Physical transformations between quantum states

TL;DR

This paper establishes necessary and sufficient conditions for physical transformations between sets of quantum states using trace-preserving completely positive maps, extending to non-trace-preserving and unital maps.

Contribution

It provides a comprehensive characterization of when one set of quantum states can be transformed into another via physical quantum operations.

Findings

Derived conditions for trace-preserving transformations

Extended analysis to non-trace-preserving maps

Considered unital transformations in quantum state space

Abstract

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.