Quantum uncertainties in sequential measurements under prediction and retrodiction

Abstract

In sequential measurements, we consider the prediction is as an inference of the subsequent observational data from the prior measurements, while the retrodiction is as an inference of the prior observational data from the subsequent measurements. We theoretically study the impact of the quantum backaction (QBA) in the sequential measurements on the inferred observational data from the prediction and retrodiction. The QBA of the prediction behaves like the disturbance caused by prior measurements affecting subsequent measurements, whereas the QBA of the retrodiction behaves through the disturbance caused by the subsequent measurements affecting the prior measurements. In particular, we consider the sequential measurements of two observables A and B, one after another, i.e., A first and B later, and then we theoretically formulate the quantum uncertainties in the value of these observables (for both prediction and retrodiction) as figures of merit for the disturbances. These results are illustrated in spin systems, where we present the dependence of the uncertainty in subsequent measurement on the prior measurement and vice versa. We further find a hint for beyond the stronger uncertainty relation. The work is finally extended to N-sequential measurements.Comment: 11 pages, 4 figure