论文标题
量子随机过程和量子非马克维亚现象
Quantum stochastic processes and quantum non-Markovian phenomena
论文作者
论文摘要
经典随机过程的领域构成了数学的主要分支。当然，它们在生物学，化学，生态学，地质，金融，物理学以及许多自然和社会科学领域的研究中也非常有理。但是，当涉及量子随机过程时，该主题困扰着病理问题，这些问题导致了研究人员之间的激烈辩论。最近的发展已经开始解开这些问题，并为将经典随机过程的理论推广到没有歧义的量子领域铺平了道路。该教程详细介绍了量子梳子的现代语言的量子随机过程的结构，并针对量子物理学和量子信息理论的学生。我们从经典随机过程的基本知识开始，并将相同的思想推广到量子领域。一路上，我们讨论了量子物理学的微妙结构，这导致了形成量子随机过程的总体理论的麻烦。我们通过提出许多令人兴奋的问题来结束教程，这些问题在这一科学分支中。
The field of classical stochastic processes forms a major branch of mathematics. They are, of course, also very well studied in biology, chemistry, ecology, geology, finance, physics, and many more fields of natural and social sciences. When it comes to quantum stochastic processes, however, the topic is plagued with pathological issues that have led to fierce debates amongst researchers. Recent developments have begun to untangle these issues and paved the way for generalizing the theory of classical stochastic processes to the quantum domain without ambiguities. This tutorial details the structure of quantum stochastic processes, in terms of the modern language of quantum combs, and is aimed at students in quantum physics and quantum information theory. We begin with the basics of classical stochastic processes and generalize the same ideas to the quantum domain. Along the way, we discuss the subtle structure of quantum physics that has led to troubles in forming an overarching theory for quantum stochastic processes. We close the tutorial by laying out many exciting problems that lie ahead in this branch of science.
