The effect of non-Markovianity on the measurement-based uncertainty

Abstract

The uncertainty principle is one of fundamental traits in quantum mechanics, which essentially lies at the heart of quantum theory. The principle manifests that the measurement outcomes with respect to two incompatible observables cannot be predicted accurately. In fact, it can be expressed in terms of entropic measurement in the quantum information theory, since Berta et al. have indicated that uncertainty’s bound can be reduced when considering a particle as a quantum memory correlated with the particle to be measured. In this paper, we investigate the dynamical features of the entropic uncertainty within the non-Markovian regimes, and also compare several proposed bounds in such a scenario. We find that the uncertainty exhibits a non-monotonic behavior, and certify that the lower bound proposed by Adabi et al. is optimized. Besides, Stimulatingly, it turns out that the lower bound is not fully anti-correlated with the quantum correlation of the system, and associated with the A’s minimal conditional entropy $ {S}_{\mathrm{min}}^{A|B}$ . Besides, we offer a possible physical explanation for this behavior. Noteworthily, we propose a simple and working approach to manipulate the magnitude of the measurement uncertainty via a type of non-unitary operations.