林德布拉德净化
Lindbladian purification
摘要：
在最近的工作[D. K. Burgarth等人，国家通信5，5173（2014）]表明，一系列频繁的测量可以将量子系统的动力学投影到动力学可能更复杂的子空间上。在这个子空间中，甚至可以实现完全的可控性，尽管在投影之前系统的可控性非常差，因为控制哈密顿量彼此交换。我们也可以考虑相反的情况：量子系统的任何哈密顿算符，一般来说彼此之间是不可交换的，可以通过将它们嵌入到扩展的希尔伯特空间中而使它们成为可交换的，因此扩展空间中的动力学变得平凡而简单。这种使非对易的哈密尔顿算子成为对易的思想叫做“哈密尔顿纯化"。“通过频繁的测量将系统投影回原始希尔伯特空间，恢复了原始的非对易哈密顿算子。在这里，我们将这个想法推广到开放系统动力学，提出了一个简单的结构，使Lindbladian，以及哈密顿，交换的一个更大的空间与辅助系统。我们表明，原来的动态可以恢复通过经常测量辅助系统在一个非选择性的方式。此外，我们还提供了一个通用的Lindbladian对，它描述了一个“可访问的”开放量子系统的通用系统大小。这使我们能够得出结论，通过一系列频繁的非选择性测量，一个不可访问的开放量子系统通常变得可访问。这进一步阐明了测量反作用对量子系统控制的作用。
英文摘要：
In a recent work [D. K. Burgarth et al., Nat. Commun. 5, 5173 (2014)] it was shown that a series of frequent measurements can project the dynamics of a quantum system onto a subspace in which the dynamics can be more complex. In this subspace even full controllability can be achieved, although the controllability over the system before the projection is very poor since the control Hamiltonians commute with each other. We can also think of the opposite: any Hamiltonians of a quantum system, which are in general noncommutative with each other, can be made commutative by embedding them in an extended Hilbert space, and thus the dynamics in the extended space becomes trivial and simple. This idea of making noncommutative Hamiltonians commutative is called "Hamiltonian purification." The original noncommutative Hamiltonians are recovered by projecting the system back onto the original Hilbert space through frequent measurements. Here we generalize this idea to open-system dynamics by presenting a simple construction to make Lindbladians, as well as Hamiltonians, commutative on a larger space with an auxiliary system. We show that the original dynamics can be recovered through frequently measuring the auxiliary system in a non-selective way. Moreover, we provide a universal pair of Lindbladians which describes an "accessible" open quantum system for generic system sizes. This allows us to conclude that through a series of frequent non-selective measurements a nonaccessible open quantum system generally becomes accessible. This sheds further light on the role of measurement backaction on the control of quantum systems.
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