State-Dependent Approach to Entropic Measurement-Disturbance Relations

Abstract

Heisenberg's intuition was that there should be a tradeoff between measuring a particle's position with greater precision and disturbing its momentum. Recent formulations of this idea have focused on the question of how well two complementary observables can be jointly measured. Here, we provide an alternative approach based on how enhancing the predictability of one observable necessarily disturbs a complementary one. Our measurement-disturbance relation refers to a clear operational scenario and is expressed by entropic quantities with clear statistical meaning. We show that our relation is perfectly tight for all measurement strengths in an existing experimental setup involving qubit measurements.

9 pages, 2 figures. v4: published version

References in corpus (4)

• Heisenberg's Uncertainty Principle
• Operational constraints on state-dependent formulations of quantum error-disturbance trade-off relations
• Entropic information-disturbance tradeoff
• Operationally-Motivated Uncertainty Relations for Joint Measurability and the Error-Disturbance Tradeoff

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