arXiv:quant-ph/0606040

On the additivity conjecture for the Weyl channels being covariant with respect to the maximum commutative group of unitaries

Grigori Gennadievich Amosov

Published Jun 6, 2006• 0 citations

Abstract

Some new examples of quantum channels for which the infimum of the output entropy is additive under taking a tensor product of channels are given.

DOI: 10.48550/arxiv.quant-ph/0606040

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arXiv:quant-ph/0606040

On the additivity conjecture for the Weyl channels being covariant with respect to the maximum commutative group of unitaries

Grigori Gennadievich Amosov

Published Jun 6, 2006• 0 citations

arXiv HTML PDF

Abstract

Some new examples of quantum channels for which the infimum of the output entropy is additive under taking a tensor product of channels are given.

DOI: 10.48550/arxiv.quant-ph/0606040

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Jun 6, 20060 citations

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International Journal of Quantum InformationDec 16, 200441 citations

d=2

our approach allows to prove the additivity conjecture for the Holevo-Schumacher-Westmoreland bound. Our method is based upon using the decreasing property of the relative entropy. Earlier we had shown that the method gives the proof of the additivity conjecture for the quantum depolarizing channel in any dimension.

\\Phi (x)=\\sum \\limits _{m=0}^{2}(r_{m}W_{m,0}xW_{m,0}^{*}+p_{1}W_{m,1}xW_{m,1}^{*}+p_{2}W_{m,2}x W_{m,2}^{*})

. Here

x

runs the set of states

\\sigma (H)

in the Hilbert space

H, dimH=3,

W_{m,n}

are the Weyl operators satisfying the relation

W_{m,n}W_{m',n'}=e^{\\frac {2\\pi i(m'n-mn')}{3}}W_{m+m',n+n'}, 0\\le m,n\\le 2,

and

0\\le r_{m},p_{1},p_{2}\\le 1, \\sum \\limits _{m=0}^{2}r_{m}+3(p_{1}+p_{2})=1

. This class includes the quantum depolarizing channel as well as a number of the other channels being covariant with respect to the maximum commutative group of unitaries.