Comments on multiplicativity of maximalp-norms whenp=2

Authors:
Christopher King;Mary Beth Ruskai
Affiliations:
Department of Mathematics, Northeastern University, Boston MA;Department of Mathematics, Tufts University, Medford, Massachusetts
Venue:
Quantum Information & Computation
Year:
2004

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Abstract

We consider the maximal p-norm associated with a completely positivemap and the question of its multiplicativity under tensor products. Wegive a condition under which this multiplicativity holds when p = 2, andwe describe some maps which satisfy our condition. This class includesmaps 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.