Phase-space noncommutative formulation of Ozawa's uncertainty principle

TL;DR

This paper extends Ozawa's uncertainty principle to a phase-space noncommutative quantum mechanics framework, revealing new effects such as noiseless measurements becoming disturbed and violations of the original trade-off relations.

Contribution

It introduces a noncommutative extension of Ozawa's relation, uncovering novel measurement-disturbance phenomena and violations of universal trade-offs in quantum mechanics.

Findings

Measurement interactions can be noiseless yet disturbed in noncommutative QM.

States can violate Ozawa's original noise-disturbance relation but satisfy its noncommutative version.

Noncommutative effects lead to new measurement and disturbance behaviors.

Abstract

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.