Quantum root-mean-square error and measurement uncertainty relations

Understand

Recent years have witnessed a controversy over Heisenberg's famous error-disturbance relation.

• Here we resolve the conflict by way of an analysis of the possible conceptualizations of measurement error and disturbance in quantum mechanics.
• We discuss two approaches to adapting the classic notion of root-mean-square error to quantum measurements.
• One is based on the concept of noise operator; its natural operational content is that of a mean deviation of the values of two observables measured jointly, and thus its applicability is limited to cases where such joint measurements are available.