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Phase-space noncommutative formulation of Ozawa’s uncertainty principle

2014; American Physical Society; Volume: 90; Issue: 4 Linguagem: Inglês

10.1103/physrevd.90.045023

1550-7998

Catarina Bastos, Alex E. Bernardini, Orfeu Bertolami, Nuno Costa Dias, João Nuno Prata,

Advanced Operator Algebra Research

Ozawa's measurement-disturbance relation is generalized to a phase-space noncommutative extension of quantum mechanics. It is shown that the measurement-disturbance relations have additional terms for backaction evading quadrature amplifiers and for noiseless quadrature transducers. Several distinctive features appear as a consequence of the noncommutative extension: measurement interactions which are noiseless, and observables which are undisturbed by a measurement, or of independent intervention in ordinary quantum mechanics, may acquire noise, become disturbed by the measurement, or no longer be an independent intervention in noncommutative quantum mechanics. It is also found that there can be states which violate Ozawa's universal noise-disturbance trade-off relation, but verify its noncommutative deformation.