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arXiv · 1308.0270

Unification of Bell, Leggett-Garg and Kochen-Specker inequalities: A hybrid spatio-temporal inequality

Siddhartha Das·S. Aravinda·R. Srikanth·Dipankar Home
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Abstract

The Bell-type (spatial), Kochen-Specker (contextuality) or Leggett-Garg (temporal) inequalities are based on classically plausible but otherwise quite distinct assumptions. For any of these inequalities, satisfaction is equivalent to a joint probability distribution for all observables in the experiment. This implies a joint distribution for all pairs of observables, and is indifferent to whether or not they commute in the theory. This indifference underpins a unification of the above inequalities into a general framework of correlation inequalities. When the physical scenario is such that the correlated pairs are all compatible, the resulting correlation is non-signaling, which may be local or multi-particle, corresponding to contextuality or Bell-type inequalities. If the pairs are incompatible, the resulting correlation corresponds to Leggett-Garg (LG) inequalities. That quantum mechanics (QM) violates all these inequalities suggests a close connection between the local, spatial and temporal properties of the theory. As a concrete manifestation of the unification, we extend the method due to Roy and Singh (J. Phys. A, 11, L167 (1978)) to derive and study a new class of hybrid spatio-temporal inequalities, where the correlated pairs in the experiment are both compatible or incompatible. The implications for cryptography and monogamy inequalities of the unification are briefly touched upon.

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Siddhartha Das, S. Aravinda, R. Srikanth, Dipankar Home. 2014-02-19. Unification of Bell, Leggett-Garg and Kochen-Specker inequalities: A hybrid spatio-temporal inequality. https://doi.org/10.1209/0295-5075%2F104%2F60006

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