: 12/16/2021] [Indexed: 05/28/2023]
Abstract
Quantum measurements cannot be thought of as revealing preexisting results, even when they do not disturb any other measurement in the same trial. This feature is called contextuality and is crucial for the quantum advantage in computing. Here, we report the observation of quantum contextuality simultaneously free of the detection, sharpness, and compatibility loopholes. The detection and sharpness loopholes are closed by adopting a hybrid two-ion system and highly efficient fluorescence measurements offering a detection efficiency of 100% and a measurement repeatability of >98%. The compatibility loophole is closed by targeting correlations between observables for two different ions in a Paul trap, a 171Yb+ ion and a 138Ba+ ion, chosen so measurements on each ion use different operation laser wavelengths, fluorescence wavelengths, and detectors. The experimental results show a violation of the bound for the most adversarial noncontextual models and open a way to certify quantum systems.
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Affiliation(s)
- Pengfei Wang
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People’s Republic of China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, People’s Republic of China
| | - Junhua Zhang
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, People’s Republic of China
| | - Chun-Yang Luan
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People’s Republic of China
| | - Mark Um
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People’s Republic of China
| | - Ye Wang
- Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA
| | - Mu Qiao
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People’s Republic of China
| | - Tian Xie
- Kavli Nanoscience Institute and Thomas J. Watson Sr., Laboratory of Applied Physics, California Institute of Technology, Pasadena, CA 91125, USA
| | - Jing-Ning Zhang
- Beijing Academy of Quantum Information Sciences, Beijing 100193, People’s Republic of China
| | - Adán Cabello
- Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Sevilla, E-41012 Sevilla, Spain
| | - Kihwan Kim
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People’s Republic of China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, People’s Republic of China
- Frontier Science Center for Quantum Information, Beijing 100084, People’s Republic of China
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5
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A Knot Theoretic Extension of the Bloch Sphere Representation for Qubits in Hilbert Space and Its Application to Contextuality and Many-Worlds Theories. Symmetry (Basel) 2020. [DOI: 10.3390/sym12071135] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
We argue that the usual Bloch sphere is insufficient in various aspects for the representation of qubits in quantum information theory. For example, spin flip operations with the quaternions I J K = e 2 π i 2 = − 1 and J I K = + 1 cannot be distinguished on the Bloch sphere. We show that a simple knot theoretic extension of the Bloch sphere representation is sufficient to track all unitary operations for single qubits. Next, we extend the Bloch sphere representation to entangled states using knot theory. As applications, we first discuss contextuality in quantum physics—in particular the Kochen-Specker theorem. Finally, we discuss some arguments against many-worlds theories within our knot theoretic model of entanglement. The key ingredients of our approach are symmetries and geometric properties of the unitary group.
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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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9
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Zhang A, Xu H, Xie J, Zhang H, Smith BJ, Kim MS, Zhang L. Experimental Test of Contextuality in Quantum and Classical Systems. PHYSICAL REVIEW LETTERS 2019; 122:080401. [PMID: 30932576 DOI: 10.1103/physrevlett.122.080401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2018] [Revised: 01/07/2019] [Indexed: 06/09/2023]
Abstract
Contextuality is considered as an intrinsic signature of nonclassicality and a crucial resource for achieving unique advantages of quantum information processing. However, recently, there have been debates on whether classical fields may also demonstrate contextuality. Here, we experimentally configure a contextuality test for optical fields, adopting various definitions of measurement events, and analyze how the definitions affect the emergence of nonclassical correlations. The heralded single-photon state, which is a typical nonclassical light field, manifests contextuality in our setup; whereas contextuality for classical coherent fields strongly depends on the specific definition of measurement events, which is equivalent to filtering the nonclassical component of the input state. Our results highlight the importance of the definition of measurement events to demonstrate contextuality, and they link the contextual correlations to nonclassicality defined by quasiprobabilities in phase space.
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Affiliation(s)
- Aonan Zhang
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation (Ministry of Education), College of Engineering and Applied Sciences and School of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Huichao Xu
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation (Ministry of Education), College of Engineering and Applied Sciences and School of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Jie Xie
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation (Ministry of Education), College of Engineering and Applied Sciences and School of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Han Zhang
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation (Ministry of Education), College of Engineering and Applied Sciences and School of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Brian J Smith
- Department of Physics and Oregon Center for Optical, Molecular, and Quantum Science, University of Oregon, Eugene, Oregon 97403, USA
| | - M S Kim
- QOLS, Blackett Laboratory, Imperial College London, London, England SW7 2AZ, United Kingdom
- Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Lijian Zhang
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation (Ministry of Education), College of Engineering and Applied Sciences and School of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
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10
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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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11
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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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12
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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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13
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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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14
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Hu XM, Chen JS, Liu BH, Guo Y, Huang YF, Zhou ZQ, Han YJ, Li CF, Guo GC. Experimental Test of Compatibility-Loophole-Free Contextuality with Spatially Separated Entangled Qutrits. PHYSICAL REVIEW LETTERS 2016; 117:170403. [PMID: 27824461 DOI: 10.1103/physrevlett.117.170403] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2016] [Indexed: 06/06/2023]
Abstract
The physical impact and the testability of the Kochen-Specker (KS) theorem is debated because of the fact that perfect compatibility in a single quantum system cannot be achieved in practical experiments with finite precision. Here, we follow the proposal of A. Cabello and M. T. Cunha [Phys. Rev. Lett. 106, 190401 (2011)], and present a compatibility-loophole-free experimental violation of an inequality of noncontextual theories by two spatially separated entangled qutrits. A maximally entangled qutrit-qutrit state with a fidelity as high as 0.975±0.001 is prepared and distributed to separated spaces, and these two photons are then measured locally, providing the compatibility requirement. The results show that the inequality for noncontextual theory is violated by 31 standard deviations. Our experiments pave the way to close the debate about the testability of the KS theorem. In addition, the method to generate high-fidelity and high-dimension entangled states will provide significant advantages in high-dimension quantum encoding and quantum communication.
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Affiliation(s)
- Xiao-Min Hu
- Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Jiang-Shan Chen
- Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Bi-Heng Liu
- Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Yu Guo
- Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Yun-Feng Huang
- Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Zong-Quan Zhou
- Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Yong-Jian Han
- Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Chuan-Feng Li
- Laboratory of Quantum Information, University of Science and Technology of China, 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
- Laboratory of Quantum Information, University of Science and Technology of China, 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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15
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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: 21] [Impact Index Per Article: 2.6] [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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16
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Grudka A, Horodecki K, Horodecki M, Horodecki P, Horodecki R, Joshi P, Kłobus W, Wójcik A. Quantifying contextuality. PHYSICAL REVIEW LETTERS 2014; 112:120401. [PMID: 24724629 DOI: 10.1103/physrevlett.112.120401] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2013] [Indexed: 06/03/2023]
Abstract
Contextuality is central to both the foundations of quantum theory and to the novel information processing tasks. Despite some recent proposals, it still faces a fundamental problem: how to quantify its presence? In this work, we provide a universal framework for quantifying contextuality. We conduct two complementary approaches: (i) the bottom-up approach, where we introduce a communication game, which grasps the phenomenon of contextuality in a quantitative manner; (ii) the top-down approach, where we just postulate two measures, relative entropy of contextuality and contextuality cost, analogous to existent measures of nonlocality (a special case of contextuality). We then match the two approaches by showing that the measure emerging from the communication scenario turns out to be equal to the relative entropy of contextuality. Our framework allows for the quantitative, resource-type comparison of completely different games. We give analytical formulas for the proposed measures for some contextual systems, showing in particular that the Peres-Mermin game is by order of magnitude more contextual than that of Klyachko et al. Furthermore, we explore properties of these measures such as monotonicity or additivity.
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Affiliation(s)
- A Grudka
- Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland
| | - K Horodecki
- National Quantum Information Center of Gdańsk, 81-824 Sopot, Poland and Institute of Informatics, University of Gdańsk, 80-952 Gdańsk, Poland
| | - M Horodecki
- National Quantum Information Center of Gdańsk, 81-824 Sopot, Poland and Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland
| | - P Horodecki
- National Quantum Information Center of Gdańsk, 81-824 Sopot, Poland and Faculty of Applied Physics and Mathematics, Technical University of Gdańsk, 80-233 Gdańsk, Poland
| | - R Horodecki
- National Quantum Information Center of Gdańsk, 81-824 Sopot, Poland and Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland
| | - P Joshi
- National Quantum Information Center of Gdańsk, 81-824 Sopot, Poland and Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland
| | - W Kłobus
- Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland
| | - A Wójcik
- Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland
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17
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Zu C, Wang YX, Deng DL, Chang XY, Liu K, Hou PY, Yang HX, Duan LM. State-independent experimental test of quantum contextuality in an indivisible system. PHYSICAL REVIEW LETTERS 2012; 109:150401. [PMID: 23102277 DOI: 10.1103/physrevlett.109.150401] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2012] [Indexed: 06/01/2023]
Abstract
We report the first state-independent experimental test of quantum contextuality on a single photonic qutrit (three-dimensional system), based on a recent theoretical proposal [Phys. Rev. Lett. 108, 030402 (2012)]. Our experiment spotlights quantum contextuality in its most basic form, in a way that is independent of either the state or the tensor product structure of the system.
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Affiliation(s)
- C Zu
- Center for Quantum Information, IIIS, Tsinghua University, Beijing, China
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18
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Schlosshauer M, Fine A. Implications of the Pusey-Barrett-Rudolph quantum no-go theorem. PHYSICAL REVIEW LETTERS 2012; 108:260404. [PMID: 23004942 DOI: 10.1103/physrevlett.108.260404] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2012] [Indexed: 06/01/2023]
Abstract
Pusey, Barrett, and Rudolph introduce a new no-go theorem for hidden-variables models of quantum theory. We make precise the class of models targeted and construct equivalent models that evade the theorem. The theorem requires assumptions for models of composite systems, which we examine, determining compactness as the weakest assumption needed. On that basis, we demonstrate results of the Bell-Kochen-Specker theorem. Given compactness and the relevant class of models, the theorem can be seen as showing that some measurements on composite systems must have built-in inefficiencies, complicating its testing.
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Affiliation(s)
- Maximilian Schlosshauer
- Department of Physics, University of Portland, 5000 North Willamette Boulevard, Portland, Oregon 97203, USA
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19
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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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20
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Lapkiewicz R, Li P, Schaeff C, Langford NK, Ramelow S, Wieśniak M, Zeilinger A. Experimental non-classicality of an indivisible quantum system. Nature 2011; 474:490-3. [PMID: 21697945 DOI: 10.1038/nature10119] [Citation(s) in RCA: 61] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2011] [Accepted: 04/15/2011] [Indexed: 11/09/2022]
Abstract
In contrast to classical physics, quantum theory demands that not all properties can be simultaneously well defined; the Heisenberg uncertainty principle is a manifestation of this fact. Alternatives have been explored--notably theories relying on joint probability distributions or non-contextual hidden-variable models, in which the properties of a system are defined independently of their own measurement and any other measurements that are made. Various deep theoretical results imply that such theories are in conflict with quantum mechanics. Simpler cases demonstrating this conflict have been found and tested experimentally with pairs of quantum bits (qubits). Recently, an inequality satisfied by non-contextual hidden-variable models and violated by quantum mechanics for all states of two qubits was introduced and tested experimentally. A single three-state system (a qutrit) is the simplest system in which such a contradiction is possible; moreover, the contradiction cannot result from entanglement between subsystems, because such a three-state system is indivisible. Here we report an experiment with single photonic qutrits which provides evidence that no joint probability distribution describing the outcomes of all possible measurements--and, therefore, no non-contextual theory--can exist. Specifically, we observe a violation of the Bell-type inequality found by Klyachko, Can, Binicioğlu and Shumovsky. Our results illustrate a deep incompatibility between quantum mechanics and classical physics that cannot in any way result from entanglement.
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Affiliation(s)
- Radek Lapkiewicz
- Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria
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21
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Moussa O, Ryan CA, Cory DG, Laflamme R. Testing contextuality on quantum ensembles with one clean qubit. PHYSICAL REVIEW LETTERS 2010; 104:160501. [PMID: 20482033 DOI: 10.1103/physrevlett.104.160501] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2009] [Indexed: 05/29/2023]
Abstract
We present a protocol to evaluate the expectation value of the correlations of measurement outcomes for ensembles of quantum systems, and use it to experimentally demonstrate--under an assumption of fair sampling--the violation of an inequality that is satisfied by any noncontextual hidden-variables theory. The experiment is performed on an ensemble of molecular nuclear spins in the solid state, using established nuclear magnetic resonance techniques for quantum-information processing.
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Affiliation(s)
- Osama Moussa
- Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, N2L3G1, Canada.
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22
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Amselem E, Rådmark M, Bourennane M, Cabello A. State-independent quantum contextuality with single photons. PHYSICAL REVIEW LETTERS 2009; 103:160405. [PMID: 19905677 DOI: 10.1103/physrevlett.103.160405] [Citation(s) in RCA: 53] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2009] [Indexed: 05/28/2023]
Abstract
We present an experimental state-independent violation of an inequality for noncontextual theories on single particles. We show that 20 different single-photon states violate an inequality which involves correlations between results of sequential compatible measurements by at least 419 standard deviations. Our results show that, for any physical system, even for a single system, and independent of its state, there is a universal set of tests whose results do not admit a noncontextual interpretation. This sheds new light on the role of quantum mechanics in quantum information processing.
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Affiliation(s)
- Elias Amselem
- Department of Physics, Stockholm University, S-10691, Stockholm, Sweden
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25
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Cabello A. Experimentally testable state-independent quantum contextuality. PHYSICAL REVIEW LETTERS 2008; 101:210401. [PMID: 19113394 DOI: 10.1103/physrevlett.101.210401] [Citation(s) in RCA: 67] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2008] [Indexed: 05/27/2023]
Abstract
We show that there are Bell-type inequalities for noncontextual theories that are violated by any quantum state. One of these inequalities between the correlations of compatible measurements is particularly suitable for testing this state-independent violation in an experiment.
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Affiliation(s)
- Adán Cabello
- Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain.
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26
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Hasegawa Y, Loidl R, Badurek G, Baron M, Rauch H. Quantum contextuality in a single-neutron optical experiment. PHYSICAL REVIEW LETTERS 2006; 97:230401. [PMID: 17280181 DOI: 10.1103/physrevlett.97.230401] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2005] [Indexed: 05/13/2023]
Abstract
An experimental demonstration of quantum contextuality with neutrons is presented, which intended to exhibit a Kochen-Specker-like phenomenon. Since no perfect correlation is expected in practical experiments, inequalities are derived to distinguish quantitatively the obtained results from predictions by a noncontextual hidden variable theory. Experiments were accomplished with the use of a neutron interferometer combined with spinor manipulation devices. The results clearly violate the prediction of noncontextual theories.
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Affiliation(s)
- Yuji Hasegawa
- Atominstitut der Osterreichischen Universitäten, Stadionallee 2, A-1020 Vienna, Austria
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