Detecting Entanglement by Pure Bosonic Extension

TL;DR

This paper introduces a new 'pure bosonic extension' method to improve the detection and quantification of quantum entanglement, especially bound entanglement, by enabling efficient characterization of $k$-bosonic extendible states and providing better lower bounds for the relative entropy of entanglement.

Contribution

The paper proposes a hierarchical pure bosonic extension approach that outperforms existing SDP methods in handling larger dimensions and higher extension values for entanglement detection.

Findings

Supports larger dimensions than SDP methods

Provides more accurate lower bounds for REE

Enables efficient characterization of $k$-bosonic extendible states

Abstract

In the realm of quantum information theory, the detection and quantification of quantum entanglement stand as paramount tasks. The relative entropy of entanglement (REE) serves as a prominent measure of entanglement, with extensive applications spanning numerous related fields. The positive partial transpose (PPT) criterion, while providing an efficient method for the computation of REE, unfortunately, falls short when dealing with bound entanglement. In this study, we propose a method termed "pure bosonic extension" to enhance the practicability of $k$-bosonic extensions, which approximates the set of separable states from the "outside", through a hierarchical structure. It enables efficient characterization of the set of $k$-bosonic extendible states, facilitating the derivation of accurate lower bounds for REE. Compared to the Semi-Definite Programming (SDP) approach, such as the symmetric/bosonic extension function in QETLAB, our algorithm supports much larger dimensions and higher values of extension $k$.