Bell's theorem with and without inequalities for the three-qubit Greenberger-Horne-Zeilinger and W states

Abstract

A proof of Bell's theorem without inequalities valid for both inequivalent classes of three-qubit entangled states under local operations assisted by classical communication, namely Greenberger-Horne-Zeilinger (GHZ) and W, is described. This proof leads to a Bell inequality that allows more conclusive tests of Bell's theorem for three-qubit systems. Another Bell inequality involving both tri- and bipartite correlations is introduced which illustrates the different violations of local realism exhibited by the GHZ and W states.

REVTeX4, 5 pages, 3 figures

References in corpus (3)

• All multipartite Bell correlation inequalities for two dichotomic observables per site
• New optimal tests of quantum nonlocality
• "All versus nothing" inseparability for two observers

Cited by in corpus (88)

• Circuit Quantum Electrodynamics
• Perfect Teleportation and Superdense Coding With W-States
• Efficient engineering of multi-atom entanglement through single-photon detections
• Nonlocality of cluster states of qubits
• Deterministic Dicke state preparation with continuous measurement and control
• Experimental violation of Svetlichny's inequality
• Experimental violation of a cluster state Bell inequality
• GHZ-type and W-type entangled coherent states: generation and Bell-type inequality tests without photon counting
• Family of Zeilinger-Horne-Greenberger "W" states lead to stronger nonclassicality than family of Greenberger-Horne-Zeilinger "GHZ" states
• The Inflation Technique for Causal Inference with Latent Variables
• Scheme for the generation of an entangled four-photon W-state
• A Comprehensive Review of Quantum Random Number Generators: Concepts, Classification and the Origin of Randomness
• Polarization Entangled W State using Parametric Down-Conversion
• Testing the Structure of Multipartite Entanglement with Bell Inequalities
• The states of W-class as shared resources for perfect teleportation and superdense coding
• Extreme nonlocality with one photon
• Semidefinite tests for quantum network topologies
• Proposal for generating and detecting multi-qubit GHZ states in circuit QED
• Joint remote state preparation (JRSP) of two-qubit equatorial state in quantum noisy channels
• Error mitigation for variational quantum algorithms through mid-circuit measurements
• Nonlocality of Symmetric States
• Rydberg superatoms: An artificial quantum system for quantum information processing and quantum optics
• Super-radiant and Sub-radiant Cavity Scattering by Atom Arrays
• The controlled SWAP test for determining quantum entanglement
• Tripartite entanglement: Foundations and applications
• New Possibilities for Testing Local Realism in High Energy Physics
• Three-particle entanglement versus three-particle nonlocality
• Pictures of Processes: Automated Graph Rewriting for Monoidal Categories and Applications to Quantum Computing
• Generation of Three-Qubit Entangled W-State by Nonlinear Optical State Truncation
• Three-Photon Discrete-Energy-Entangled W State in Optical Fiber
• JRSP of three-particle state via three tripartite GHZ class in quantum noisy channels
• Measurement-driven navigation in many-body Hilbert space: Active-decision steering
• Feasibility of loophole-free nonlocality tests with a single photon
• Preparing Greenberger-Horne-Zeilinger and $W$ states on a long-range Ising spin model by global controls
• On the entanglement structure in quantum cloning
• The dynamic behaviors of local quantum uncertainty for three-qubit X states under decoherence channels
• Complete proof of Gisin's theorem for three qubits
• Systems Architecture for Quantum Random Access Memory
• Bound on Hardy's non-locality from the principle of Information Causality
• Nonlocality of $W$ and Dicke states subject to losses
• Generation of any superposition of Dicke state of excitons in coupled quantum dots
• Distinction of Tripartite Greenberger-Horne-Zeilinger and W States Entangled in Time (or Energy) and Space
• Nonlocality without inequality for almost all two-qubit entangled state based on Cabello's nonlocality argument
• Generation of n-qubit W states using Spin Torque
• Persistence of nonlocality for bipartite quantum spin systems
• Interaction-Free Effects Between Distant Atoms
• Graph-theoretic strengths of contextuality
• Work extraction from tripartite entanglement
• Nonlocality without inequality for spin-s system
• Scheme for preparation of W state via cavity QED
• Unified generation and fast emission of arbitrary single-photon multimode $W$ states
• Criteria for non-$k$-separability of $n$-partite quantum states
• Nonlocal Position Changes of a Photon Revealed by Quantum Routers
• Quantum correlations on the no-signaling boundary: self-testing and more
• Device and semi-device independent random numbers based on non-inequality paradox
• Device-independent bounds from Cabello's nonlocality argument
• EPR argument and Bell inequalities for Bose-Einstein spin condensates
• Realism and single-quanta nonlocality
• General entanglement
• Bounding the persistency of the nonlocality of W states
• Local Orthogonality provides better upper bound for Hardy's nonlocality
• Tight upper bound for the maximal expectation value of the Mermin operators
• Single photon generation and non-locality of perfect W-state
• Realistic limits on the nonlocality of an N-partite single-photon superposition
• Generation of polarization entanglement via the quantum Zeno effect
• Strong coupling of two interacting excitons confined in a nanocavity-quantum-dot system
• Relations among $k$-ME concurrence, negativity, polynomial invariants, and tangle
• The relation between Hardy's non-locality and violation of Bell inequality
• Chain of Hardy-type local reality constraints for $n$ qubits
• Classifying space for quantum contextuality
• Geometric extension of Clauser-Horne inequality to more qubits
• Switchable selective interactions in a Dicke Model with Driven Biased term
• Multipartite States under Elementary Local Operations
• Geometric Multiaxial Representation of N-qubit Mixed Symmetric Separable States
• Generalising multipartite concentratable entanglement for practical applications: mixed, qudit, and optical states
• Detection Efficiency Bounds in (Semi-)Device-Independent Scenarios
• Hardy-type paradoxes for an arbitrary symmetric bipartite Bell scenario
• Deep Quantum Graph Dreaming: Deciphering Neural Network Insights into Quantum Experiments
• Generation of perfectly entangled two and three qubits states by classical random interaction
• Hardy's argument and successive spin-s measurements
• Deterministic all-versus-nothing proofs of Bell nonlocality based on non-stabilizer states
• Multipartite entanglement classes of a multiport beam-splitter
• The Hardy's nonlocality argument
• Stabilizer Rényi Entropy for Translation-Invariant Matrix Product States
• Hexagons govern three-qubit contextuality
• Energy entanglement in neutron interferometry
• Scheme for demonstrating Bell theorem in tripartite entanglement between atomic ensembles
• Degrees, Levels, and Profiles of Contextuality