Abstract
To control a quantum system via feedback, we generally have two options in choosing a 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 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 and disadvantages, depending on the system and the control goal; hence, their comparison in several situations is important. This paper considers a general open linear quantum system with the following specific control goals: backaction evasion, generation of a quantum nondemolished variable, and generation of a decoherence-free subsystem, all of which have important roles in quantum information science. 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 the above three notions in terms of controllability and observability properties or transfer functions of linear systems, which are consistent with their standard definitions.
- Received 3 July 2014
DOI:https://doi.org/10.1103/PhysRevX.4.041029
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Published by the American Physical Society
Popular Summary
Measurement is an essential concept in quantum physics, which often poses a fundamental question: Should one perform a measurement or not in order to accomplish a certain task? A specific aspect of this broad question focuses on studying whether or not a measurement process should be involved in the feedback loop for controlling a quantum system. We compare a classical feedback method with a fully quantum one, where the former is called measurement feedback and the latter is called coherent feedback. We focus on a general linear system, such as an optomechanical system and an interferometer composed of two identical mechanical oscillators used for gravitation wave detection.
Our aim is to realize backaction evasion (subject only to shot noise), generate a quantum nondemolished variable, and generate a decoherence-free subsystem, all of which play important roles in quantum information science. We characterize these notions in a systematic way in terms of systems and control theory, which is at the core of modern technologies such as car suspensions, chemical plants, and tracking microscopes. We prove several theorems, clarifying that these goals cannot be achieved by any measurement feedback control. Moreover, we show, for each control goal, that there exists a coherent feedback controller accomplishing the task. These facts lead us to an interpretation that, for the problems considered here, quantum feedback is always better than classical feedback.
Our analysis, which has focused on linear quantum systems such as large ensembles of atoms and mechanical oscillators, can be logically extended to nonlinear systems, including arrays of photonic crystals.
