A Note on the p->q norms of Completely Positive Maps

Abstract

King and Ruskai asked whether the $p\to q$ norm of a completely positive map $\Phi$, acting between Schatten $p$ and $q$ classes of self-adjoint operators, $||\Phi |{|}_{p\to q}={\max }_{A=A^{\ast }}\frac{||\Phi (A)|{|}_q}{||A|{|}_p}$, is equal to the $p\to q$ norm of that map when acting between Schatten classes of general, not necessarily self-adjoint, operators. The first proof has been given by Watrous. We give an alternative proof of this statement.

1.5 pages; a different proof of the main statement has already appeared in: J. Watrous, QIC 5, 58-68 (2005)

References in corpus (1)

• On the multiplicativity conjecture for quantum channels

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