1
|
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.
Collapse
|
2
|
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.
Collapse
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
| |
Collapse
|
3
|
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.
Collapse
|
4
|
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.
Collapse
|
5
|
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.
Collapse
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
| |
Collapse
|
6
|
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.
Collapse
|
7
|
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.
Collapse
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:
| | | |
Collapse
|
8
|
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.
Collapse
|
9
|
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.
Collapse
Affiliation(s)
- Maximilian Schlosshauer
- Department of Physics, University of Portland, 5000 North Willamette Boulevard, Portland, Oregon 97203, USA
| | | |
Collapse
|
10
|
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.
Collapse
Affiliation(s)
- Osama Moussa
- Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, N2L3G1, Canada.
| | | | | | | |
Collapse
|
11
|
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.
Collapse
Affiliation(s)
- Elias Amselem
- Department of Physics, Stockholm University, S-10691, Stockholm, Sweden
| | | | | | | |
Collapse
|
12
|
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]
|
13
|
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.
Collapse
Affiliation(s)
- Adán Cabello
- Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain.
| |
Collapse
|
14
|
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.
Collapse
Affiliation(s)
- Yuji Hasegawa
- Atominstitut der Osterreichischen Universitäten, Stadionallee 2, A-1020 Vienna, Austria
| | | | | | | | | |
Collapse
|
15
|
Huang YF, Li CF, Zhang YS, Pan JW, Guo GC. Experimental test of the Kochen-Specker theorem with single photons. PHYSICAL REVIEW LETTERS 2003; 90:250401. [PMID: 12857117 DOI: 10.1103/physrevlett.90.250401] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2002] [Revised: 04/07/2003] [Indexed: 05/24/2023]
Abstract
Using the spontaneous parametric down-conversion process in a type-I phase matching beta-barium-borate crystal as a single photon source, we perform an all-or-nothing-type Kochen-Specker experiment proposed by Simon et al. [Phys. Rev. Lett. 85, 1783 (2000)]] to verify whether noncontextual hidden variables or quantum mechanics is right. The results strongly agree with quantum mechanics.
Collapse
Affiliation(s)
- Yun-Feng Huang
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei, Anhui, People's Republic of China, 230026.
| | | | | | | | | |
Collapse
|
16
|
Chen ZB, Pan JW, Zhang YD, Brukner C, Zeilinger A. All-versus-nothing violation of local realism for two entangled photons. PHYSICAL REVIEW LETTERS 2003; 90:160408. [PMID: 12731967 DOI: 10.1103/physrevlett.90.160408] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2002] [Indexed: 05/24/2023]
Abstract
It is shown that the Greenberger-Horne-Zeilinger theorem can be generalized to the case with only two entangled particles. The reasoning makes use of two photons which are maximally entangled both in polarization and in spatial degrees of freedom. In contrast to Cabello's argument of "all versus nothing" nonlocality with four photons [Phys. Rev. Lett. 87, 010403 (2001)]], our proposal to test the theorem can be implemented with linear optics and thus is well within the reach of current experimental technology.
Collapse
Affiliation(s)
- Zeng-Bing Chen
- Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230027, China
| | | | | | | | | |
Collapse
|
17
|
Breuer T. Kochen-Specker theorem for finite precision spin-one measurements. PHYSICAL REVIEW LETTERS 2002; 88:240402. [PMID: 12059287 DOI: 10.1103/physrevlett.88.240402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2001] [Indexed: 05/23/2023]
Abstract
Unsharp spin-one observables arise from the fact that a residual uncertainty about the actual orientation of the measurement device remains. If the uncertainty is below a certain level, and if the distribution of measurement errors is covariant under rotations, a Kochen-Specker theorem for the unsharp spin observables follows: There are finite sets of directions such that not all the unsharp spin observables in these directions can consistently be assigned approximate truth values in a noncontextual way.
Collapse
Affiliation(s)
- Thomas Breuer
- Department of Computer Science, FH Vorarlberg, Achstrasse 1, A-6850 Dornbirn, Austria.
| |
Collapse
|
18
|
Cabello A. "All versus nothing" inseparability for two observers. PHYSICAL REVIEW LETTERS 2001; 87:010403. [PMID: 11461451 DOI: 10.1103/physrevlett.87.010403] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2001] [Indexed: 05/23/2023]
Abstract
A recent proof of Bell's theorem without inequalities [A. Cabello, Phys. Rev. Lett. 86, 1911 (2001)] is formulated as a Greenberger-Horne-Zeilinger-type proof involving just two observers. On one hand, this new approach allows us to derive an experimentally testable Bell inequality which is violated by quantum mechanics. On the other hand, it leads to a new state-independent proof of the Kochen-Specker theorem and provides a wider perspective on the relations between the major proofs of no hidden variables.
Collapse
Affiliation(s)
- A Cabello
- Departamento de Física Aplicada II, Universidad de Sevilla, 41012 Sevilla, Spain. adan.cica.es
| |
Collapse
|
19
|
Simon C, Brukner C, Zeilinger A. Hidden-variable theorems for real experiments. PHYSICAL REVIEW LETTERS 2001; 86:4427-4430. [PMID: 11384251 DOI: 10.1103/physrevlett.86.4427] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2000] [Revised: 01/29/2001] [Indexed: 05/23/2023]
Abstract
It has recently been questioned whether the Kochen-Specker theorem is relevant to real experiments, which by necessity only have finite precision. We give an affirmative answer to this question by showing how to derive hidden-variable theorems that apply to real experiments, so that noncontextual hidden variables can indeed be experimentally disproved. The essential point is that for the derivation of hidden-variable theorems one does not have to know which observables are really measured by the apparatus. Predictions can be derived for observables that are defined in an entirely operational way.
Collapse
Affiliation(s)
- C Simon
- Institut für Experimentalphysik, Universität Wien, Boltzmanngasse 5, A-1090 Wien, Austria
| | | | | |
Collapse
|