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.

arXiv commentv2, 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 (14)

• Heisenberg's Uncertainty Principle
• Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement
• Violation of Heisenberg's Measurement-Disturbance Relationship by Weak Measurements
• Experimental demonstration of a universally valid error-disturbance uncertainty relation in spin-measurements
• Uncertainty Relations for Noise and Disturbance in Generalized Quantum Measurements
• Prior information: how to circumvent the standard joint-measurement uncertainty relation
• Measuring measurement--disturbance relationships with weak values
• Physical content of Heisenberg's uncertainty relation: Limitation and reformulation
• Noise and disturbance in quantum mechanics
• Position measuring interactions and the Heisenberg uncertainty principle
• Sequential measurement of conjugate variables as an alternative quantum state tomography
• Simultaneous minimum-uncertainty measurement of discrete-valued complementary observables
• Maximal Accuracy and Minimal Disturbance in the Arthurs-Kelly Simultaneous Measurement Process
• Strong correspondence principle for joint measurement of conjugate observables

Cited by in corpus (16)

• Joint quantum measurements with minimum uncertainty
• Experimental test of Heisenberg's measurement uncertainty relation based on statistical distances
• Deriving tight error-trade-off relations for approximate joint measurements of incompatible quantum observables
• Uncertainties in Successive Measurements
• Error-Disturbance Trade-off in Sequential Quantum Measurements
• Precision optical displacement measurements using biphotons
• Improved Error-Tradeoff and Error-Disturbance Relations
• Experimental study of a phase-sensitive heterodyne detector
• Quantum state tomography from sequential measurement of two variables in a single setup
• Focusing in Arthurs-Kelly-type Joint Measurements with Correlated Probes
• Weak values and weak coupling maximizing the output of weak measurements
• Measures of disturbance and incompatibility for quantum measurements
• 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
• Postselection induced entanglement swapping from a vacuum--excitation entangled state to separate quantum systems
• Advances in Position-Momentum Entanglement: A Versatile Tool for Quantum Technologies