Bell operator and Gaussian squeezed states in noncommutative quantum mechanics

Author(s)

Bastos, Catarina ^[1] ; Bernardini, Alex E. ^[2] ; Bertolami, Orfeu ^{[3, 4]} ; Dias, Nuno Costa ^{[5, 6]} ; Prata, Joao Nuno ^[5]

Affiliation

^[1] Univ Lisbon, Inst Super Tecn, GoLP Inst Plasmas & Fusao Nucl, Ave Rovisco Pais 1, P-1049001 Lisbon - Portugal

^[2] Univ Fed Sao Carlos, Dept Fis, POB 676, BR-13565905 Sao Carlos, SP - Brazil

^[3] Univ Porto, Fac Ciencias, Dept Fis & Astron, Rua Campo Alegre 687, P-4169007 Oporto - Portugal

^[4] Ctr Fis Porto, Rua Campo Alegre, 687, P-4169007 Oporto - Portugal

^[5] Escola Super Naut Infante D Henrique, Ave Engn Bonneville Franco, P-2770058 Paco De Arcos - Portugal

^[6] UL, Grp Fis Matemat, Ave Prof Gama Pinto 2, P-1649003 Lisbon - Portugal

• Document type: Journal article
• Source: Physical Review D; v. 93, n. 10 MAY 26 2016.
• Web of Science Citations: 9

Abstract

We examine putative corrections to the Bell operator due to the noncommutativity in the phase space. Starting from a Gaussian squeezed envelope whose time evolution is driven by commutative (standard quantum mechanics) and noncommutative dynamics, respectively, we conclude 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 mechanics remain as nonlocal as quantum mechanics itself. (AU)

• FAPESP's process: 15/05903-4 - SU(2) x SU(2) bi-spinor structure entanglement and additional quantum correlations exhibited by Dirac-like systems as graphene and trapped ions
• Grantee: Alex Eduardo de Bernardini
• Support type: Regular Research Grants