arXiv 2101.086932021-01-21quant-phcond-mat.mes-hallhep-th

时空中的量子关联：基础与应用

Quantum Correlations in Space-Time: Foundations and Applications

Tian Zhang

备注：: PhD Thesis. 154 pages, 4 figures, comments are welcome

摘要：

关于空间和时间的绝对/相对性质的争论已经持续了几千年。在这里，我们试图从信息论的角度来研究空间和时间，以了解在相对假设下的空间和时间的相关性。相关性作为两个量之间关系的度量，在经典概率论中并不区分空间和时间;空间中的量子相关性得到了很好的研究，但时间相关性还没有得到很好的理解。本文研究时空中的量子关联，将时间关联与空间关联同等对待，统一了时空中的量子关联。特别地，我们遵循伪密度矩阵形式主义，其中时空中的量子态由测量的相关性适当地定义。我们首先回顾了经典关联，量子关联在空间和时间，激发伪密度矩阵形式主义在有限维。接下来，我们将伪密度矩阵公式推广到高斯情况，通过维格纳表示的一般连续变量，以及弱测量等一般测量过程。然后，我们比较了伪密度矩阵形式主义与其他时空公式：不定因果结构，一致的历史，广义非局部游戏，出的时间顺序关联函数，和路径积分。我们认为，在非相对论性量子力学中，除了路径积分之外，不同的时空公式通过量子关联是紧密相关的。最后，我们将赝密度矩阵公式应用于时间晶体。通过将时间晶体定义为时间上的长程序，分析了连续和离散时间平移对称性，并从代数角度讨论了时间晶体的存在性。最后，我们总结了我们的工作，并展望了未来的发展方向。

英文摘要：

The absolute/relative debate on the nature of space and time is ongoing for thousands of years. Here we attempt to investigate space and time from the information theoretic point of view to understand spatial and temporal correlations under the relative assumption. Correlations, as a measure of relationship between two quantities, do not distinguish space and time in classical probability theory; quantum correlations in space are well-studied but temporal correlations are not well understood. The thesis investigates quantum correlations in space-time, by treating temporal correlations equally in form as spatial correlations and unifying quantum correlations in space and time. In particular, we follow the pseudo-density matrix formalism in which quantum states in spacetime are properly defined by correlations from measurements. We first review classical correlations, quantum correlations in space and time, to motivate the pseudo-density matrix formalism in finite dimensions. Next we generalise the pseudo-density matrix formulation to the Gaussian case, general continuous variables via Wigner representations, and general measurement processes like weak measurements. Then we compare the pseudo-density matrix formalism with other spacetime formulations: indefinite causal structures, consistent histories, generalised non-local games, out-of-time-order correlation functions, and path integrals. We argue that in non-relativistic quantum mechanics, different spacetime formulations are closely related via quantum correlations, except path integrals. Finally, we apply the pseudo-density matrix formulation to time crystals. By defining time crystals as long-range order in time, we analyse continuous and discrete time translation symmetry as well as discuss the existence of time crystals from an algebraic point of view. Finally, we summarise our work and provide the outlook for future directions.

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。

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英文摘要：

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