题目：Standard symmetrized variance with applications to coherence, uncertainty, and entanglement

作者：费少明 教授

简介：Variance is a ubiquitous quantity in quantum information theory. Given a basis, we consider the averaged

variances of a fixed diagonal observable in a pure state under all possible permutations on the components of the

pure state and call it symmetrized variance. Moreover, we work out the analytical expression of the symmetrized

variance and find that such an expression is in the factorized form where two factors separately depend on the

diagonal observable and quantum state. By shifting the factor corresponding to the diagonal observable, we

introduce the notion referred to as standard symmetrized variance for the pure state which is independent of

the diagonal observable. We then extend the standard symmetrized variance to mixed states in three different

ways, which characterize the uncertainty, the coherence, and the coherence of assistance, respectively. These

quantities are evaluated analytically and the relations among them are established. In addition, we show that

standard symmetrized variance is also an entanglement measure for bipartite systems. In this way, these different

quantumnesses of quantum states are unified by the variance.