Measurement-Device-Independent Approach to Entanglement Measures

TL;DR

This paper introduces a measurement-device-independent method to quantify entanglement using a subset of semiquantum nonlocal games, providing a universal, convex, and continuous measure accessible without trusting measurement devices.

Contribution

It demonstrates that a small subset of nonlocal games suffices for entanglement quantification, including negative-partial-transpose entanglement, in a measurement-device-independent manner.

Findings

Maximum pay-off serves as a universal entanglement measure.

The measure is convex and continuous.

Extension to multipartite entanglement quantification.

Abstract

Within the context of semiquantum nonlocal games, the trust can be removed from the measurement devices in an entanglement-detection procedure. Here we show that a similar approach can be taken to quantify the amount of entanglement. To be specific, first, we show that in this context a small subset of semiquantum nonlocal games is necessary and sufficient for entanglement detection in the LOCC paradigm. Second, we prove that the maximum pay-off for these games is a universal measure of entanglement which is convex and continuous. Third, we show that for the quantification of negative-partial-transpose entanglement, this subset can be further reduced down to a single arbitrary element. Importantly, our measure is operationally accessible in a measurement-device-independent way by construction. Finally, our approach is simply extended to quantify the entanglement within any partitioning of multipartite quantum states.