Comments on multiplicativity of maximal p-norms when p = 2

Abstract

We consider the maximal p-norm associated with a completely positive map and the question of its multiplicativity under tensor products. We give a condition under which this multiplicativity holds when p = 2, and we describe some maps which satisfy our condition. This class includes maps for which multiplicativity is known to fail for large p. Our work raises some questions of independent interest in matrix theory; these are discussed in two appendices.

16 pages. For the Festschrift in honor of A. Holevo's 60th birthday

References in corpus (2)

• Additivity for a class of unital qubit channels
• On the multiplicativity conjecture for quantum channels

Cited by in corpus (4)

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• There, and Back Again: Quantum Theory and Global Optimisation
• Analysis of the Entanglement Cost and Calculation of the Holevo Capacity