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Title: | Unification of Bell, Leggett-Garg and kochen-specker inequalities: Hybrid spatio-temporal inequalities. |
Authors: | Das, Siddhartha Aravinda, S. Srikanth, R. Home, D. |
Issue Date: | Dec-2013 |
Publisher: | IOP Publishing Ltd. |
Citation: | Europhysics Letters, 2013, Vol. 104, p.60006 |
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 nonsignaling, 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 (1978) L167) 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. |
Description: | Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations) |
URI: | http://hdl.handle.net/2289/5879 |
ISSN: | 0295-5075 1286-4854 (Online). |
Alternative Location: | http://arxiv.org/abs/1308.0270 http://dx.doi.org/10.1209/0295-5075/104/60006 |
Copyright: | 2013 EPLA |
Appears in Collections: | Research Papers (LAMP) |
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