Entropic Uncertainty Relations in Quantum Physics

Dong Wang, Wei‐Nan Shi, Ross D. Hoehn +4 more

Abstract 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.

Iwo Białynicki‐Birula

G. M. Bosyk, M. Portesi, Steeve Zozor

Dong Wang, Fei Ming, Ai-Jun Huang +3 more

Abstract The uncertainty principle offers a bound to show accuracy of the simultaneous measurement outcome for two incompatible observables. In this letter, we investigate quantum-memory-assisted entropic uncertainty relation (QMA–EUR) when the particle to be measured stays at an open system, and another particle is treated as quantum memory under a noninertial frame. In such a scenario, the collective influence of the unital and nonunital noise environment, and of the relativistic motion of the system, on the QMA–EUR is examined. By numerical analysis, we conclude that, firstly, the noises and the Unruh effect can both increase the uncertainty, due to the decoherence of the bipartite system induced by the noise or Unruh effect; secondly, the uncertainty is more affected by the noises than by the Unruh effect from the acceleration; thirdly, unital noises can reduce the uncertainty in long-time regime. We give a possible physical interpretation for those results: that the information of interest is redistributed among the bipartite, the noisy environment and the physically inaccessible region in the noninertial frame. Therefore, we claim that our observations provide an insight into dynamics of the entropic uncertainty in a noninertial frame, and might be important to quantum precision measurement under relativistic motion.

Shan Huang, Hua‐Lei Yin, Zeng‐Bing Chen +1 more

The entropic way of formulating Heisenberg's uncertainty principle not only plays a fundamental role in applications of quantum information theory but also is essential for manifesting genuine nonclassical features of quantum systems. In this paper we investigate Rényi entropic uncertainty relations (EURs) in the scenario where measurements on individual copies of a quantum system are selected with nonuniform probabilities. In contrast with EURs that characterize an observer's overall lack of information about outcomes with respect to a collection of measurements, we establish state-dependent lower bounds on the weighted sum of entropies over multiple measurements. Conventional EURs thus correspond to the special cases when all weights are equal, and in such cases we show our results are generally stronger than previous ones. Moreover, taking the entropic steering criterion as an example, we numerically verify that our EURs could be advantageous in practical quantum tasks by optimizing the weights assigned to different measurements. Importantly, this optimization does not require quantum resources and is efficiently computable on classical computers. Published by the American Physical Society 2024

Ivan Damgård, Serge Fehr, Renato Renner +2 more