Quantifying mixed-state quantum entanglement by optimal entanglement witness

TL;DR

This paper introduces a method to quantify mixed-state quantum entanglement using optimal entanglement witnesses, simplifying computation and experimental detection, demonstrated on specific noisy quantum states.

Contribution

It presents a novel approach leveraging optimal witnesses to accurately measure entanglement in mixed states, reducing computational and experimental complexity.

Findings

Successfully quantified bound entanglement in four-qubit noisy Smolin states.

Measured three-qubit GHZ entanglement under white noise.

Provided a numerical method for optimizing entanglement witnesses.

Abstract

We develop an approach of quantifying entanglement in mixed quantum states by the optimal entanglement witness operator. We identify the convex set of mixed states for which a single witness provides the exact value of an entanglement measure, and show that the convexity, properties, and symmetries of entanglement or of a target state considerably fix the form of the optimal witness. This greatly reduces difficulty in computing and experimentally determining entanglement measures. As an example, we show how to experimentally quantify bound entanglement in four-qubit noisy Smolin states and three-qubit Greenberger-Horne-Zeilinger (GHZ) entanglement under white noise. For general measures and states, we provide a numerical method to efficiently optimize witness.