Panahyazdan Forough, Akhound Ahmad
Department of Physics, Payame Noor University, P.O. Box 19395-3697, Tehran, Islamic Republic of Iran.
Sci Rep. 2025 Apr 12;15(1):12583. doi: 10.1038/s41598-025-95598-3.
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.
在本文中，我们研究了在存在量子记忆和量子纠缠的情况下，由两比特相干态构建的非正交态的熵不确定性关系。我们的结果表明，对于所研究的态，量子记忆条件下的熵不确定性关系在广泛的参数范围内保持紧密，从而在可观测量预测中导致更低的错误率和更高的精度。我们明确证明，在存在量子记忆的情况下，预测可观测量的能力从根本上与纠缠相关。更强的纠缠导致熵不确定性降低和预测精度提高。另一方面，随着纠缠减弱，尽管不确定性关系仍然紧密，但预测误差相应增加。在最大纠缠态下，预测的准确性也最大化。随着纠缠减少，尽管不确定性关系收紧，但预测的准确性降低。预测准确性与纠缠量完全成正比，并且可以根据问题的要求实现所需的最小熵不确定性和高相关性。与此同时，构成熵不确定性关系上限的各分量的数值在所有情况下并不都相等。关于从所呈现的态中研究的变化，量子关联、熵不确定性以及构成上限的各分量，无论纠缠量如何，各自都分别趋于一个恒定值。
