The standard symmetrized skew information and its applications

In this paper, we propose two new measures: one is symmetrized skew information and the other one is standard symmetrized skew information. Firstly, we prove their properties, such as non-negativity, convexity, invariance, additivity, monotonicity and strong monotonicity. Next, we conduct research on relationships between standard symmetrized skew information and several well-known measures in one-qubit state, aiming to compare their similarities and differences. In addition, standard symmetrized skew information is used to study quantum uncertainty. We also give the definition of standard symmetrized skew information of assistance, and provide it a straightforward operational explanation for better understanding. Finally, standard symmetrized skew information can be applied to detect entanglement.