@article{76bc83ee086c45eb9d99832810affcf7,
title = "Contractivity of positive and trace-preserving maps under L P norms",
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.",
author = "David P{\'e}rez-Garc{\'i}a and Wolf, {Michael M.} and Denes Petz and Ruskai, {Mary Beth}",
note = "Funding Information: The authors thank J. I. Cirac and M. Junge for valuable discussions, A. Harrow for raising the question of contractivity on the traceless hyperplane, and A. Jencova for the remark following Theorem 2.4. The work of two of the authors (D.P. and M.B.R.) was partially supported by the U.S. National Science Foundation under Grant No. DMS-0314228. One of the authors (D.P.) is supported by the Hungarian grant OTKA T032662. Another author (D.P-G). is supported by Spanish Project No. MEC MTM-2005-00082. Parts of this work were done when one author (D.P.) was visiting Tufts University, when another author (M.B.R.) was visiting the Max-Planck Institut f{\"u}r Quantenoptik, and during the workshop on quantum information in Benasque.",
year = "2006",
doi = "10.1063/1.2218675",
language = "English",
volume = "47",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "American Institute of Physics",
number = "8",
}