Correlations between detectors allow violation of the Heisenberg noise-disturbance principle for position and momentum measurements

Abstract

Heisenberg formulated a noise-disturbance principle stating that there is a tradeoff between noise and disturbance when a measurement of position and a measurement of momentum are performed sequentially, and another principle imposing a limitation on the product of the uncertainties in a joint measurement of position and momentum. We prove that the former, the Heisenberg sequential noise-disturbance principle, holds when the detectors are assumed to be initially uncorrelated from each other, but that it can be violated for some properly correlated initial preparations of the detectors.

v2, minor changes. "Resolution" substitutes "sensitivity," according to current usage; v3, changed title and abstract, simplified derivation, corrected an error about the joint measurement, extra appendix to appear as part of a longer version of the paper

References in corpus (4)

• Heisenberg's Uncertainty Principle
• Measuring measurement--disturbance relationships with weak values
• Sequential measurement of conjugate variables as an alternative quantum state tomography
• Strong correspondence principle for joint measurement of conjugate observables

Cited by in corpus (6)

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• Focusing in Arthurs-Kelly-type Joint Measurements with Correlated Probes
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• Effects of the free evolution in the Arthurs-Kelly model of simultaneous measurement and in the retrodictive predictions of the Heisenberg uncertainty relations
• Quantum enhanced beam tracking surpassing the Heisenberg uncertainty limit
• Advances in Position-Momentum Entanglement: A Versatile Tool for Quantum Technologies