Quantum measurements and maps preserving strict convex combinations and pure states

TL;DR

This paper characterizes quantum state maps that preserve pure states and convex combinations, providing structural insights into multipartite states and addressing conjectures on injective quantum measurements.

Contribution

It offers a new characterization of maps preserving pure states and convex combinations, and applies this to multipartite states and quantum measurement conjectures.

Findings

Characterization of maps preserving pure states and convex combinations

Structural theorem for multipartite quantum states

Resolution of conjectures on injective quantum measurements

Abstract

In this paper, a characterization of maps between quantum states that preserve pure states and strict convex combinations is obtained. Based on this characterization, a structural theorem for maps between multipartite quantum states that preserve separable pure states and strict convex combinations is established. Then these results are applied to characterize injective (local) quantum measurements and answer some conjectures proposed in [J.Phys.A:Math.Theor. 45 (2012) 205305].