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

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

2005-05-31

arxiv.org/abs/math-ph/0505085v2

Physics

Mathematical Physics

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

Scientific paper

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, $||\Phi||_{p\to q} = \max_{A=A^*} \frac{||\Phi(A)||_q}{||A||_p}$, 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.

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