Physical transformations between quantum states

Abstract

Given two sets of quantum states A1, ..., Ak and B1, ..., Bk, 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(Ai) = Bi for i = 1, ..., k. General completely positive maps without the trace-preserving requirement, and unital completely positive maps transforming the states are also considered.

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