Families of bipartite states classifiable by the positive partial transposition criterion

TL;DR

This paper introduces a family of bipartite quantum states with a structure that allows straightforward determination of their PPT property, aiding entanglement classification and analysis.

Contribution

It constructs a new class of bipartite states where PPT criteria can be directly inferred from the block structure, expanding tools for entanglement detection.

Findings

Identified subfamilies where PPT is necessary and sufficient

Derived a new sufficient separability criterion

Connected known states to the new family for classification

Abstract

We construct a family of bipartite states of arbitrary dimension whose eigenvalues of the partially transposed matrix can be inferred directly from the block structure of the global density matrix. We identify from this several subfamilies in which the PPT criterion is both necessary and sufficient. A sufficient criterion of separability is obtained, which is fundamental for the discussion. We show how several examples of states known to be classifiable by the PPT criterion indeed belong to this general set. Possible uses of these states in numerical analysis of entanglement and in the search of PPT bound entangled states are briefly discussed.