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

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

Research output: Article

53 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 - 2006

Fingerprint

Contractivity
norms
preserving
Trace
Norm
If and only if
Hermitian matrix
Qubit
Unital
Subspace
Arbitrary

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Contractivity of positive and trace-preserving maps under L P norms. / Pérez-García, David; Wolf, Michael M.; Petz, D.; Ruskai, Mary Beth.

In: Journal of Mathematical Physics, Vol. 47, No. 8, 083506, 2006.

Research output: Article

Pérez-García, David ; Wolf, Michael M. ; Petz, D. ; Ruskai, Mary Beth. / Contractivity of positive and trace-preserving maps under L P norms. In: Journal of Mathematical Physics. 2006 ; Vol. 47, No. 8.
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