Nonlocality of cluster states of qubits

Abstract

We investigate cluster states of qubits with respect to their non-local properties. We demonstrate that a Greenberger-Horne-Zeilinger (GHZ) argument holds for any cluster state: more precisely, it holds for any partial, thence mixed, state of a small number of connected qubits (five, in the case of one-dimensional lattices). In addition, we derive a new Bell inequality that is maximally violated by the 4-qubit cluster state and is not violated by the 4-qubit GHZ state.

5 pages; paragraph V.B contains a comparison with Guehne et al., quant-ph/0410059

References in corpus (14)

• Persistent entanglement in arrays of interacting particles
• Measurement-based quantum computation with cluster states
• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• Multi-party entanglement in graph states
• Optical quantum computation using cluster states
• All multipartite Bell correlation inequalities for two dichotomic observables per site
• Bell's theorem for general N-qubit states
• Quantum error-correcting codes associated with graphs
• Valence Bond Solids for Quantum Computation
• Bell's theorem with and without inequalities for the three-qubit Greenberger-Horne-Zeilinger and W states
• Spectral decomposition of Bell's operators for qubits
• Do all pure entangled states violate Bell's inequalities for correlation functions?
• Gisin's Theorem for Three Qubits
• Quantum codewords contradict local realism

Cited by in corpus (77)

• Bell nonlocality
• Entanglement detection
• Experimental entanglement of six photons in graph states
• Experimental Analysis of a 4-Qubit Cluster State
• Entanglement Detection in the Stabilizer Formalism
• Bell Inequalities for Graph States
• Experimental violation of Svetlichny's inequality
• Experimental violation of a cluster state Bell inequality
• Contextuality and Wigner function negativity in qubit quantum computation
• Testing the Structure of Multipartite Entanglement with Bell Inequalities
• Experimental Realization of a Controlled-NOT Gate with Four-Photon Six-Qubit Cluster States
• Experimental violation of multipartite Bell inequalities with trapped ions
• Quantum states with a positive partial transpose are useful for metrology
• All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering
• Efficient Verification of Hypergraph States
• General framework for verifying pure quantum states in the adversarial scenario
• Device-independent tomography of multipartite quantum states
• Entanglement and nonclassical properties of hypergraph states
• Fully nonlocal quantum correlations
• Nonlocality and entanglement in qubit systems
• Quantum nonlocality of four-qubit entangled states
• Two-setting Bell Inequalities for Graph States
• Cluster-type entangled coherent states
• Autonomous multipartite entanglement engines
• Mermin inequalities for perfect correlations
• On the local and non-local content of bipartite qubit and qutrit correlations
• Changing the circuit-depth complexity of measurement-based quantum computation with hypergraph states
• Entanglement in eight-qubit graph states
• Bell inequalities for Continuous-Variable Measurements
• Discriminating multi-partite entangled states
• Increasing the statistical significance of entanglement detection in experiments
• Two-Setting Bell Inequalities for Many Qubits
• Generalized Ardehali-Bell inequalities for graph states
• One-way quantum computation with two-photon multiqubit cluster states
• Modeling Pauli measurements on graph states with nearest-neighbor classical communication
• Generation of two-dimensional cluster states by using high-finesse bimodal cavities
• Macroscopic bound entanglement in thermal graph states
• Experimental generation of a high-fidelity four-photon linear cluster state
• A scheme for tunable quantum phase gate and effective preparation of graph-state entanglement
• Exploring Bell inequalities for the device-independent certification of multipartite entanglement depth
• Bipartite all-versus-nothing proofs of Bell's theorem with single-qubit measurements
• Incompatible local hidden-variable models of quantum correlations
• A Witness of Multipartite Entanglement Strata
• Quantum computational advantage attested by nonlocal games with the cyclic cluster state
• One-way quantum computation via manipulation of polarization and momentum qubits in two-photon cluster states
• Practical and efficient experimental characterization of multiqubit stabilizer states
• Experimental Test of Bell inequalities with Six-Qubit Graph States
• Genuine multipartite nonlocality of entangled thermal states
• Experimental Test of Irreducible Four-Qubit Greenberger-Horne-Zeilinger Paradox
• Generation of four-photon polarization entangled state based on EPR entanglers
• Graph states in phase space
• Bell-type inequality and quantum nonlocality in four-qubit systems
• The criterion for maximally entangled four-qubit state
• Multipartite entangled states with two bosonic modes and qubits
• Entanglement Purification of Hypergraph States
• Bell's Inequalities: Foundations and Quantum Communication
• Scalable Bell inequalities for multiqubit systems
• Greenberger-Horne-Zeilinger-type violation of local realism by mixed states
• Generating multipartite nonlocality to benchmark quantum computers
• All-versus-nothing proofs with n qubits distributed between m parties
• Quantum Random State Generation with Predefined Entanglement Constraint
• Normalizer Circuits and Quantum Computation
• Discrimination strategies for inequivalent classes of multipartite entangled states
• Undetectable Werner states using linear Bell inequalities
• On the logical structure of Bell theorems without inequalities
• Correlations, Bell Inequality Violation & Quantum Entanglement
• Stabilizer states and local realism
• Efficient scheme for one-way quantum computing in thermal cavities
• The genuinely multipartite nonlocality of graph states is model-dependent
• Robustness of Bell Violation of Graph States to Qubit Loss
• Exploring Bell nonlocality of quantum networks with stabilizing and logical operators
• Self-Testing Graph States Permitting Bounded Classical Communication
• Optimal GHZ Paradox for Three Qubits
• Maximally nonlocal subspaces
• Blindly Verifying Unknown Entanglement without State Tomography
• On a different expression of the classical limit of quantum mechanics
• No-cost Bell nonlocality certification from quantum tomography and its applications in quantum-magic-resource witnessing