Phase-space noncommutative formulation of Ozawa's uncertainty principle

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.

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Cited by in corpus (9)

• Phase-space noncommutative extension of the Robertson-Schroedinger formulation of Ozawa's uncertainty principle
• Klein-Gordon theory in noncommutative phase space
• Generalized phase-space description of non-linear Hamiltonian systems and the Harper-like dynamics
• Classical and statistical limits of the quantum singular oscillator
• Phase-space elementary information content of confined Dirac spinors
• Relativistic dispersion relation and putative metric structure in noncommutative phase-space
• Noncommutative Classical Dynamics on Velocity Phase Space and Souriau Formalism
• Emergent time crystals from phase-space noncommutative quantum mechanics
• Test of Space-Time Non-Commutativity at the Future Circular Collider