Discriminating three mirror-symmetric states with a restricted contextual advantage

Mukherjee, Sumit; Naonit, Shivam; Pan, A. K.

doi:10.1103/physreva.106.012216

Cited by 9 publications

(1 citation statement)

References 23 publications

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“…Later, Spekkens [24] generalized the notion of non-contextuality for arbitrary operational theories and extended the formulation to preparation, transformation and unsharp measurement. In recent times, the quantum preparation contextuality has been extensively studied [25][26][27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Sharing preparation contextuality in a Bell experiment by an arbitrary pair of sequential observers

Kumari

Pan

2023

Phys. Rev. A

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Based on the quantum violation of bipartite Bell inequality, it has been demonstrated that the sharing of nonlocality can be demonstrated for at most two sequential observers at one end and at most one-pair of observers at both ends. In this work, we study the sharing of non-locality and preparation contextuality based on a bipartite Bell inequality, involving arbitrary n measurements by one party and 2 n−1 measurements by other party. Such a Bell inequality has two bounds, the local bound and the preparation non-contextual bound, which is smaller than the local bound. We show that while non-locality can be shared only by first pair of the sequential observers, the preparation contextuality can be shared by arbitrary pair of independent sequential observers at both ends.

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Section: Introductionmentioning

confidence: 99%

Sharing preparation contextuality in a Bell experiment by an arbitrary pair of sequential observers

Kumari

Pan

2023

Phys. Rev. A

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Demonstration of $$\mathcal{P}\mathcal{T}$$-symmetric quantum state discrimination

Wang,

Zhu,

Xiao

et al. 2024

Quantum Inf Process

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Constrained measurement incompatibility from generalised contextuality of steered preparation

Mukherjee,

Pan

2024

New J. Phys.

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In a bipartite Bell scenario involving two local measurements per party and two outcome per measurement, the measurement incompatibility in one wing is both necessary and sufficient to reveal the nonlocality. However, such a one-to-one correspondence fails when one of the observers performs more than two measurements. In such a scenario, the measurement incompatibility is necessary but not sufficient to reveal the nonlocality. In this work, within the formalism of general probabilistic theory (GPT), we demonstrate that unlike the nonlocality, the incompatibility of $N$ arbitrary measurements in one wing is both necessary and sufficient for revealing the generalised contextuality for the sub-system in the other wing. Further, we formulate an elegant form of inequality for any GPT that is necessary for $N$-wise compatibility of $N$ arbitrary observables. Moreover, we argue that any theory that violates the proposed inequality possess a degree of incompatibility that can be quantified through the amount of violation. We claim that it is the generalised contextuality that provides a restriction to the allowed degree of measurement incompatibility of any viable theory of nature and thereby super-select the quantum theory. Finally, we discuss the geometrical implications of our results.

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Discriminating three mirror-symmetric states with a restricted contextual advantage

Cited by 9 publications

References 23 publications

Sharing preparation contextuality in a Bell experiment by an arbitrary pair of sequential observers

Sharing preparation contextuality in a Bell experiment by an arbitrary pair of sequential observers

Demonstration of $$\mathcal{P}\mathcal{T}$$-symmetric quantum state discrimination

Constrained measurement incompatibility from generalised contextuality of steered preparation

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