On the Alberti-Uhlmann Condition for Unital Channels

Alberti-Uhlmann判据在量子比特二分法之外的推广

Extension of the Alberti-Uhlmann criterion beyond qubit dichotomies

本文将Alberti-Uhlmann判据从量子比特二分法推广到任意数量的量子比特或qutrit态及测量，并展示了其在半设备无关场景下的应用可行性。

Characterization of preorders induced by positive maps in the set of Hermitian matrices

Uhlmann showed that there exists a positive, unital and trace-preserving map transforming a Hermitian matrix $A$ into another $B$ if and only if the vector of eigenvalues of $A$ majorizes that of $B$. In this work I characterize the existence of such a transformation when one of the conditions of unitality or trace preservation is dropped. This induces two possible preorders in the set of Hermitian matrices and I argue how this can be used to construct measures quantifying the lack of positive semidefiniteness of any given Hermitian matrix with relevant monotonicity properties. It turns out th…