Measurement-Device-Independent Approach to Entanglement Measures

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.