Abstract
To control a quantum system via feedback, we generally have two options in choosing control scheme. One is the coherent feedback, which feeds the output field of the system, through a fully quantum device, back to manipulate the system without involving any measurement process. The other one is the measurement-based feedback, which measures the output field and performs a real-time manipulation on the system based on the measurement results. Both schemes have advantages/disadvantages, depending on the system and the control goal, hence their comparison in several situation is important. This paper considers a general open linear quantum system with the following specific control goals; back-action evasion (BAE), generation of a quantum non-demolished (QND) variable, and generation of a decoherence-free subsystem (DFS), all of which have important roles in quantum information science. Then some no-go theorems are proven, clarifying that those goals cannot be achieved by any measurement-based feedback control. On the other hand it is shown that, for each control goal, there exists a coherent feedback controller accomplishing the task. The key idea to obtain all the results is system theoretic characterizations of BAE, QND, and DFS in terms of controllability and observability properties or transfer functions of linear systems, which are consistent with their standard definitions.
Highlights
Should we perform measurement or not? This question appears to be critical in quantum physics, in quantum information science
This paper focuses on a specific aspect of this abstract and broad question: we consider feedback control problems
In the literature we find some feedback-based approaches realizing backaction evasion (BAE) [43,44,45], quantum nondemolished (QND) [46], and decoherence-free subsystem (DFS) [47,48,49]
Summary
Should we perform measurement or not? This question appears to be critical in quantum physics, in quantum information science. In the literature we find some feedback-based approaches realizing BAE [43,44,45], QND [46], and DFS [47,48,49] Another feature of this paper is that we focus on general open linear quantum systems [1,36,37]. We do not use the terminology “observable” to represent a measurable physical quantity (i.e., a self-adjoint operator), because it has a different meaning in systems theory; a physical quantity is called a “variable,” e.g., a QND variable rather than a QND observable
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