Partitioned trace distances

Details Partitioned trace distances Partitioned trace distances

2009-03-26

arxiv.org/abs/0903.4543v2

Quantum Inf. Process. 9, 61-73 (2010)

Physics

Quantum Physics

8 pages, no figures. Significant changes are made. New section on majorization is added. Theorem 4.1 is extended. The bibliogr

Scientific paper

10.1007/s11128-009-0128-7

New quantum distance is introduced as a half-sum of several singular values of difference between two density operators. This is, up to factor, the metric induced by so-called Ky Fan norm. The partitioned trace distances enjoy similar properties to the standard trace distance, including the unitary invariance, the strong convexity and the close relations to the classical distances. The partitioned distances cannot increase under quantum operations of certain kind including bistochastic maps. All the basic properties are re-formulated as majorization relations. Possible applications to quantum information processing are briefly discussed.

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