The relativity of quantum predictions

Fedor Herbut

Theodore P. Jorgensen

Forough Panahyazdan, Ahmad Akhound

In this paper, we examine entropy uncertainty relations in the presence of quantum memory and quantum entanglement for non-orthogonal states constructed from two-qubit coherent states. Our results reveal that for the studied state, the entropy uncertainty relations under quantum memory conditions remain tight across a broad range of parameters, leading to lower error rates and higher precision in observable predictions. We explicitly demonstrate that in the presence of quantum memory, the ability to predict observables is fundamentally tied to entanglement. Stronger entanglement leads to reduced entropy uncertainty and greater predictive accuracy. On the other hand, as entanglement weakens, even though the uncertainty relations remain tight, prediction errors increase accordingly. In the maximum entanglement state, the accuracy of the predictions is also maximized. As the entanglement decreases, despite the tightening of the uncertainty relations, the accuracy of the predictions decreases. The prediction accuracy is fully proportional to the amount of entanglement, and it is possible to achieve the desired minimum entropy uncertainty and high correlation according to the problem's requirements. This is while the numerical values of the components forming the upper bound of the entropy uncertainty relations are not equal in all cases. With respect to the changes examined from the presented state, quantum correlation, entropy uncertainty, and the components forming the upper bound, regardless of the amount of entanglement, each separately tend to a constant value.

Tabish Qureshi

Recent times have seen a spurt of research activity focused on "completing" certain wave-particle duality relations using entanglement or polarization. These studies use a duality relation involving path-predictability, and not path-distinguishability. Quantum origins of these results are explored here, in the more general framework of multipath quantum interference. Multipath interference with a path-detector is theoretically analyzed to find the connection between predictability and distinguishability. It is shown that entanglement is what quantitatively connects distinguishability with predictability. Thus, a duality relation between distinguishability and coherence can also be viewed as a triality between predictability, entanglement, and coherence. There exist two different kinds of duality relations in the literature, which pertain to two different kinds of interference experiments, with or without a path-detector. Results of this study show that the two duality relations are quantitatively connected via entanglement. The roots of the new, to the best of our knowledge, results in the classical optical domain, including the polarization coherence theorem, can be understood in the light of this work.

Gleb Wataghin

William G. Faris

In probability theory an event is characterized by a set of outcomes. The probability of an event is a prediction of the relative frequency of the outcomes that lie in the set, when the experiment is repeated independently. In quantum mechanics an event is identified with a closed subspace of Hilbert space. Do the probabilities of quantum events predict relative frequencies in the same way? The famous analysis of Bell shows that this cannot happen in general, for all quantum events. Nevertheless the probabilities must predict something, and if not relative frequencies then what? There are several answers to the question of how to interpret quantum probabilities as relative frequencies, but they all involve restrictions on the events that are considered. This article surveys three such interpretations, which correspond to three possible choices: measured events, macroscopic events, and position events. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 389–398, 1997