Robertson-Schroedinger type formulation of Ozawa's noise-disturbance uncertainty principle

Abstract

In this work we derive a matrix formulation of a noise-disturbance uncertainty relation, which is akin to the Robertson-Schrödinger uncertainty principle. Our inequality is stronger than Ozawa's uncertainty principle and takes noise-disturbance correlations into account. Moreover, we show that, for certain types of measurement interactions, it is covariant with respect to linear symplectic transformations of the noise and disturbance operators.

5 pages, revtex4

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• Proof of Heisenberg's error-disturbance relation
• How well can one jointly measure two incompatible observables on a given quantum state?
• Joint quantum measurements with minimum uncertainty
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