Entanglement Detection by Approximate Entanglement Witnesses

TL;DR

This paper proposes an approach to detect quantum entanglement efficiently by approximating convex polytopes with polynomial-sized sets of entanglement witnesses, potentially enabling high-probability entanglement determination.

Contribution

It introduces a method using high-dimensional convex polytope approximations to identify entanglement with polynomial resources, advancing the computational tools for quantum state analysis.

Findings

Convex polytope approximates Euclidean ball in high dimensions

Polynomial-sized set of entanglement witnesses may suffice

High probability of correctly determining entanglement

Abstract

The problem of determining whether a given quantum state is separable is known to be computationally difficult. We develop an approach to this problem based on approximations of convex polytopes in high dimensions. By showing that a convex polytope constructed from a polynomial number of hyperplanes approximates the Euclidean ball arbitrarily well in high dimensions, we find evidence that a polynomial-sized set of approximate entanglement witnesses is potentially sufficient to determine the entanglement of a state with high probability.