Quantum State Engineering in Open Systems: Harnessing Dissipation and Measurement

弱测量（WM）是冯·诺依曼量子波函数“坍缩”教条的替代方案。WM避免了波函数的完全破坏，同时能够从被测系统中提取部分信息。同时，测量与检测器对系统状态的反作用相关联。本理论方案的核心思想是利用WM的几乎非破坏性的性质，同时利用其反作用用于非平凡态的量子工程。这一进展将通过三个关键步骤来实现：（i）WM诱导的状态生成，（ii）状态稳定化和（iii）状态操纵。我们将把这一思想应用到具有少量准粒子的拓扑系统以及多体系统。在某些限制下，WM定义的协议产生的动力学密切相关的开放耗散系统。在该上下文中，代替采用WM协议，还可以通过使系统经受时间相关驱动力和由于外部环境引起的耗散的组合来实现状态生成、稳定和操纵。虽然这种驱动和耗散协议在过去已经被广泛研究并用于产生奇异状态，但我们提议中的新元素是暗空间的出现，即，退化暗态的流形特别地，设计暗空间为在具有拓扑零模式的设备中进行稳健的量子态操纵打开了大门，例如，马约拉纳州或副费米子。从只有几个拓扑准粒子的系统开始，我们将以强关联的多体态为目标。我们将按需设计少准粒子态，操纵它们（结果，例如，在几何相位和编织协议），并开发基于WM或驱动耗散的协议，以设计一系列相关的多体状态，包括非平凡的基态和激发态以及新的非平衡态。该项目的成功完成将带来几个关键进展：（1）我们将引入一个新的多体物理学范式，维斯产生和操纵量子态。(2)我们将阐明以前不知道的测量操作的关键方面。(3)我们期望通过我们新颖的量子比特操纵技术对量子信息处理领域产生影响。

Weak measurement (WM) is an alternative to the dogma of von Neumann’s “collapse” of a quantum wave function. WM avoids a complete destruction of the wave function while being capable of extracting partial information from the measured system. Concomitantly, measurement is associated with the back-action of the detector on the system state. The core idea of the present theoretical proposal is to exploit the almost non-destructive nature of WM and, at the same time, harness its back-action for the purpose of quantum engineering of non-trivial states. This advance will be accomplished through three key steps: (i) The WM-induced generation of states, (ii) state stabilization, and (iii) state manipulation. We will apply this idea to topological systems with few quasi-particles as well as for many-body systems. In certain limits, WM-defined protocols give rise to dynamics closely related to that of open dissipative systems. In that context, instead of employing WM protocols, it is also possible to achieve state generation, stabilization, and manipulation by subjecting the system to a combination of time-dependent driving forces and dissipation due to an external environment. While such drive-and-dissipation protocols have been extensively studied and employed for generating exotic states in the past, the new element in our proposal is the emergence of a dark space, i.e., a manifold of degenerate dark states. In particular, engineering a dark space opens the door to robust quantum state manipulation in devices harboring topological zero modes, e.g., Majorana states or parafermions. Starting with systems hosting only a few topological quasiparticles, we will target strongly correlated many-body states. We will design on-demand few-quasiparticle states, manipulate them (resulting, e.g., in geometric phases and braiding protocols), and develop WM-based or driven-dissipative protocols to engineer a host of correlated many-body states, including non-trivial ground and excited states as well as novel non-equilibrium states. The successful completion of this project will result in several key advances: (1) We will introduce a new paradigm of many-body physics vis-à-vis generation and manipulation of quantum states. (2) We will elucidate crucial facets of the measurement operation not known before. (3) We expect an impact on the field of quantum information processing through our novel qubit manipulation techniques.