Disturbance trade-off principle for quantum measurements

Prabha Mandayam and M. D. Srinivas
Phys. Rev. A 90, 062128 – Published 23 December 2014

Abstract

We demonstrate a fundamental principle of disturbance tradeoff for quantum measurements, along the lines of the celebrated uncertainty principle: The disturbances associated with measurements performed on distinct yet identically prepared ensembles of systems in a pure state cannot all be made arbitrarily small. Indeed, we show that the average of the disturbances associated with a set of projective measurements is strictly greater than zero whenever the associated observables do not have a common eigenvector. For such measurements, we show an equivalence between disturbance tradeoff measured in terms of fidelity and the entropic uncertainty tradeoff formulated in terms of the Tsallis entropy (T2). We also investigate the disturbances associated with the class of nonprojective measurements, where the difference between the disturbance tradeoff and the uncertainty tradeoff manifests quite clearly.

  • Received 28 February 2014
  • Revised 18 October 2014

DOI:https://doi.org/10.1103/PhysRevA.90.062128

©2014 American Physical Society

Authors & Affiliations

Prabha Mandayam

  • Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India

M. D. Srinivas

  • Centre for Policy Studies, Mylapore, Chennai 600004, India

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Issue

Vol. 90, Iss. 6 — December 2014

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