Least Maximum Entropy and Minimum Uncertainty Coherent States

Kaifeng Bu, Uttam Singh, Shao-Ming Fei +2 more

The operational characterization of quantum coherence is the cornerstone in the development of the resource theory of coherence. We introduce a new coherence quantifier based on maximum relative entropy. We prove that the maximum relative entropy of coherence is directly related to the maximum overlap with maximally coherent states under a particular class of operations, which provides an operational interpretation of the maximum relative entropy of coherence. Moreover, we show that, for any coherent state, there are examples of subchannel discrimination problems such that this coherent state allows for a higher probability of successfully discriminating subchannels than that of all incoherent states. This advantage of coherent states in subchannel discrimination can be exactly characterized by the maximum relative entropy of coherence. By introducing a suitable smooth maximum relative entropy of coherence, we prove that the smooth maximum relative entropy of coherence provides a lower bound of one-shot coherence cost, and the maximum relative entropy of coherence is equivalent to the relative entropy of coherence in the asymptotic limit. Similar to the maximum relative entropy of coherence, the minimum relative entropy of coherence has also been investigated. We show that the minimum relative entropy of coherence provides an upper bound of one-shot coherence distillation, and in the asymptotic limit the minimum relative entropy of coherence is equivalent to the relative entropy of coherence.

Tatyana Barron, Alexander Kazachek

A. K. Rajagopal, S. Teitler

The maximum-entropy method is here generalized to obtain many possible extrema of the uncertainty product corresponding to the generalized minimum uncertainty products recently discussed by Lahiri and Menon (LM) [Phys. Rev. A 38, 5412 (1988)]. Unlike the LM work, the present work applies to mixed states and leads to a new annealing algorithm for obtaining the extrema of the entropy functional.

Angel Ricardo Plastino, Angel Ricardo Plastino

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.

Alexandra Musat, Andrei Tănăsescu, Pantelimon George Popescu