The Heisenberg uncertainty principle describes a basic restriction on an observer's ability of precisely predicting the measurement of a pair of noncommuting observables, and virtually is at the core of quantum mechanics. Herein, the aim is to study the entropic uncertainty relation (EUR) under the background of a Schwarzschild black hole and its control. Explicitly, dynamical features of the measuring uncertainty via entropy are developed in a practical model where a stationary particle interacts with its surrounding environment while another particle-serving as a quantum memory reservoir-undergoes free fall in the vicinity of the event horizon of the Schwarzschild space-time. It shows higher Hawking temperatures would give rise to an inflation of the entropic uncertainty on the measured particle. This is suggestive of the fact the measurement uncertainty is strongly correlated with degree of mixing present in the evolving particles. Additionally, based on information flow theory, a physical interpretation for the observed dynamical behaviors related with the entropic uncertainty in such a genuine scenario is provided. Finally, an efficient strategy is proposed to reduce the uncertainty by non-tracing-preserved operations. Therefore, our explorations may improve the understanding of the dynamic entropic uncertainty in a curved space-time, and illustrate predictions of quantum measurements in relativistic quantum information sciences.
The uncertainty principle is viewed as one of the appealing properties in the context of quantum mechanics, which intrinsically offers a lower bound with regard to the measurement outcomes of a pair of incompatible observables within a given system. In this letter, we attempt to observe entropic uncertainty in the presence of quantum memory under different local noisy channels. To be specific, we develop the dynamics of the measured uncertainty under local bit-phase-flipping (unital) and depolarization (nonunital) noise, respectively, and attractively put forward an effective strategy to manipulate its magnitude of the uncertainty of interest by means of parity-time symmetric (-symmetric) operations on the subsystem to be measured. It is interesting to find that there exist different evolution characteristics of the uncertainty in the channels considered here, i.e. the monotonic behavior in the nonunital channels, and the non-monotonic behavior in the unital channels. Moreover, the amount of the measured uncertainty can be reduced to some degree by properly modulating the -symmetric operations.
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