Several families of entanglement criteria for multipartite quantum systems based on generalized Wigner-Yanase skew information and variance

TL;DR

This paper introduces new entanglement detection criteria for multipartite quantum systems using generalized Wigner-Yanase skew information and variance, demonstrating improved detection capabilities over existing methods.

Contribution

It proposes multiple families of entanglement criteria based on generalized Wigner-Yanase skew information and variance, revealing their complementary nature and enhanced detection power.

Findings

Criteria can detect entanglement unrecognized by other methods

Combination of criteria improves detection strength

Examples demonstrate the effectiveness of the new criteria

Abstract

Quantum entanglement plays a critical role in many quantum applications, but detecting entanglement, especially in multipartite or high-dimensional quantum systems, remains a challenge. In this paper, we propose several families of entanglement criteria for detecting entanglement in multipartite or high-dimensional quantum states by the generalized Wigner-Yanase skew information $I^s(\rho,X)$ for $-1\leq s\leq0$ and variance. We also reveal a complementary character between the criteria based on the generalized Wigner-Yanase skew information and an alternative one based on variance through specific examples. We illustrate the merits of these criteria and show that the combination of the entanglement criteria has a stronger detection capability, as it is capable of detecting entangled states that remain unrecognized by other criteria.