#### Document Type

Article

#### Department/Program

Mathematics

#### Journal Title

Journal of Functional Analysis

#### Pub Date

2013

#### Volume

264

#### Issue

2

#### First Page

464

#### Abstract

A geometric characterization is given for invertible quantum measurement maps. Denote by S(H) the convex set of all states (i.e., trace I positive operators) on Hilbert space H with dim H S(H) satisfies phi ([rho(1), rho(2)]) subset of [phi(rho(1)), phi(rho(2))] for any rho(1), rho(2) is an element of S if and only if phi has one of the following forms rho bar right arrow M rho M*/tr(M rho M*) or rho bar right arrow M rho T M*/tr(M rho T M*), where M is an invertible bounded linear operator and rho(T) is the transpose of rho with respect to an arbitrarily fixed orthonormal basis. (C) 2012 Published by Elsevier Inc.

#### Recommended Citation

He, K., Hou, J. C., & Li, C. K. (2013). A geometric characterization of invertible quantum measurement maps. Journal of Functional Analysis, 264(2), 464-478.

#### DOI

10.1016/j.jfa.2012.11.005