Phase-space noncommutative extension of the Robertson-Schroedinger formulation of Ozawa's uncertainty principle
Dec 26, 2014
15 pages
Published in:
- Phys.Rev.D 91 (2015) 6, 065036
- Published: Mar 30, 2015
e-Print:
- 1412.7948 [quant-ph]
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Citations per year
Abstract: (APS)
We revisit Ozawa’s uncertainty principle (OUP) in the framework of noncommutative (NC) quantum mechanics. We derive a matrix version of OUP accommodating any NC structure in the phase space, and compute NC corrections to lowest order for two measurement interactions, namely the backaction evading quadrature amplifier and noiseless quadrature transducers. These NC corrections alter the nature of the measurement interaction, as a noiseless interaction may acquire noise, and an interaction of independent intervention may become dependent on the object system. However the most striking result is that noncommutativity may lead to a violation of the OUP itself. The NC corrections for the backaction evading quadrature amplifier reveal a new term which may potentially be amplified in such a way that the violation of the OUP becomes experimentally testable. On the other hand, the NC corrections to the noiseless quadrature transducer shows an incompatibility of this model with NC quantum mechanics. We discuss the implications of this incompatibility for NC quantum mechanics and for Ozawa’s uncertainty principle.Note:
- 31 pages
- 03.65.Ta
- 02.40.Gh
- phase space: noncommutative
- uncertainty relations
- quantum mechanics
- transducer
- amplifier
- noise
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