Measurement-Device-Independent Approach to Entanglement Measures

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 local operations and classical communication paradigm. Second, we prove that the maximum payoff 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 measurement device independent by construction and operationally accessible. Finally, our approach straightforwardly extends to quantify the entanglement within any partitioning of multipartite quantum states.

Figure 1

The scheme of a semiquantum nonlocal game. Charlie asks the players quantum questions while the players return classical answers. The shared state between the players helps them to obtain a maximum payoff in the game. Here, we allow LOCC operations to be applied to the shared state and quantum questions and introduce a device-independent measure of entanglement.