Mirrored entanglement witnesses

Joonwoo Bae,Beatrix C Hiesmayr,Dariusz Chruściński

doi:10.1038/s41534-020-0242-z

Abstract

Entanglement detection, which signifies the task of distinguishing entangled states from separable states, can be generally performed by realizing entanglement witnesses via local measurements on a single-copy level and classical communication, and are known to be experimenter friendly. We introduce a framework of constructing mirrored entanglement witnesses by showing that an experimental observable is twice as effective since it generally provides bounds from above and below for separable states. Differently stated, a pair of witnesses, mirrored witnesses, exists for the characterization of the bounds, which are two faces of one observable. We show how to generally construct those witnesses and provide examples for bipartite and multipartite systems. We also show that both mirrored witnesses can be improved by introducing nonlinearities, by which a larger set of entangled states can be certified.

Highlights

Revealing properties of an unknown quantum state of a physical system is of fundamental importance in quantum information theory and its application
We have presented the framework of mirrored Entanglement witnesses (EWs)
Mirrored Entanglement witnesses (EWs) can be rephrased that npj Quantum Information (2020) 15

Summary

Introduction

Revealing properties of an unknown quantum state of a physical system is of fundamental importance in quantum information theory and its application. EWs typically require less experimental setups to unambiguously verify the existence of entanglement and even additional information on the type of entanglement may be revealed. This concept relies on the fact that the set of separable states is convex, i.e. EWs correspond to hyperplanes separating some entangled states from the set of separable states in the Hilbert−Schmidt space.[1] In high-dimensional and multipartite systems the entanglement structure itself becomes of interest which has a nested convex structure.[2,3,4] In the recent years, there has been much progress in the theory and experimental realization of EWs for multipartite entangled states In high-dimensional and multipartite systems the entanglement structure itself becomes of interest which has a nested convex structure.[2,3,4] In the recent years, there has been much progress in the theory and experimental realization of EWs for multipartite entangled states (see e.g. refs. 5–7)

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Discussion

Conclusion