ENTROPIC CHARACTERIZATION OF QUANTUM OPERATIONS

  • WOJCIECH ROGA
    Instytut Fizyki im. Smoluchowskiego, Uniwersytet Jagielloński, PL-30-059 Kraków, Poland
  • KAROL ŻYCZKOWSKI
    Instytut Fizyki im. Smoluchowskiego, Uniwersytet Jagielloński, PL-30-059 Kraków, Poland
  • MARK FANNES
    Instituut voor Theoretische Fysica, Universiteit Leuven, B-3001 Leuven, Belgium

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<jats:p>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 Φ<jats:sub>1</jats:sub>acting on a finite dimensional system, there exists a class of channels Φ<jats:sub>2</jats:sub>sufficiently close to a unitary map such that additivity of minimal output entropy for Ψ<jats:sub>1</jats:sub>⊗ Ψ<jats:sub>2</jats:sub>holds.</jats:p>

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