基于 Robertson、Maccone-Pati 和 Robertson-Schrödinger 不确定性关系的开放量子动力学中的权衡关系
Tradeoff relations in open quantum dynamics via Robertson, Maccone-Pati, and Robertson-Schrödinger uncertainty relations
AI总结：
本研究利用缩放连续矩阵乘积态表示，基于 Robertson、Maccone-Pati 和 Robertson-Schrödinger 不确定性关系，推导出开放量子动力学中更紧的热力学不确定性关系与量子速度极限。
摘要：
Heisenberg 不确定性关系连同 Robertson 的推广，作为量子力学中的一个基本概念，表明不可对易的观测量对无法被精确测量。在本研究中，我们探索 Robertson 型不确定性关系，以证明其在建立开放量子动力学中的一系列热力学不确定性关系和量子速度极限方面的有效性。推导过程利用了缩放连续矩阵乘积态表示，将量子连续测量的时间演化映射到系统和场的时间演化。具体而言，我们考虑 Maccone-Pati 不确定性关系（Robertson 不确定性关系的一种改进），来推导热力学不确定性关系和量子速度极限。这些新推导出的关系使用了一个与初态正交的状态，产生的界限比先前已知的界限更紧。此外，我们考虑了 Robertson-Schrödinger 不确定性，它扩展了 Robertson 不确定性关系。我们的发现不仅强化了 Robertson 型不确定性关系的重要性，还扩展了其在识别开放量子动力学中不确定性关系方面的适用性。
英文摘要：
The Heisenberg uncertainty relation, together with Robertson's generalisation, serves as a fundamental concept in quantum mechanics, showing that noncommutative pairs of observables cannot be measured precisely. In this study, we explore the Robertson-type uncertainty relations to demonstrate their effectiveness in establishing a series of thermodynamic uncertainty relations and quantum speed limits in open quantum dynamics. The derivation utilises a scaled continuous matrix product state representation that maps the time evolution of the quantum continuous measurement to the time evolution of the system and field. Specifically, we consider the Maccone-Pati uncertainty relation, a refinement of the Robertson uncertainty relation, to derive thermodynamic uncertainty relations and quantum speed limits. These newly derived relations, which use a state orthogonal to the initial state, yield bounds that are tighter than previously known bounds. Moreover, we consider the Robertson-Schrödinger uncertainty, which extends the Robertson uncertainty relation. Our findings not only reinforce the significance of the Robertson-type uncertainty relations, but also expand its applicability in identifying uncertainty relations in open quantum dynamics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
