Entropic characterization of quantum operations

Details Entropic characterization of quantum operations Entropic characterization of quantum operations

2011-01-21

arxiv.org/abs/1101.4105v1

International Journal of Quantum Information, 9, pp. 1031 (2011)

Physics

Quantum Physics

21 pages, 4 figures

Scientific paper

We investigate decoherence induced by a quantum channel in terms of minimal output entropy and of map entropy. The latter is the von Neumann entropy of the Jamiolkowski state of the channel. Both quantities admit q-Renyi versions. We prove additivity of the map entropy for all q. For the case q = 2, we show that the depolarizing channel has the smallest map entropy among all channels with a given minimal output Renyi entropy of order two. This allows us to characterize pairs of channels such that the output entropy of their tensor product acting on a maximally entangled input state is larger than the sum of the minimal output entropies of the individual channels. We conjecture that for any channel {\Phi}1 acting on a finite dimensional system there exists a class of channels {\Phi}2 sufficiently close to a unitary map such that additivity of minimal output entropy for {\Psi}1 x {\Psi}2 holds.

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