Gisin's Theorem for Three Qubits

Abstract

We present a Theorem that all generalized Greenberger-Horne-Zeilinger states of a three-qubit system violate a Bell inequality in terms of probabilities. All pure entangled states of a three-qubit system are shown to violate a Bell inequality for probabilities; thus, one has Gisin's theorem for three qubits.

5 pages, 2 figures. v2: journal-ref is added and some corrections are made

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• Quantum entanglement
• Research on Hidden Variable Theories: a review of recent progresses
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• All entangled pure states violate a single Bell's inequality
• Quantum nonlocality of four-qubit entangled states
• Gisin's Theorem for Arbitrary Dimensional Multipartite States
• Trade-off Relations of Bell Violations among Pairwise Qubit Systems
• Two-Setting Bell Inequalities for Many Qubits
• Experimental Determination of Entanglement for Arbitrary Pure States
• Identification of three-qubit entanglement
• Complete proof of Gisin's theorem for three qubits
• Tight upper bound for the maximal quantum value of the Svetlichny operators
• Bell inequalities for multipartite qubit quantum systems and their maximal violation
• Bell inequalities for three particles
• Quantum Nonlocality of N-qubit W states
• Nonlocality of three-qubit Greenberger-Horne-Zeilinger-symmetric states
• Multiparticle Interference, GHZ Entanglement, and Full Counting Statistics
• Gisin's theorem for two d-dimensional systems based on the Collins-Gisin-Linden-Masser-Popescu inequality
• Factorized Three-body S-Matrix Restrained by Yang-Baxter Equation and Quantum Entanglements
• Multi-Component Bell Inequality and its Violation for Continuous Variable Systems
• Conditional quantum nonlocality in dimeric and trimeric arrays of organic molecules
• Continuous Multipartite Entangled State in Wigner Representation and the Violation of Zukowski-Brukner Inequality
• Tight Correlation-Function Bell Inequality for Multipartite $d$-Dimensional System
• Bell inequality for qubits based on the Cauchy-Schwarz inequality
• Concurrence of assistance and Mermin inequality on three-qubit pure states
• Violation of generalized Bell inequality and its optimal measurement settings
• Mesoscopic and macroscopic quantum correlations in photonic, atomic and optomechanical systems
• Scalable Bell inequalities for multiqubit systems
• Proposed all-versus-nothing violation of local realism in the Kitaev spin-lattice model
• Mean first-passage time of quantum transition processes
• Verifying Hierarchic Multipartite and Network Nonlocalities with a Unified Method
• Relation between three-qubit entanglement invariants and two-qubit concurrence
• Chain of Hardy-type local reality constraints for $n$ qubits
• Undetectable Werner states using linear Bell inequalities
• Correlations, Bell Inequality Violation & Quantum Entanglement
• Bipartite Bell Inequality and Maximal Violation
• Nonlocality of two-qubit and three-qubit Schmidt-Correlated states
• Characterization of multiqubit pure-state entanglement
• Testing quantum entanglement with local measurement
• The Hardy's nonlocality argument
• Investigations in quantum games using EPR-type set-ups
• The CHSH-type inequalities for infinite-dimensional quantum systems
• Characterization of four-qubit states via Bell inequalities
• Trade-off relations on CHSH tests for multi-qubit pure states
• Testing Genuine Multipartite Nonlocality via an Inflated Network with Multi-copy Entangled States