Operational nonclassicality of local multipartite correlations in the limited-dimensional simulation scenario

Abstract

For a bipartite local quantum correlation, superlocality refers to the requirement for a larger dimension of the random variable in the classical simulation protocol than that of the quantum states that generate the correlations. In this work, we consider the classical simulation of local tripartite quantum correlations P among three parties A, B and C. If at least one of the bipartitions (A|BC), (B|AC) and (C|AB) is superlocal, then P is said to be absolutely superlocal, whereas if all three bipartitions are superlocal, then P is said to be genuinely superlocal. We present specific examples of genuine superlocality for tripartite correlations derived from three-qubit states. It is argued that genuine quantumness as captured by the notion of genuine discord is necessary for demonstrating genuine superlocality. Finally, the notions of absolute and genuine superlocality are also defined for multipartite correlations. arXiv:1701.04363v3 [quant-ph] 9 Jul 2018Operational nonclassicality of local multipartite correlations

Superunsteerability as a quantifiable resource for random access codes assisted by Bell-diagonal states

“…It remains to be studied whether superunsteerability is the unique resource for the above two RACs in the presence of finite shared randomness using other separable states. Moreover, further studies of local resources such as superlocality [17,19,21] and superunsteerability [22,23] for other quantum information processing tasks using separable states admitting local correlations, should be worthwhile. Such studies may provide the scope for shedding further light on the larger question of the boundary between classical and quantum theory.…”

“…When the amount of accessible randomness is limited, separable states may provide further benefit over classical protocols [17][18][19][20][21][22][23]. In such scenarios the notion of superlocality [17,19,21] refers to the requirement for a larger dimension of the preshared randomness to simulate the respective local correlations, than that of the quantum systems generating them. Recently, by generalizing the concept of superlocality, the quantumness of certain unsteerable correlations has been pointed out by defining the notion of superunsteerability [22,23].…”

Characterization of the quantumness of unsteerable tripartite correlations

“…where 0 < V ≤ 1. Since the noisy Svetlichny family has nonzero Svetlichny strength for any V > 0, the quantum simulation of these correlations by using a 2 ⊗ 2 ⊗ 2 quantum state necessarily requires genuine quantum discord [37,38] in the state [40,46]. Following the similar argument presented earlier in case noisy Mermin family, it can be stated that the bi-unsteerable noisy Svetlichny family demonstrates genuine super-bi-unsteerablity in one sided device independent scenario for 0 < V ≤ 1 √ 2 [55].…”

“…The minimal amount of communication between these disjoint groups required to reproduce a given nonlocal correlation determines the extent of multipartite quantum nonlocality of that correlation. Recently, the operational characterization of genuine nonclassicality of local multipartite correlations has been presented and the notion of superlocality has been generalised in the context of local multipartite correlations [46].…”

Operational characterization of quantumness of unsteerable bipartite states

“…It has been demonstrated that there exists some local correlations for which the dimension of the pre-shared randomness required to simulate the correlations exceeds the dimension of the quantum system reproducing them by applying suitable measurements. This is known as superlocality [40][41][42][43][44][45]. On the other hand, any unsteerable correlation can be reproduced by appropriate measurements on an appropriate separable state [46,47].…”