Bell's inequality for a single spin-1/2 particle and quantum contextuality

Basu, Sayandeb; Bandyopadhyay, Somshubhro; Kar, Guruprasad; Home, Dipankar

doi:10.1016/s0375-9601(00)00747-7

Cited by 79 publications

(99 citation statements)

References 16 publications

(23 reference statements)

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“…It is thus quite hard to pin down what exactly a purported experimental test of contextuality proves, or could prove, that we do not know already. In our opinion, this key point is not adequately addressed in the papers under discussion (Cabello & García-Alcaine, 1998;Simon et al, 2000;Basu et al, 2001;Huang et al, 2003;Hasegawa et al, 2003).…”

Section: Querying the Scope Of The Ks Theoremmentioning

confidence: 94%

“…The arguments set out by Meyer, Kent, and Clifton and Kent (MKC) have evoked some controversy (see, e.g., Mermin, 1999;Cabello, 1999;Basu et al, 2001;Simon et al, 2001;Larsson, 2002;Appleby, 2000Appleby, , 2001Appleby, , 2002Appleby, , 2003Havlicek et al, 2001;Cabello, 2002;Breuer, 2002) and even a parodyPeres (2003). Among other things, it has been suggested (Cabello, 2002) that the CK models do not in fact reproduce correctly the predictions of quantum mechanics, even when finite precision is taken into account.…”

Section: Querying the Scope Of The Ks Theoremmentioning

confidence: 99%

“…Quite a few experiments purporting to test contextuality have recently been proposed (Cabello & García-Alcaine, 1998;Simon et al, 2000;Basu et al, 2001) and performed (Huang et al, 2003;Hasegawa et al, 2003). Several authors have suggested an analogy between these purported experimental tests of contextuality and Bell experiments testing local causality.…”

Section: Querying the Scope Of The Ks Theoremmentioning

confidence: 99%

“…The CK models then show us that even if it is assumed that the operation of each experimental device is well described by the Hilbert space formalism, a non-contextual, classical simulation of the experiment is possible. 10 We make a brief remark about the experiment of Hasegawa et al (2003), and the proposal of Basu et al (2001). In both cases, an inequality is derived, formally identical to the Clauser-Horne-Shimony-Holt inequality (Clauser et al, 1969), that concerns the spin and path degrees of freedom of a single neutron.…”

Section: Experiments and Finite Precisionmentioning

confidence: 99%

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Non-contextuality, finite precision measurement and the Kochen–Specker theorem

Barrett

Kent

2004

Studies in History and Philosophy of Science Part B: Studies in

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Meyer originally raised the question of whether non-contextual hidden variable models can, despite the Kochen-Specker theorem, simulate the predictions of quantum mechanics to within any fixed finite experimental precision (Meyer, D. 1999. Phys. Rev. Lett., 83, 3751-3754). Meyer's result was extended by Kent (Kent, A. 1999. Phys. Rev. Lett., 83, 3755-3757). Clifton and Kent later presented constructions of non-contextual hidden variable theories which, they argued, indeed simulate quantum mechanics in this way (Clifton, R and Kent, A. 2000. Proc. Roy. Soc. Lond. A, 456, 2101-2114.These arguments have evoked some controversy. Among other things, it has been suggested that the Clifton-Kent models do not in fact reproduce correctly the predictions of quantum mechanics, even when finite precision is taken into account. It has also been suggested that careful analysis of the notion of contextuality in the context of finite precision measurement motivates definitions which imply that the Clifton-Kent 1 models are in fact contextual. Several critics have also argued that the issue can be definitively resolved by experimental tests of the KochenSpecker theorem or experimental demonstrations of the contextuality of Nature.One aim of this paper is to respond to and rebut criticisms of the Meyer-Clifton-Kent papers. We thus elaborate in a little more detail how the Clifton-Kent models can reproduce the predictions of quantum mechanics to arbitrary precision. We analyse in more detail the relationship between classicality, finite precision measurement and contextuality, and defend the claims that the Clifton-Kent models are both essentially classical and non-contextual. We also examine in more detail the senses in which a theory can be said to be contextual or non-contextual, and in which an experiment can be said to provide evidence on the point. In particular, we criticise the suggestion that a decisive experimental verification of contextuality is possible, arguing that the idea rests on a conceptual confusion.

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Section: Querying the Scope Of The Ks Theoremmentioning

confidence: 94%

Section: Querying the Scope Of The Ks Theoremmentioning

confidence: 99%

Section: Querying the Scope Of The Ks Theoremmentioning

confidence: 99%

Section: Experiments and Finite Precisionmentioning

confidence: 99%

See 2 more Smart Citations

Non-contextuality, finite precision measurement and the Kochen–Specker theorem

Barrett

Kent

2004

Studies in History and Philosophy of Science Part B: Studies in

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“…In this case it is physically rather contextuality than nonlocality which is tested experimentally [118,112,119,120].…”

Section: Geometric Phase -Entanglementmentioning

confidence: 99%

Entanglement, Bell Inequalities and Decoherence in Particle Physics

Bertlmann¹

Quantum Coherence

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We demonstrate the relevance of entanglement, Bell inequalities and decoherence in particle physics. In particular, we study in detail the features of the "strange" K 0K 0 system as an example of entangled meson-antimeson systems. The analogies and differences to entangled spin-1 2 or photon systems are worked out, the effects of a unitary time evolution of the meson system is demonstrated explicitly. After an introduction we present several types of Bell inequalities and show a remarkable connection to CP violation. We investigate the stability of entangled quantum systems pursuing the question of how possible decoherence might arise due to the interaction of the system with its "environment". The decoherence is strikingly connected to the entanglement loss of common entanglement measures. Finally, some outlook of the field is presented.

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Single‐Particle Entanglement

et al. 2020

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This review is about single-particle entanglement. Entanglement occurs when the state of a quantum system with at least two degrees of freedom has a particular non-separable form. In the case of single-particle entanglement, this quantum correlation is shared by the same particle being it a photon, a neutron, an ion, or an atom. Here, the basics of quantum entanglement are discussed focusing on the case it is related to the degrees of freedom of a single particle. It is discussed how the violation of peculiar inequalities in this context rules out any realistic non-contextual hidden variable theory alternative to quantum mechanics. Moreover, experiments that demonstrate single-particle entanglement for photons, neutrons, and atoms are discussed. Finally, the applications of single-particle entanglement as a resource for quantum information are discussed and specifically quantum key distribution is detailed, where the use of single-particle entangled photons allows to improve the security of the BB84 protocol.

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Bell's inequality for a single spin-1/2 particle and quantum contextuality

Cited by 79 publications

References 16 publications

Non-contextuality, finite precision measurement and the Kochen–Specker theorem

Non-contextuality, finite precision measurement and the Kochen–Specker theorem

Entanglement, Bell Inequalities and Decoherence in Particle Physics

Single‐Particle Entanglement

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