On lower semicontinuity of the quantum conditional mutual information
and its corollaries
- URL: http://arxiv.org/abs/2001.08691v1
- Date: Thu, 23 Jan 2020 17:34:54 GMT
- Title: On lower semicontinuity of the quantum conditional mutual information
and its corollaries
- Authors: M.E. Shirokov
- Abstract summary: We show that the recently established lower semicontinuity of the quantum conditional mutual information implies (in fact) the lower semicontinuity of the loss of the quantum (conditional) mutual information under local channels.
New continuity conditions for the quantum mutual information and for the squashed entanglement in both bipartite and multipartite infinite-dimensional systems are obtained.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: It is well known that the quantum mutual information and its conditional
version do not increase under local channels. I this paper we show that the
recently established lower semicontinuity of the quantum conditional mutual
information implies (in fact, is equivalent to) the lower semicontinuity of the
loss of the quantum (conditional) mutual information under local channels
considered as a function on the Cartesian product of the set of all states of a
composite system and the sets of all local channels (equipped with the strong
convergence).
Some applications of this property are considered. New continuity conditions
for the quantum mutual information and for the squashed entanglement in both
bipartite and multipartite infinite-dimensional systems are obtained. It is
proved, in particular, that the multipartite squashed entanglement of any
countably-non-decomposable separable state with finite marginal entropies is
equal to zero.
Special continuity properties of the information gain of a quantum
measurement with and without quantum side information are established that can
be treated as robustness (stability) of these quantities w.r.t. perturbation of
the measurement and the measured state.
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