Detecting separable states via semidefinite programs

TL;DR

This paper presents a semidefinite programming-based method for detecting separable quantum states, providing both a numerical technique and an analytical criterion, with high detection coverage.

Contribution

The authors introduce a novel semidefinite programming approach that offers a new sufficient condition for quantum state separability, including explicit decompositions.

Findings

Detects all interior separable states except possibly a measure-zero set.

Provides explicit convex decompositions for confirmed separable states.

Enables both numerical detection and analytical criteria for separability.

Abstract

We introduce a new technique to detect separable states using semidefinite programs. This approach provides a sufficient condition for separability of a state that is based on the existence of a certain local linear map applied to a known separable state. When a state is shown to be separable, a proof of this fact is provided in the form of an explicit convex decomposition of the state in terms of product states. All states in the interior of the set of separable states can be detected in this way, except maybe for a set of measure zero. Even though this technique is more suited for a numerical approach, a new analytical criterion for separability can also be derived.