A classification of multipartite states by degree of non-locality

Abstract

We propose a novel form of classification of multipartite states, in terms of the maximum degree of non-locality they can exhibit under any choice of local observables. This uses the hierarchy of notions previously introduced by Abramsky and Brandenburger: strong contextuality, logical contextuality, and probabilistic contextuality. We study n-qubit pure states. We conjecture that for more than 2 parties, all entangled states are logically contextual. We prove a number of results in support of this conjecture: (1) We show that all permutation-symmetric states are logically non-local. (2) We study the class of balanced states with functional dependencies. These states are described by Boolean functions and have a rich structure, allowing a detailed analysis, which again confirms the conjecture in this case.

arXiv commentIn Proceedings QPL 2013, arXiv:1412.7917

References in corpus (6)

• Three qubits can be entangled in two inequivalent ways
• The Sheaf-Theoretic Structure Of Non-Locality and Contextuality
• Bell's theorem without inequalities and without probabilities for two observers
• Logical Bell Inequalities
• Inductive classification of multipartite entanglement under SLOCC
• Nonlocality of Symmetric States

Cited by in corpus (11)

• The contextual fraction as a measure of contextuality
• Extreme violation of local realism in quantum hypergraph states
• Scattering effect on entanglement propagation in RCFTs
• Extendability in the Sheaf-theoretic Approach: Construction of Bell Models from Kochen-Specker Models
• Consequences and applications of the completeness of Hardy's nonlocality
• Hardy is (almost) everywhere: nonlocality without inequalities for almost all entangled multipartite states
• On monogamy of non-locality and macroscopic averages: examples and preliminary results
• A representation of the wave function on the three-dimensional space
• Closing Bell: Boxing black box simulations in the resource theory of contextuality
• Sheaf-Theoretic Methods in Quantum Mechanics and Quantum Information Theory
• An Entanglement Monotone from the Contextual Fraction