Bell operator and Gaussian squeezed states in noncommutative quantum mechanics

2015, December 11
Catarina Bastos (Lisbon, IST), Alex E. Bernardini (Sao Carlos Federal U.), Orfeu Bertolami (Porto U.), Nuno Costa Dias (GFMUL, Lisbon & Lusofona U.), João Nuno Prata (Escola Superior Nautica Infante D. Henrique)
Phys.Rev. D93 (2016) no.10, 104055
  1512.03792.pdf

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.