Fully nonlocal quantum correlations (1105.3598v3)

Abstract: Quantum mechanics is a nonlocal theory, but not as nonlocal as the no-signalling principle allows. However, there exist quantum correlations that exhibit maximal nonlocality: they are as nonlocal as any non-signalling correlations and thus have a local content, quantified by the fraction $p_L$ of events admitting a local description, equal to zero. Exploiting the link between the Kochen-Specker and Bell's theorems, we derive, from every Kochen-Specker proof, Bell inequalities maximally violated by quantum correlations. We then show that these Bell inequalities lead to experimental bounds on the local content of quantum correlations which are significantly better than those based on other constructions. We perform the experimental demonstration of a Bell test originating from the Peres-Mermin Kochen-Specker proof, providing an upper bound on the local content $p_L\lesssim 0.22$.

Fully Nonlocal Quantum Correlations

This paper explores the robust domain of quantum correlations, examining the nuances that differentiate quantum correlations from classical ones and probing scenarios where quantum correlations exhibit maximal nonlocality. The authors, Aolita et al., extend the theoretical framework to provide experimental bounds, particularly focusing on the implications from the perspectives of the Kochen-Specker (KS) and Bell theorems.

Theoretical Foundation

Quantum mechanics inherently features nonlocal characteristics, yet these characteristics do not fully extend to the nonlocal bounds allowed by the no-signalling principle. Quantum and classical correlations are both subsets of the allowable nonsignalling correlations, but the extent of their nonlocalities varies significantly. Typically, quantum correlations can be observed when measurements on entangled states violate a Bell inequality, which classical systems cannot do.

The paper focuses on the internal gaps between classical, quantum, and nonsignalling correlations. The authors explore a special class of quantum correlations that achieve the maximum possible violation of a Bell inequality while adhering to the nonsignalling principle, thereby being 'fully' nonlocal. They propose that such quantum correlations have a local content (quantified by $p_L$) equal to zero, suggesting that no proportion of these correlations can be described by a local model.

Maximal Violation Approach

Through a novel application of KS theorem proofs, the authors derive conditions where Bell inequalities are maximally violated by quantum states. This derivation utilizes the inherent connection between KS and Bell's theorems. By focusing on those configurations where quantum correlations push the boundary of nonsignalling correlations, the authors triangulate the conditions for maximal nonlocality.

Their analysis is cast in the framework of a Bell test derived from the Peres-Mermin KS proof. When implemented, this approach leads to experimental bounds on local contents that are sharper than those provided by configurations based on more traditional Bell inequalities.

Experimental Implementation

The work includes an experimental verification using a hyperentangled state of photons. The setup was designed to test the derived Bell inequality based on the Peres-Mermin square. Remarkably, the experiment provided an observed Bell violation yielding an upper bound on the local fraction at $p_L \lesssim 0.22$, which is the most stringent bound reported thus far.

Implications and Future Directions

This research is pivotal for illustrating the limits of quantum nonlocality, contributing both to foundational quantum theory and to practical implications in quantum information processing. The rigorous procedures laid out for deriving and testing fully nonlocal quantum correlations promise enhancements in verifying quantum advantage.

Future endeavors could explore extending these results in scenarios with greater complexity or different multipartite systems. Importantly, it becomes relevant for developments in quantum computing and quantum cryptography, where realizing the potential of nonlocal correlations is critical. The paper opens pathways for further reducing the local content of observed quantum correlations, thus advancing our capacity to harness quantum mechanics in practice.