Conditional Mutual Information and Quantum Steering. (arXiv:1612.03875v2 [quant-ph] UPDATED)

Quantum steering has recently been formalized in the framework of a resource
theory of steering, and several quantifiers have already been introduced. Here,
we propose an information-theoretic quantifier for steering called intrinsic
steerability, which uses conditional mutual information to measure the
deviation of a given assemblage from one having a local hidden-state model. We
thus relate conditional mutual information to quantum steering and introduce
monotones that satisfy certain desirable properties. The idea behind the
quantifier is to suppress the correlations that can be explained by an
inaccessible quantum system and then quantify the remaining intrinsic
correlations. A variant of the intrinsic steerability finds operational meaning
as the classical communication cost of sending the measurement choice and
outcome to an eavesdropper who possesses a purifying system of the underlying
bipartite quantum state that is being measured.

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