Entanglement Witness $2.0$: Compressed/Mirrored Entanglement Witnesses

TL;DR

This paper introduces a framework to enhance entanglement witnesses by leveraging a second bound, effectively doubling their detection power and enabling the creation of more powerful, compressed witnesses for complex quantum systems.

Contribution

The authors develop a method to upgrade any entanglement witness to a more powerful version, called witness 2.0, by utilizing a second bound and structural physical approximation.

Findings

Enhanced entanglement detection with the second bound.

Applicable to bipartite and multipartite qubit/qudit systems.

Demonstrated power increase via theoretical and practical examples.

Abstract

An entanglement witness is an observable detecting entanglement for a subset of states. We present a framework that makes an entanglement witness twice as powerful due to the general existence of a second (lower) bound, in addition to the (upper) bound of the very definition. This second bound, if non-trivial, is violated by another subset of entangled states. Differently stated, we prove via the structural physical approximation that two witnesses can be compressed into a single one. Consequently, our framework shows that any entanglement witness can be upgraded to a witness $2.0$. The generality and its power are demonstrate by applications to bipartite and multipartite qubit/qudit systems.