Volume 104, Number 6, December 2013
|Number of page(s)||6|
|Published online||27 January 2014|
Unification of Bell, Leggett-Garg and Kochen-Specker inequalities: Hybrid spatio-temporal inequalities
1 Indian Institute of Science Education and Research - Pune-411008, India
2 Poornaprajna Institute of Scientific Research - Sadashivnagar, Bengaluru-560080, India
3 Raman Research Institute - Sadashivnagar, Bengaluru-560060, India
4 CAPSS, Bose Institute - Kolkata-700 091, India
Received: 26 August 2013
Accepted: 2 January 2014
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.
PACS: 03.65.Ta – Foundations of quantum mechanics; measurement theory / 03.65.Ud – Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.) / 42.50.Xa – Optical tests of quantum theory
© EPLA, 2013
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.