Contractivity of positive and trace-preserving maps under L P norms

David Pérez-García, Michael M. Wolf, Denes Petz, Mary Beth Ruskai

Research output: Contribution to journalArticle

56 Citations (Scopus)

Abstract

We provide a complete picture of contractivity of trace preserving positive maps with respect to p-norms. We show that for p > 1 contractivity holds in general if and only if the map is unital. When the domain is restricted to the traceless subspace of Hermitian matrices, then contractivity is shown to hold in the case of qubits for arbitrary p ≥ 1 and in the case of qutrits if and only if p=1, ∞. In all noncontractive cases best possible bounds on the p-norms are derived.

Original languageEnglish
Article number083506
JournalJournal of Mathematical Physics
Volume47
Issue number8
DOIs
Publication statusPublished - Sep 11 2006

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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