Physical transformations between quantum states

Zejun Huang, Chi-Kwong Li, Edward Poon, Nung-Sing Sze

Published 2012-03-25, updated 2012-10-26Version 2

Given two sets of quantum states {A_1, ..., A_k} and {B_1, ..., B_k}, represented as sets of density matrices, necessary and sufficient conditions are obtained for the existence of a physical transformation T, represented as a trace-preserving completely positive map, such that T(A_i) = B_i for i = 1, ..., k. General completely positive maps without the trace-preserving requirement, and unital completely positive maps transforming the states are also considered.