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arXiv 2011.10349quant-ph
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用四种数学观点研究粗粒化和涌现量子动力学

Investigating Coarse-Grainings and Emergent Quantum Dynamics with Four Mathematical Perspectives

Cristhiano Duarte, Barbara Amaral, Marcelo Terra Cunha, Matthew Leifer

摘要:

随着量子信息科学的诞生,人们开发了许多处理多体量子系统的工具。尽管需要对这种系统进行完整的描述,但并不总是能够实现这一目标,因为这种描述的复杂性往往会随着颗粒的数量而增加。因此,建立有效的量子理论是至关重要的,目的是理解一个尺度上的描述如何从更深尺度的描述中出现。这一贡献探讨了不同的数学工具,紧急有效的动态研究的情况下,一个系统是受到一个单一的演变和粗粒度的描述,它是由CPTP地图将原系统到一个\emph{effective}希尔伯特空间的较小尺寸。我们看到,一个定义良好的有效动力学只能定义当某种匹配之间的基础酉和粗粒度的映射是满意的。我们的主要目标是使用这些不同的工具,以获得必要和充分条件,在一般情况下,这种匹配。

英文摘要:

With the birth of quantum information science, many tools have been developed to deal with many-body quantum systems. Although a complete description of such systems is desirable, it will not always be possible to achieve this goal, as the complexity of such description tends to increase with the number of particles. It is thus crucial to build effective quantum theories aiming to understand how the description in one scale emerges from the description of a deeper scale. This contribution explores different mathematical tools to the study of emergent effective dynamics in scenarios where a system is subject to a unitary evolution and the coarse-grained description of it is given by a CPTP map taking the original system into an \emph{effective} Hilbert space of smaller dimension. We see that a well-defined effective dynamics can only be defined when some sort of matching between the underlying unitary and the coarse-graining map is satisfied. Our main goal is to use these different tools to derive necessary and sufficient conditions for this matching in the general case.

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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