Generalized Circulant Densities and a Sufficient Condition for Separability

TL;DR

This paper explores the structure of certain quantum densities using finite geometry, providing new criteria for checking the PPT property and establishing a novel sufficient condition for separability.

Contribution

It introduces a geometric framework for analyzing densities and derives a new sufficient separability condition based on this structure.

Findings

Support of densities expressed via lines in finite geometry

New method for verifying PPT property

Novel sufficient condition for separability

Abstract

In a series of papers with Kossakowski, the first author has examined properties of densities for which the positive partial transpositrionm (PPT) property can be readily checked. These densities were also investigated from a different perspective by Baumgartner, Hiesmayr and Narnhofer. In this paper we show how the support of such densities can be expressed in terms of lines in a finite geometry and how that same structure lends itself to checking the necessary PPT condition and to a novel sufficient condition for separability.