Almost quantum correlations

Abstract

There have been a number of attempts to derive the set of quantum non-local correlations from reasonable physical principles. Here we introduce $\tilde{Q}$, a set of multipartite supra-quantum correlations that has appeared under different names in fields as diverse as graph theory, quantum gravity and quantum information science. We argue that $\tilde{Q}$ may correspond to the set of correlations of a reasonable physical theory, in which case the research program to reconstruct quantum theory from device-independent principles is met with strong obstacles. In support of this conjecture, we prove that $\tilde{Q}$ is closed under classical operations and satisfies the physical principles of Non-Trivial Communication Complexity, No Advantage for Nonlocal Computation, Macroscopic Locality and Local Orthogonality. We also review numerical evidence that almost quantum correlations satisfy Information Causality.

15+2 pages, 1 figure

References in corpus (8)

• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• A derivation of quantum theory from physical requirements
• Recovering part of the quantum boundary from information causality
• (Non-)Contextuality of Physical Theories as an Axiom
• Macroscopically local correlations can violate information causality
• Maximally nonlocal theories cannot be maximally random
• Bounding quantum contextuality with lack of third-order intereference
• Generalizing Quantum Mechanics for Quantum Spacetime

Cited by in corpus (11)

• Maximally nonlocal theories cannot be maximally random
• What does an experimental test of quantum contextuality prove or disprove?
• Maximum nonlocality in the (3,2,2) scenario
• Bounding quantum contextuality with lack of third-order intereference
• Simple explanation of the quantum limits of genuine $n$-body nonlocality
• Bell scenarios with communication
• Consequences and applications of the completeness of Hardy's nonlocality
• Nonlocality Distillation and Quantum Voids
• The Information Content of Systems in General Physical Theories
• Many-box locality
• Composing decoherence functionals