Quantifying multipartite nonlocality via the size of the resource

Abstract

The generation of (Bell-)nonlocal correlations, i.e., correlations leading to the violation of a Bell-like inequality, requires the usage of a nonlocal resource, such as an entangled state. When given a correlation (a collection of conditional probability distributions) from an experiment or from a theory, it is desirable to determine the extent to which the participating parties would need to collaborate nonlocally for its (re)production. Here, we propose to achieve this via the minimal group size (MGS) of the resource, i.e., the smallest number of parties that need to share a given type of nonlocal resource for the above-mentioned purpose. In addition, we provide a general recipe-based on the lifting of Bell-like inequalities-to construct MGS witnesses for nonsignaling resources starting from any given ones. En route to illustrating the applicability of this recipe, we also show that when restricted to the space of full-correlation functions, nonsignaling resources are as powerful as unconstrained signaling resources. Explicit examples of correlations where their MGS can be determined using this recipe and other numerical techniques are provided.

Maximal violation of a broad class of Bell inequalities and its implication on self-testing

“…That the maximal quantum and nonsignaling violation remain unchanged under Pironio's party-lifting operation [41] follows directly from the results shown in Section 2.4 of [42], as well as a special case (with n = k) of Theorem 2 of [43]. For the convenience of subsequent discussions, however, we provide below an alternative proof of this observation.…”

“…Although the above result of [43] can be applied to an arbitrary number of (n + h) parties, Observation 1 implies that if the seed inequality is that applicable to an n-partite Bell scenario, the extended scenario can never be used to certify an entanglement depth that is larger than n. This follows from the fact that the maximal quantum value of these party-lifted Bell-like inequalities is the same as the original Bell-like inequality [cf. Eq.…”

“…It is worth noting that such Bell inequalities has found applications in the foundations of quantum theory [57,58], as well as in the systematic generation [43] of device-independent witnesses for entanglement depth [26].…”

Bipartite Bell inequalities with three ternary-outcome measurements—from theory to experiments

“…A common feature shared by all the Bell inequalities that we present here is that they cannot be cast in a form involving only full (bipartite) correlators [21,42,43]. Interestingly, except in Bell experiments [44,45] related to the closing of detection loophole [46], there is almost no other experimental exploration of this generic kind of Bell inequalities (see however [47]).…”

Exploring Bell inequalities for the device-independent certification of multipartite entanglement depth

“…In the terminology of Ref. [32], this means that Eq. (6) is a constraint that has to be satisfied by a nonlocal quantum resource of minimal group size k. Likewise, a device-independent witness for entanglement intactness:…”