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arXiv:quant-ph/0312006 · Physics Letters A

Noise and disturbance in quantum measurement

Paul Busch, Teiko Heinonen, PEKKA J. LAHTI

Published Dec 6, 2003• 48 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2003.11.036

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The inherent connection between noise and disturbance is one of the most fundamental features of quantum measurements. In the two well-known extreme cases a measurement either makes no disturbance but then has to be totally noisy or is as accurate as possible but then has to disturb so much that all subsequent measurements become redundant. Most of the measurements are, however, somewhere between these two extremes. We derive a structural connection between certain order relations defined on observables and channels, and we explain how this connection properly explains the trade-off between noise and disturbance. A link to a quantitative noise-disturbance relation is demonstrated.
The Heisenberg uncertainty relation for measurement noise and disturbance states that any position measurement with noise /spl epsiv/ brings the momentum disturbance not less than h/2/spl epsiv/. However, this relation holds only for restricted class of measurements. Here, a generalized uncertainty relation for measurement noise and disturbance is formalized and proven, which holds for all the possible quantum measurements. For this purpose, all the possible quantum measurements are characterized by naturally acceptable axioms. The measurement noise and disturbance are defined rigorously for any such general quantum measurements.