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Biased causal inseparable game | | Some Sankar Bhattacharya
; Manik Banik
; | | Date: |
9 Sep 2015 | | Abstract: | Here we study the emph{causal inseparable} game introduced in
[href{this http URL}{Nat.
Commun. {f3}, 1092 (2012)}], but it’s biased version. Two separated parties,
Alice and Bob, generate biased bits (say input bit) in their respective local
laboratories. Bob generates another biased bit (say decision bit) which
determines their goal: whether Alice has to guess Bob’s bit or vice-verse.
Under the assumption that events are ordered with respect to some global causal
relation, we show that the success probability of this biased causal game is
upper bounded, giving rise to emph{biased causal inequality} (BCI). In the
emph{process matrix} formalism, which is locally in agreement with quantum
physics but assume no global causal order, we show that there exist
emph{inseparable} process matrices that violate the BCI for arbitrary bias in
the decision bit. In such scenario we also derive the maximal violation of the
BCI under local operations involving traceless binary observables. However, for
biased input bit this is not the case. There is a threshold bias beyond which,
we find that no valid qubit process matrix can violate the causal inequality
under emph{measurement-repreparation} type operation and we believe this to
hold even for general process matrix under general local operations involving
traceless binary observables. | | Source: | arXiv, 1509.2721 | | Services: | Forum | Review | PDF | Favorites | |
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