Entanglement witnesses and separability criteria based on generalized equiangular tight frames
Katarzyna Siudzińska
TL;DR
This paper develops a framework for entanglement detection based on generalized equiangular measurements (GEAMs). By exploiting conical 2-designs, it constructs positive but not completely positive maps and the associated entanglement witnesses, with witnesses depending only on two partial indices of coincidence. It also introduces separability criteria derived from the GEAM-based correlation matrix, recovering and generalizing several known criteria and illustrating effectiveness on Werner, isotropic and bound-entangled states. The results extend to indecomposable witnesses that can detect bound entanglement and provide a practical toolkit for entanglement verification using GEAMs in arbitrary dimensions.
Abstract
We use operators from generalized equiangular measurements to construct positive maps. Their positivity follows from the inequality for indices of coincidence corresponding to few equiangular tight frames. These maps give rise to entanglement witnesses, which include as special cases many important classes considered in the literature. Additionally, we introduce separability criteria based on the correlation matrix and analyze them for various types of measurements.