Quantum measurements and maps preserving strict convex combinations and pure states

摘要

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 structure 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 Hou and Liu (2012 J. Phys. A: Math. Theor. 45 205305).