Compatibility and noncontextuality for sequential measurements

Gühne, Otfried; Kleinmann, Matthias; Cabello, Adán; Larsson, Jan‐Åke; Kirchmair, Gerhard; Zähringer, F.; Gerritsma, R.; Roos, C. F.

doi:10.1103/physreva.81.022121

Cited by 104 publications

(165 citation statements)

References 58 publications

(121 reference statements)

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“…It should be remarked how the falsification of a KS inequality faces rather challenging hurdles related to the feasibility of tests that, while are capable of maintaining state independence, also guarantee that all the necessary observables are measured in a context-independent way [7]. Cabello [8] has recently addressed these points by providing inequalities that strictly meet the criteria mentioned above.…”

Section: Introductionmentioning

confidence: 99%

Testing quantum contextuality of continuous-variable states

2011

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We investigate the violation of non-contextuality by a class of continuous variable states, including variations of entangled coherent states (ECS's) and a two-mode continuous superposition of coherent states. We generalise the Kochen-Specker (KS) inequality discussed in A. Cabello, Phys. Rev. Lett. 101, 210401 (2008) by using effective bidimensional observables implemented through physical operations acting on continuous variable states, in a way similar to an approach to the falsification of Bell-CHSH inequalities put forward recently. We test for state-independent violation of KS inequalities under variable degrees of state entanglement and mixedness. We then demonstrate theoretically the violation of a KS inequality for any two-mode state by using pseudo-spin observables and a generalized quasi-probability function.

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Section: Introductionmentioning

confidence: 99%

Testing quantum contextuality of continuous-variable states

2011

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“…It adopts two forms: (i) that there is no operational definition of compatibility, and (ii) that there is no experimental way to guarantee that the sequential measurements are perfectly compatible-the so-called compatibility loophole [15]. However, there is an operational definition of compatibility [16]; the problem lies in experimentally testing it, since it is difficult to implement the sharp repeatable quantum measurements assumed in the textbooks.…”

Section: Introductionmentioning

confidence: 99%

Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality

et al. 2012

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Recent experiments have demonstrated ququart state-independent quantum contextuality and qutrit state-dependent quantum contextuality. So far, the most basic form of quantum contextuality pointed out by Kochen and Specker, and Bell, has eluded experimental confirmation. Here we present an experimentally feasible test to observe qutrit state-independent quantum contextuality using single photons in a three-path setup. In addition, we show that if the same measurements are performed on two entangled qutrits, rather than sequentially on the same qutrit, then the noncontextual inequality becomes a Bell inequality. We show that this connection also applies to other recently introduced noncontextual inequalities.

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“…However, none of these experiments on SIQC is free of the compatibility loophole [11]. With the imperfections in the sequential measurements of these experiments we would need an inequality tolerating ε ≈ 0.48.…”

Section: Resistance To Imperfectionsmentioning

confidence: 99%

“…This correction takes the form b → b ′ = b + N i=1 φ i , where φ i > 0 can be obtained from additional experiments [11].…”

Section: Resistance To Imperfectionsmentioning

confidence: 99%

Proposed test of macroscopic quantum contextuality

Cabello

2010

Phys. Rev. A

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We show that, for any system with a number of levels which can be identified with n qubits, there is an inequality for the correlations between three compatible dichotomic measurements which must be satisfied by any noncontextual theory, but is violated by any quantum state. Remarkably, the violation grows exponentially with n, and the tolerated error per correlation also increases with n, showing that state-independent quantum contextuality is experimentally observable in complex systems.

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Compatibility and noncontextuality for sequential measurements

Cited by 104 publications

References 58 publications

Testing quantum contextuality of continuous-variable states

Testing quantum contextuality of continuous-variable states

Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality

Proposed test of macroscopic quantum contextuality

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