Bell's theorem without inequalities and without probabilities for two observers

Abstract

A proof of Bell's theorem using two maximally entangled states of two qubits is presented. It exhibits a similar logical structure to Hardy's argument of ``nonlocality without inequalities''. However, it works for 100% of the runs of a certain experiment. Therefore, it can also be viewed as a Greenberger-Horne-Zeilinger-like proof involving only two spacelike separated regions.

REVTeX, 4 pages

References in corpus (6)

• Experimental quantum teleportation
• Hidden Variables and the Two Theorems of John Bell
• Complete quantum teleportation with a Kerr nonlinearity
• Optical Bell Measurement by Fock Filtering
• A scheme for total quantum teleportation
• Nonlocality without inequalities has not been proved for maximally entangled states

Cited by in corpus (64)

• Quantum entanglement
• Bell nonlocality
• Multi-photon entanglement and interferometry
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• Kochen-Specker Contextuality
• Quantum Pseudo-Telepathy
• "All versus nothing" inseparability for two observers
• All-Versus-Nothing Violation of Local Realism by Two-Photon, Four-Dimensional Entanglement
• Experimental demonstration of the Einstein-Podolsky-Rosen steering game based on the All-Versus-Nothing proof
• "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
• Quantum advantages in classically defined tasks
• Proofs of the Kochen-Specker theorem based on a system of three qubits
• Quantum Proofs
• Bell's theorem without inequalities and without alignments
• Stronger two-observer all-versus-nothing violation of local realism
• Tests of Bell Inequalities
• Parity proofs of the Kochen-Specker theorem based on the 24 rays of Peres
• Graph-theoretic strengths of contextuality
• Bipartite all-versus-nothing proofs of Bell's theorem with single-qubit measurements
• Deterministic and Efficient Quantum Cryptography Based on Bell's Theorem
• A classification of multipartite states by degree of non-locality
• Loophole-free Bell's experiment and two-photon all-versus-nothing violation of local realism
• Hardy is (almost) everywhere: nonlocality without inequalities for almost all entangled multipartite states
• GHZ paradoxes based on an even number of qubits
• Entanglement-induced provable and robust quantum learning advantages
• Equivalence between face nonsignaling correlations, full nonlocality, all-versus-nothing proofs, and pseudotelepathy
• Multipartite quantum cryptography based on the violation of Svetlichny's inequality
• Possibilities Determine the Combinatorial Structure of Probability Polytopes
• Simplest bipartite perfect quantum strategies
• Two-player quantum pseudo-telepathy based on recent all-versus-nothing violations of local realism
• Nonlocality without inequalities for almost all entangled states of any quantum system
• Greenberger-Horne-Zeilinger-type violation of local realism by mixed states
• Quantum Magic Rectangles: Characterization and Application to Certified Randomness Expansion
• Reply to Marinatto's comment on "Bell's theorem without inequalities and without probabilities for two observers"
• All-versus-nothing proofs with n qubits distributed between m parties
• Hardy-like Quantum Pigeonhole Paradox and the Projected-Coloring Graph State
• Schrödinger's paradox and proofs of nonlocality using only perfect correlations
• Proposed all-versus-nothing violation of local realism in the Kitaev spin-lattice model
• Comment on "Bell's Theorem without Inequalities and without Probabilities for Two Observers"
• Some Comments on Three Suggested Postulates for Quantum Theory
• Irreducible magic sets for $n$-qubit systems
• Experimental Quantum Advantage in the Odd-Cycle Game
• A computational test of quantum contextuality, and even simpler proofs of quantumness
• Entanglement measures for two-particle quantum histories
• EPR-Bell-Schrödinger proof of nonlocality using position and momentum
• Bell's Theorem and Random Variables
• Two fundamental solutions to the rigid Kochen-Specker set problem and the solution to the minimal Kochen-Specker set problem under one assumption
• Nonclassical Structures within the N-qubit Pauli Group
• Optimal conversion of Kochen-Specker sets into bipartite perfect quantum strategies
• Deterministic all-versus-nothing proofs of Bell nonlocality based on non-stabilizer states
• Beating one bit of communication with and without quantum pseudo-telepathy
• Phase transitions in (2 + 1)D subsystem-symmetric monitored quantum circuits
• Bell's theorem without inequalities and without unspeakable information
• Quantitative comparison of quantum pseudo-telepathy games and Bell inequalities
• Impact of imperfect measurements on multi-party quantum key distribution
• From EPR, Schrödinger paradox to nonlocality based on perfect correlation
• Investigations in quantum games using EPR-type set-ups
• Optimal GHZ Paradox for Three Qubits
• Two Party Non-Local Games