Robust entanglement measure for mixed quantum states

TL;DR

This paper presents the Modified Bloch Norm (MBN), a new entanglement measure for mixed quantum states, which effectively analyzes bound entanglement dynamics and outperforms negativity under measurement limitations.

Contribution

Introduction of MBN, a robust entanglement measure based on Bloch matrix criteria, for analyzing bound entanglement and practical measurement scenarios.

Findings

MBN accurately estimates Entanglement Sudden Death time.

MBN detects freezing of bound entanglement.

MBN has lower error rate than negativity with limited measurements.

Abstract

We introduce an entanglement measure, the Modified Bloch Norm (MBN), for finite-dimensional bipartite mixed states, based on the improved Bloch matrix criteria. MBN is demonstrated to be effective in analyzing the dynamics of bound entanglement--a valuable resource for quantum protocols where free entanglement may not be available. Through examples, we illustrate the applications of MBN in accurately estimating the Entanglement Sudden Death (ESD) time and detecting behavior such as the freezing of bound entanglement. Additionally, we show that the error rate for entanglement measured using state estimation from a limited number of measurement copies is significantly lower when using MBN compared to negativity. This demonstrates the robustness of MBN under practical constraints.