Berlin 2014 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 3: Quanten-Information III

MP 3.1: Talk

Tuesday, March 18, 2014, 10:30–10:50, SPA SR125

Operationally-Motivated Uncertainty Relations for Joint Measurability and the Error-Disturbance Tradeoff — •Joseph M. Renes and Volkher B. Scholz — Institute for Theoretical Physics, ETH Zurich, Wolfgang-Pauli-Str. 27, 8093 Zurich, Switzerland

We derive uncertainty relations for both joint measurability and the error-disturbance tradeoff in terms of the probability of distinguishing the actual operation of a device from its hypothetical ideal. Our relations provide a clear operational interpretation of two main aspects of the uncertainty principle, as originally formulated by Heisenberg. The first restricts the joint measurability of observables, stating that noncommuting observables can only be simultaneously determined with a characteristic amount of indeterminacy. The second describes an error-disturbance tradeoff, noting that the more precise a measurement of one observable is made, the greater the disturbance to noncommuting observables.

Our relations are explicitly state-independent and valid for arbitrary observables of discrete quantum systems, and are also applicable to the case of position and momentum observables. They may be directly applied in information processing settings, for example to infer that devices which can faithfully transmit information regarding one observable do not leak information about conjugate observables to the environment. Though intuitively apparent from Heisenberg's original arguments, only limited versions of this statement have previously been formalized.