Optimization of ultrafine entanglement witnesses

TL;DR

This paper enhances ultrafine entanglement witnesses by combining operators to rotate the hyperplane, resulting in more effective detection of entangled states beyond previous capabilities.

Contribution

It introduces a method to improve ultrafine entanglement witnesses through operator combination and hyperplane rotation, enabling detection of previously undetectable entangled states.

Findings

New ultrafine entanglement witnesses detect more entangled states.

The method retains the advantages of original ultrafine witnesses.

Enhanced witnesses outperform original in various scenarios.

Abstract

The ultrafine entanglement witness, introduced in [F. Shahandeh, M. Ringbauer, J.C. Loredo, and T.C. Ralph, Phys. Rev. Lett. \textbf{118}, 110502 (2017)], can seamlessly and easily improve any standard entanglement witness. In this paper, by combining the constraint and the test operators, we rotate the hyperplane determined by the test operator and improve further the original ultrafine entanglement witness. In particular, we present a series of new ultrafine entanglement witnesses, which not only can detect entangled states that the original ultrafine entanglement witnesses cannot detect, but also have the merits that the original ultrafine entanglement witnesses have.