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 phasespace. 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 nonlocal as quantum mechanics itself.

Quantum information aspects of noncommutative quantum mechanics

“…The results obtained in Ref. [32] indicate that the non-locality encountered in the NC case is qualitatively similar to the one of the usual QM.…”

“…From the perspective of a deformed Heisenberg-Weyl algebra of QM [2,3,4], several issues on NC QM related to missing information in gaussian quantum systems [5,6,7], quantum correlations and information collapse [8,9,10], and violations of the uncertainty relations [11,12,13,14] have been investigated.…”

“…obtained by turning on the NC algebra [5,6,11]. In the simplified scenario where Wigner functions are identified with gaussian functions, if Σ denotes the covariance matrix of W ρ and Σ that of W ρ, then the two are related by:…”

Generalized Lewis-Riesenfeld invariance for dynamical effective mass in jammed granullar media under a potential well in non-commutative space

“…There is a consensus that the fundamental concept of space-time is mostly compatible with quantum theory in noncommutative space. It has become a Gospel that the physics in Planck-scale will exhibit the noncommutative structure of space [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. However, lack of any direct experimental evidence is the major criticism for the unified quantum theory of gravity.…”

Phase-space elementary information content of confined Dirac spinors

“…Enlarging the access to elementary information features of physical systems without affecting the predictive power of quantum mechanics, the Wigner phase-space representation [1][2][3][4] of quantum mechanics has currently shed some light on the investigation of the frontiers between classical and quantum descriptions of Nature [5][6][7][8]. Besides its ferramental pragmatic utility demanded by optical quantum mechanics [9], in the theoretical front, the Wigner quantum mechanics has also worked as a robust support for the non-commutative quantum mechanics [10][11][12][13][14][15][16][17][18][19], for the description of the flux of quantum information in the phase-space [20][21][22][23] and, more generically, for probing quantumness and classicality for a relevant set of anharmonic quantum systems [22,24,25] as well as for quantitative modeling beyond the quantum physical framework [26].…”