Bell operator and Gaussian squeezed states in noncommutative quantum mechanics

Abstract

One examines putative corrections to the Bell operator due to the noncommutativity in the phase-space. Starting from a Gaussian squeezed envelop whose time evolution is driven by commutative (standard quantum mechanics) and noncommutative dynamics respectively, one concludes that, although the time evolving covariance matrix in the noncommutative case is different from the standard case, the squeezing parameter dominates and there are no noticeable noncommutative corrections to the Bell operator. This indicates that, at least for squeezed states, the privileged states to test Bell correlations, noncommutativity versions of quantum mechnics remains as non-local as quantum mechanics itself.

16 pages

References in corpus (10)

• Entanglement in continuous variable systems: Recent advances and current perspectives
• Quantum information can be negative
• Determination of continuous variable entanglement by purity measurements
• Weyl-Wigner Formulation of Noncommutative Quantum Mechanics
• Entropic Gravity, Phase-Space Noncommutativity and the Equivalence Principle
• Phase-space noncommutative formulation of Ozawa's uncertainty principle
• Non-Canonical Phase-Space Noncommutativity and the Kantowski-Sachs singularity for Black Holes
• Phase-space noncommutative extension of the Robertson-Schroedinger formulation of Ozawa's uncertainty principle
• Exact master equation for a noncommutative Brownian particle
• Different operational meanings of continuous variable Gaussian entanglement criteria and Bell inequalities

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• Klein-Gordon theory in noncommutative phase space
• Squeezed coherent states for gravitational well in noncommutative space
• Quantum cloning and teleportation fidelity in the noncommutative phase-space
• Phase-space elementary information content of confined Dirac spinors
• Quantum information aspects of noncommutative quantum mechanics
• Collapsing Shells and Black Holes: a quantum analysis
• Path-integral action of a particle in the noncommutative phase-space
• Lattice oscillator model on noncommutative space: eigenvalues problem for the perturbation theory
• Emergent time crystals from phase-space noncommutative quantum mechanics
• Test of Space-Time Non-Commutativity at the Future Circular Collider