Detection power of separability criteria based on a correlation tensor: a case study

TL;DR

This paper evaluates the effectiveness of correlation tensor-based separability criteria on generalized isotropic states, revealing their relative strength compared to PPT and realignment criteria, and supporting a conjecture about SIC-POVMs.

Contribution

It provides a comparative analysis of separability criteria, highlighting the limitations of correlation tensor criteria and supporting the superiority of SIC-POVM-based criteria over realignment.

Findings

Correlation tensor criteria are weaker than PPT for unequal dimensions.

SIC-POVM-based criterion is stronger than realignment criterion.

Analysis supports conjecture about SIC-POVM superiority.

Abstract

Detection power of separability criteria based on a correlation tensor is tested within a family of generalized isotropic state in $d_1 \otimes d_2$. For $d_1 \neq d_2$ all these criteria are weaker than positive partial transposition (PPT) criterion. Interestingly, our analysis supports the recent conjecture that a criterion based on symmetrically informationaly complete positive operator-valued measure (SIC-POVMs) is stronger than realignment criterion.