The problem of quantum correlations and the totalitarian principle

Cabello, Adán

doi:10.1098/rsta.2019.0136

Cited by 3 publications

(2 citation statements)

References 86 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, it provides an explanation of why the non-quantum behaviors in the set of almost quantum behaviors for Bell scenarios [14] are impossible: each of them belongs to TH(G S ), where G S is the graph of exclusivity of the events of the corresponding Bell scenario S, and satisfy constraints (A) and (B). However, they fail to satisfy (C) [44].…”

Section: A Characterizing Quantum Correlations From Simple Assumptionsmentioning

confidence: 99%

Quantum correlations from simple assumptions

Cabello

2019

Phys. Rev. A

Self Cite

View full text Add to dashboard Cite

We address the problem of deriving the set of quantum correlations for every Bell and Kochen-Specker (KS) contextuality scenario from simple assumptions. We show that the correlations that are possible according to quantum theory are equal to those possible under the assumptions that there is a nonempty set of correlations for every KS scenario and a statistically independent realization of any two KS experiments. The proof uses tools of the graph-theoretic approach to correlations and deals with Bell nonlocality and KS contextuality in a unified way.

show abstract

Section: A Characterizing Quantum Correlations From Simple Assumptionsmentioning

confidence: 99%

Quantum correlations from simple assumptions

Cabello

2019

Phys. Rev. A

Self Cite

View full text Add to dashboard Cite

show abstract

“…So far, all proposed principles for quantum non-local correlations, including no-signalling [2], information causality [4], macroscopic locality [5] and local orthogonality [6], have failed to identify the set of quantum correlations, even for the simplest Bell scenario [7]. However, one principle, called the totalitarian principle [8] or the principle of plenitude [9], is able to select the quantum correlations for all the scenarios where Bell non-locality or Kochen–Specker (KS) contextuality can happen, under the assumption that the observables are ideal [10]. Ideal observables are those that, they and all their coarse–grained versions, can be measured ideally (i.e.…”

Section: Motivationmentioning

confidence: 99%

The quantum maxima for the basic graphs of exclusivity are not reachable in Bell scenarios

Porto,

Rabelo,

Terra Cunha

et al. 2024

Phil. Trans. R. Soc. A.

Self Cite

View full text Add to dashboard Cite

A necessary condition for the probabilities of a set of events to exhibit Bell non-locality or Kochen–Specker contextuality is that the graph of exclusivity of the events contains induced odd cycles with five or more vertices, called odd holes, or their complements, called odd antiholes. From this perspective, events whose graph of exclusivity are odd holes or antiholes are the building blocks of contextuality. For any odd hole or antihole, any assignment of probabilities allowed by quantum theory can be achieved in specific contextuality scenarios. However, here we prove that, for any odd hole, the probabilities that attain the quantum maxima cannot be achieved in Bell scenarios. We also prove it for the simplest odd antiholes. This leads us to the conjecture that the quantum maxima for any of the building blocks cannot be achieved in Bell scenarios. This result sheds light on why the problem of whether a probability assignment is quantum is decidable, while whether a probability assignment within a given Bell scenario is quantum is, in general, undecidable. This also helps to understand why identifying principles for quantum correlations is simpler when we start by identifying principles for quantum sets of probabilities defined with no reference to specific scenarios. This article is part of the theme issue ‘Quantum contextuality, causality and freedom of choice’.

show abstract

Kochen-Specker contextuality

et al. 2022

Self Cite

View full text Add to dashboard Cite

A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics is in conflict with classical models in which the result of a measurement does not depend on which other compatible measurements are jointly performed. Here compatible measurements are those that can be implemented simultaneously or, more generally, those that are jointly measurable. This conflict is generically called quantum contextuality. In this review, an introduction to this subject and its current status is presented. Several proofs of the Kochen-Specker theorem and different notions of contextuality are reviewed. How to experimentally test some of these notions is explained, and connections between contextuality and nonlocality or graph theory are discussed. Finally, some applications of contextuality in quantum information processing are reviewed.

show abstract

The problem of quantum correlations and the totalitarian principle

Cited by 3 publications

References 86 publications

Quantum correlations from simple assumptions

Quantum correlations from simple assumptions

The quantum maxima for the basic graphs of exclusivity are not reachable in Bell scenarios

Kochen-Specker contextuality

Contact Info

Product

Resources

About