Local orthogonality provides a tight upper bound for Hardy's nonlocality

Abstract

The amount of nonlocality in quantum theory is limited compared to that allowed in generalized no-signaling theory [Found. Phys. 24, 379 (1994)]. This feature, for example, gets manifested in the amount of Bell inequality violation as well as in the degree of success probability of Hardy's (Cabello's) nonlocality argument. Physical principles like information causality and macroscopic locality have been proposed for analyzing restricted nonlocality in quantum mechanics-viz. explaining the Cirel'son bound. However, these principles are not that much successful in explaining the maximum success probability of Hardy's as well as Cabello's argument in quantum theory. Here we show that, a newly proposed physical principle namely Local Orthogonality does better by providing a tighter upper bound on the success probability for Hardy's nonlocality. This bound is relatively closer to the corresponding quantum value compared to the bounds achieved from other principles.

The Cabello Nonlocality Argument is Stronger Control than the Hardy Nonlocality Argument for Detecting Post-Quantum Correlations in the Bipartite Systems

“…where C xy = a,b (−1) a⊕b p ab|xy ,C x = a,b (−1) a p ab|xy and C y = a,b (−1) b p ab|xy . S. Das and et.al [24] numerically showed that, the maximum of success probability HNA turn out to be ≈ 0.2062 which is same as that for CNA under imposing (N S + M L) condition (please see the…”

“…In order the solve this problem, some new principles like Local Orthogonality (LO) is introduced by Fritz and et.al [27]. Next, the authors in ref [24] found that the maximum success probability of HNA under the LO principle is 0.177 which is closer to the QM value, but in the case CNA, it is same as that obtained from IC principle (0.207). On the other hand, Gazi and et.al [28] shown that in terms of local randomness (LR) of the observable for the Hardy's correlations, there is also a gap between QM and IC condition and this gap in the context of CNA is much larger than the HNA case [29].…”

“…Some of these principles are non trivial communication complexity [14,15], Information Causality (IC) [16], Macroscopic Locality (ML) [17], Exclusivity principle [18], Relativistic Causality in the Classical limit [19,20], the uncertainty principle along with steering [21] and complementarity principle [22]. It is interesting, some of these principles * Electronic address: a.ahanj@khayyam.ac.ir; ahanj@ipm.ir like IC and ML can explain the Cirel'son bound of Bell-CHSH, but they can not explain the limit HNA and CNA in the quantum theory [23,24]. It has been shown that under applying the IC, the upper bound on the success probability of both HNA and CNA is almost 0.2071 [23], and under applying the ML condition they are 0.2062 [24].…”

“…It is interesting, some of these principles * Electronic address: a.ahanj@khayyam.ac.ir; ahanj@ipm.ir like IC and ML can explain the Cirel'son bound of Bell-CHSH, but they can not explain the limit HNA and CNA in the quantum theory [23,24]. It has been shown that under applying the IC, the upper bound on the success probability of both HNA and CNA is almost 0.2071 [23], and under applying the ML condition they are 0.2062 [24]. Very soon, it has been shown that for a more than two subsystem correlations, no bipartite physical principle (like IC and ML) can completely recognize the full set of QM correlations [25,26].…”

On Quantum Possibilistic Paradoxes and Logical Contextuality

“…That is, Tsirelson-like bounds to experiments used in inequality-free proofs of quantum contextuality and nonlocality. Other possibilities include bounds provided by information causality principle [114], exclusivity principle [115], and so on. Another possible direction of future research is the possibility of a probabilistic version of Theorem 11.…”