Quantifying Multipartite Quantum Entanglement in a Semi-Device-Independent Manner

TL;DR

This paper introduces semi-device-independent methods to quantify multipartite quantum entanglement using Bell inequalities and quantum dimension, providing practical lower bounds for entanglement measures in experimental settings.

Contribution

It presents novel approaches that leverage nondegenerate Bell inequalities and quantum dimension to estimate entanglement without full device characterization.

Findings

Lower bounds for geometric measure of entanglement obtained when Bell value > 3.60.

Lower bounds for relative entropy of entanglement obtained when Bell value > 3.80.

Applicable to 5-partite qubit systems with MABK inequality.

Abstract

We propose two semi-device-independent approaches that are able to quantify unknown multipartite quantum entanglement experimentally, where the only information that has to be known beforehand is quantum dimension, and the concept that plays a key role is nondegenerate Bell inequalities. Specifically, using the nondegeneracy of multipartite Bell inequalities, we obtain useful information on the purity of target quantum state. Combined with an estimate of the maximal overlap between the target state and pure product states and a continuous property of the geometric measure of entanglement we shall prove, the information on purity allows us to give a lower bound for this entanglement measure. In addition, we show that a different combination of the above results also converts to a lower bound for the relative entropy of entanglement. As a demonstration, we apply our approach on 5-partite qubit systems with the MABK inequality, and show that useful lower bounds for the geometric measure of entanglement can be obtained if the Bell value is larger than 3.60, and those for the relative entropy of entanglement can be given if the Bell value is larger than 3.80, where the Tsirelson bound is 4.