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arXiv 1807.06345quant-ph
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量子因果结构与量子热力学

Quantum Causal Structure and Quantum Thermodynamics

Mirjam Weilenmann

摘要:

本论文报告了量子技术发展中的两个重要领域,因果结构和微观热力学的研究进展。第一部分致力于因果结构的分析,它对观测变量之间的关系进行编码,通常限制它们之间可能的相关性。我们的考虑依赖于最近的熵矢量方法。在此基础上,我们开发的技术,用于推导熵的约束,以区分因果结构。我们提供了充分的条件熵向量是可实现的因果结构,并得出新的,改进的必要条件,在所谓的非香农不等式。我们还报告说,对于一个家庭的因果结构,包括二分贝尔的情况下,bilocal因果结构,熵向量是无法区分经典和量子的原因,尽管存在的量子相关性,是经典的再现。因此,需要进一步的发展,以便从量子的角度来理解原因。在第二部分中,我们探讨了一个公理化的框架,在微观热力学建模容错过程。我们的axiomatisation允许容纳有限的精度水平,在微观制度中描述实验至关重要。它导致出现的可管理的数量,使洞察的可行性和支出的过程中,绝热过程被证明是光滑的熵措施。我们的框架还导致在宏观尺度上的热力学行为,这意味着对于热力学平衡态,一个独特的功能提供了必要和充分条件的状态转换,像在传统的第二定律。

英文摘要:

This thesis reports progress in two domains, causal structures and microscopic thermodynamics, both of which are pertinent in the development of quantum technologies. The first part is dedicated to the analysis of causal structure, which encodes the relationship between observed variables, in general restricting the set of possible correlations between them. Our considerations rely on a recent entropy vector method. Based on this, we develop techniques for deriving entropic constraints to differentiate between causal structures. We provide sufficient conditions for entropy vectors to be realisable within a causal structure and derive new, improved necessary conditions in terms of so-called non-Shannon inequalities. We also report that for a family of causal structures, including the bipartite Bell scenario and the bilocal causal structure, entropy vectors are unable to distinguish between classical and quantum causes, in spite of the existence of quantum correlations that are not classically reproducible. Hence, further development is needed in order to understand cause from a quantum perspective. In the second part we explore an axiomatic framework for modelling error-tolerant processes in microscopic thermodynamics. Our axiomatisation allows for the accommodation of finite precision levels, crucial for describing experiments in the microscopic regime. It leads to the emergence of manageable quantities that give insights into the feasibility and expenditure of processes, which for adiabatic processes are shown to be smooth entropy measures. Our framework also leads to thermodynamic behaviour at the macroscopic scale, meaning that for thermodynamic equilibrium states a unique function provides necessary and sufficient conditions for state transformations, like in the traditional second law.

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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