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ENTROPIC CHARACTERIZATION OF QUANTUM OPERATIONS

WOJCIECH ROGA

Instytut Fizyki im. Smoluchowskiego, Uniwersytet Jagielloński, PL-30-059 Kraków, Poland

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KAROL ŻYCZKOWSKI

Instytut Fizyki im. Smoluchowskiego, Uniwersytet Jagielloński, PL-30-059 Kraków, Poland

Centrum Fizyki Teoretycznej, Polska Akademia Nauk, PL-02-668 Warszawa, Poland

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MARK FANNES

Instituut voor Theoretische Fysica, Universiteit Leuven, B-3001 Leuven, Belgium

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https://doi.org/10.1142/S0219749911007794Cited by:20 (Source: Crossref)

Abstract

We investigate decoherence induced by a quantum channel in terms of minimal output entropy and map entropy. The latter is the von Neumann entropy of the Jamiołkowski 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 Φ₁ acting on a finite dimensional system, there exists a class of channels Φ₂ sufficiently close to a unitary map such that additivity of minimal output entropy for Ψ₁ ⊗ Ψ₂ holds.

Keywords:

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