arXiv:0707.1722 · Journal of Mathematical Physics

Multiplicativity of the maximal output 2-norm for depolarized Werner-Holevo channels

Spyridon Michalakis

Published Dec 1, 2007• 9 citations

Abstract

We study the multiplicativity of the output 2-norm for depolarized Werner-Holevo channels and show that multiplicativity holds for a product of two identical channels in this class. Moreover, it is shown that the depolarized Werner-Holevo channels do not satisfy the entrywise positivity condition introduced by King and Ruskai (e-print quant-ph∕0909181v2; e-print quant-ph∕0981026v1), which suggests that the main result is nontrivial.

DOI: 10.1063/1.2818737

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arXiv:0707.1722 · Journal of Mathematical Physics

Multiplicativity of the maximal output 2-norm for depolarized Werner-Holevo channels

Spyridon Michalakis

Published Dec 1, 2007• 9 citations

arXiv HTML PDF

Abstract

DOI: 10.1063/1.2818737

Related papers

Multiplicativity of Maximal p-Norms in Werner-Holevo channels for $1 \le p \le 2$ Multiplicativity of Maximal p-Norms in Werner-Holevo channels for $1 \le p \le 2$

Nilanjana Datta

Recently, King and Ruskai [1] conjectured that the maximal p-norm of the Werner--Holevo channel is multiplicative for all $1\le p \le 2$ . In this paper we prove this conjecture. Our proof relies on certain convexity and monotonicity properties of the p--norm.Recently, King and Ruskai [1] conjectured that the maximal p-norm of the Werner--Holevo channel is multiplicative for all $1\le p \le 2$. In this paper we prove this conjecture. Our proof relies on certain convexity and monotonicity properties of the p--norm.

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An application of decomposable maps in proving multiplicativity of low dimensional maps

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Multiplicativity of Maximal p-Norms in Werner-Holevo channels for

1 \le p \le 2

Recently, King and Ruskai [1] conjectured that the maximal p-norm of the Werner--Holevo channel is multiplicative for all

1\le p \le 2

. In this paper we prove this conjecture. Our proof relies on certain convexity and monotonicity properties of the p--norm.

\\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.