Nonlinear and linear entanglement witnesses for bipartite systems via exact convex optimization

TL;DR

This paper develops a method using convex optimization to construct linear and nonlinear entanglement witnesses for bipartite quantum systems, providing necessary and sufficient conditions for separability in various dimensions.

Contribution

It introduces an exact convex optimization approach based on single particle feasible regions to construct effective entanglement witnesses for bipartite systems.

Findings

Entanglement witnesses effectively identify entanglement in two qutrit systems.

The method provides necessary and sufficient conditions for separability.

Applicable to bipartite qudit systems with dimensions 3, 4, and 5.

Abstract

Linear and nonlinear entanglement witnesses for a given bipartite quantum systems are constructed. Using single particle feasible region, a way of constructing effective entanglement witnesses for bipartite systems is provided by exact convex optimization. Examples for some well known two qutrit quantum systems show these entanglement witnesses in most cases, provide necessary and sufficient conditions for separability of given bipartite system. Also this method is applied to a class of bipartite qudit quantum systems with details for d=3, 4 and 5. Keywords: non-linear and linear entanglement witnesses PACS number(s): 03.67.Mn, 03.65.Ud