Bell inequalities for arbitrarily high dimensional systems

Abstract

We develop a novel approach to Bell inequalities based on a constraint that the correlations exhibited by local realistic theories must satisfy. This is used to construct a family of Bell inequalities for bipartite quantum systems of arbitrarily high dimensionality which are strongly resistant to noise. In particular our work gives an analytic description of numerical results of D. Kaszlikowski, P. Gnacinski, M. Zukowski, W. Miklaszewski, A. Zeilinger, Phys. Rev. Lett. {\bf 85}, 4418 (2000) and T. Durt, D. Kaszlikowski, M. Zukowski, quant-ph/0101084, and generalises them to arbitrarily high dimensionality.

6 pages, latex

References in corpus (3)

• Violations of local realism with quNits up to N=16
• Entangled qutrits violate local realism stronger than qubits - an analytical proof
• Clauser-Horne inequality for qutrits

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• Full Bell locality of a noisy state for $N\ge 3$ nonlocally entangled qudits
• Maximal Entanglement: Applications in Quantum Information and Particle Physics
• Measurement incompatibility at all remote parties do not always permit Bell nonlocality
• Investigating nonclassicality of many qutrits by symmetric two-qubit operators
• Particle Collisions & Quantum Entanglement in High-Energy Collisions
• Time-resolved certification of frequency-bin entanglement over multi-mode channels
• Signaling between time steps does not allow for nonlocality beyond hidden nonlocality
• Role of Steering Inequality In Quantum Key Distribution Protocol
• Single photonic qutrit in a collective Rydberg polariton
• Multisetting Bell inequalities for $N$ spins-1 avoiding KS contradiction
• Preparation of two-particle total hyperfine spin singlet states via spin-changing dynamics
• Freezing dynamics of entanglement and nonlocality for qutrit-qutrit ($3\otimes 3$) quantum systems
• Second-second moments and two observers testing quantum nonlocality
• High-Dimensional Entanglement of Photonic Angular Qudits
• How Quantum is the Classical World?
• Wigner's approach enabled detection of multipartite nonlocality using all different bipartitions
• Conservation Laws For Every Quantum Measurement Outcome
• Quantum enhancement of qutrit dynamics through driving field and photonic band-gap crystal
• Effects of Topological Boundary Conditions on Bell Nonlocality
• Beating one bit of communication with and without quantum pseudo-telepathy
• Revealing the Boundary between Quantum Mechanics and Classical Model by EPR-Steering Inequality
• Using Linear Programming to Construct Better Criteria for Closing the Detection Loophole in Epr Experiments
• Quantum walk on a square lattice with identical particles
• An approach using geometric diagrams to generic Bell inequalities with multiple observables
• Certifying Numerical Decompositions of Compact Group Representations
• On the experimental violation of Mermin's inequality with imperfect measurements
• Qudit Clauser-Horne-Shimony-Holt Inequality and Nonlocality from Wigner Negativity
• Quantifying tolerance of a nonlocal multi-qudit state to any local noise
• Disproving hidden variable models with spin magnitude conservation
• New assessment on the nonlocality of correlation boxes
• High-dimensional entanglement between distant atomic ensemble memories
• Weak Classicality in Coupled N-Level Quantum Systems
• Trading symmetry for Hilbert-space dimension in Bell-inequality violation
• Quasi-Bell inequalities from symmetrized products of noncommuting qubit observables
• Geometrical aspects of qudits concerning Bell inequalities
• Realising high-dimensional quantum entanglement with orbital angular momentum
• Geometrical Bell inequalities for arbitrarily many qudits with different outcome strategies
• Revealing effects of local dimension on variable-range interacting model by connecting Lieb-Robinson bounds and multipartite entanglement
• Witness wedges in fidelity-deviation plane: separating teleportation advantage and Bell-inequality violation
• Quantum Random Number Generator based on Violations of the Free CHSH-3 Inequality
• Controlling nonlocality of bipartite qubit states via quantum channels
• Creating two-qudit maximally entangled quantum link through bulk
• On the separability criterion of bipartite states with certain non-Hermitian operators
• Binarisation-loophole-free observation of high-dimensional quantum nonlocality
• Colliders are not Testing Locality via Bell's Inequality nor Providing an Unconditional Proof of Entanglement
• Classifying Measurement Incompatibility under Classical Pre- and Post-Processing Operations