"All versus nothing" inseparability for two observers

Abstract

A recent proof of Bell's theorem without inequalities [A. Cabello, Phys. Rev. Lett. 86, 1911 (2001)] is formulated as a Greenberger-Horne-Zeilinger-like proof involving just two observers. On one hand, this new approach allows us to derive an experimentally testable Bell inequality which is violated by quantum mechanics. On the other hand, it leads to a new state-independent proof of the Kochen-Specker theorem and provides a wider perspective on the relations between the major proofs of no-hidden-variables.

REVTeX, 4 pages

References in corpus (2)

• Experimental quantum teleportation
• Hidden Variables and the Two Theorems of John Bell

Cited by in corpus (76)

• Quantum entanglement
• Multi-photon entanglement and interferometry
• Non-locality and Communication Complexity
• Experimentally testable state-independent quantum contextuality
• Maximally Non-Local and Monogamous Quantum Correlations
• Bell's theorem with and without inequalities for the three-qubit Greenberger-Horne-Zeilinger and W states
• Kochen-Specker Contextuality
• Experimental realization of one-way quantum computing with two-photon four-qubit cluster states
• Simple explanation of the quantum violation of a fundamental inequality
• Quantum Pseudo-Telepathy
• Realization of All-or-nothing-type Kochen-Specker Experiment with Single Photons
• All-Versus-Nothing Violation of Local Realism by Two-Photon, Four-Dimensional Entanglement
• Realization and characterization of a 2-photon 4-qubit linear cluster state
• Experimental demonstration of the Einstein-Podolsky-Rosen steering game based on the All-Versus-Nothing proof
• Testing foundations of quantum mechanics with photons
• "All-versus-nothing" nonlocality test of quantum mechanics by two-photon hyperentanglement
• Device-independent parallel self-testing of two singlets
• All-Versus-Nothing Violation of Local Realism for Two Entangled Photons
• All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering
• Enhancing the Violation of the Einstein-Podolsky-Rosen Local Realism by Quantum Hyper-entanglement
• Fully nonlocal quantum correlations
• Quantum Correlations are Tightly Bound by the Exclusivity Principle
• Fully nonlocal, monogamous, and random genuinely multipartite quantum correlations
• Converting contextuality into nonlocality
• Proofs of the Kochen-Specker theorem based on a system of three qubits
• Bell's theorem without inequalities and without alignments
• Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality
• Stronger two-observer all-versus-nothing violation of local realism
• Minimal true-implies-false and true-implies-true sets of propositions in noncontextual hidden variable theories
• New Kochen-Specker Sets in Four Dimensions
• Multigraph approach to quantum non-locality
• Device-independent quantum key distribution based on Bell inequalities with more than two inputs and two outputs
• Quantum correlations are stronger than all nonsignaling correlations produced by n-outcome measurements
• Bipartite Bell inequalities for hyperentangled states
• Device-Independent Quantum Key Distribution Based on the Mermin-Peres Magic Square Game
• Necessary detection efficiencies for secure quantum key distribution and bound randomness
• Probabilistic Generation of Quantum Contextual Sets
• Parity proofs of the Kochen-Specker theorem based on the 24 rays of Peres
• Bipartite all-versus-nothing proofs of Bell's theorem with single-qubit measurements
• The generalized Kochen-Specker theorem
• Deterministic and Efficient Quantum Cryptography Based on Bell's Theorem
• Graph-Theoretic Framework for Self-Testing in Bell Scenarios
• Bell non-locality and Kochen-Specker contextuality: How are they connected?
• Loophole-free Bell's experiment and two-photon all-versus-nothing violation of local realism
• Certifying sets of quantum observables with any full-rank state
• The future of secure communications: device independence in quantum key distribution
• GHZ paradoxes based on an even number of qubits
• Equivalence between face nonsignaling correlations, full nonlocality, all-versus-nothing proofs, and pseudotelepathy
• Entanglement-induced provable and robust quantum learning advantages
• Experimental Test of Irreducible Four-Qubit Greenberger-Horne-Zeilinger Paradox
• Multipartite quantum cryptography based on the violation of Svetlichny's inequality
• Concurrent Remote Entanglement with Quantum Error Correction
• Optimal and tight Bell inequalities for state-independent contextuality sets
• Two-player quantum pseudo-telepathy based on recent all-versus-nothing violations of local realism
• Simplest bipartite perfect quantum strategies
• Scalable Generation and Characterization of a Four-Photon Twelve-Qubit Hyperentangled State
• Upper bounds on key rates in device-independent quantum key distribution based on convex-combination attacks
• Quantum Magic Rectangles: Characterization and Application to Certified Randomness Expansion
• Greenberger-Horne-Zeilinger-type violation of local realism by mixed states
• Proposed all-versus-nothing violation of local realism in the Kitaev spin-lattice model
• Quantum nonlocality via local contextuality with qubit-qubit entanglement
• Maximum quantum nonlocality between systems that never interacted
• All-versus-nothing proofs with n qubits distributed between m parties
• Experimental Quantum Advantage in the Odd-Cycle Game
• Irreducible magic sets for $n$-qubit systems
• The simplest Kochen-Specker set
• Two fundamental solutions to the rigid Kochen-Specker set problem and the solution to the minimal Kochen-Specker set problem under one assumption
• Optimal conversion of Kochen-Specker sets into bipartite perfect quantum strategies
• Bell's theorem without inequalities and without unspeakable information
• Impact of imperfect measurements on multi-party quantum key distribution
• Twenty years of quantum contextuality at USTC
• A principle of quantumness
• Phase transitions in (2 + 1)D subsystem-symmetric monitored quantum circuits
• Supersinglets can be self-tested with perfect quantum strategies
• Simultaneous All-versus-Nothing Refutation of Local Realism and Noncontextuality by a Single System
• Two Party Non-Local Games