Spectral conditions for entanglement witnesses vs. bound entanglement

TL;DR

This paper demonstrates that spectral conditions for constructing entanglement witnesses are limited to decomposable ones, indicating that bound entanglement involves non-spectral features and cannot be detected by spectral methods.

Contribution

It proves that spectral-based entanglement witnesses are decomposable, highlighting the non-spectral nature of bound entanglement detection.

Findings

Spectral conditions lead to decomposable entanglement witnesses.

Bound entanglement exhibits non-spectral features.

Spectral methods cannot detect bound entanglement.

Abstract

It is shown that entanglement witnesses constructed via the family of spectral conditions are decomposable, i.e. cannot be used to detect bound entanglement. It supports several observations that bound entanglement reveals highly non-spectral features.