Quantum Risk-Sensitive Estimation and Robustness

Yamamoto, Naoki; Bouten, Luc

doi:10.1109/tac.2008.2009571

Cited by 62 publications

(61 citation statements)

References 53 publications

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“…Concerning applications of stochastic control, we refer for example to the existing literature of feedback control [10,25,36,37]. An important application of stochastic control is the concept of Optimal Control (see [28,34] for a classical approach and [14,15,38] for some quantum applications).…”

Section: The Diffusive Equation (Homodyne Detection Experiment) Is Gimentioning

confidence: 99%

“…Indeed, with the expression (22) the driving process is not rigorously defined since it depends on the existence of the solution (ρ u t ). With (38), everything is defined in an intrinsic way. Now, we consider (38) as the jump-model of continuous time measurement with control.…”

Section: Pellegrini Ann Henri Poincarémentioning

confidence: 99%

“…With (38), everything is defined in an intrinsic way. Now, we consider (38) as the jump-model of continuous time measurement with control. It will be justified later as limit of discrete quantum trajectories.…”

Section: Pellegrini Ann Henri Poincarémentioning

confidence: 99%

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Poisson and Diffusion Approximation of Stochastic Master Equations with Control

Pellegrini

2009

Ann. Henri Poincaré

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Quantum Trajectories are solutions of stochastic differential equations. Such equations are called Stochastic Master Equations and describe random phenomena in the continuous measurement theory of Open Quantum System. Many recent developments deal with the control of such models, i.e. optimization, monitoring and engineering. In this article, stochastic models with control are mathematically and physically justified as limits of concrete discrete procedures called Quantum Repeated Measurements. In particular, this gives a rigorous justification of the Poisson and diffusion approximations in quantum measurement theory with control.

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Section: The Diffusive Equation (Homodyne Detection Experiment) Is Gimentioning

confidence: 99%

Section: Pellegrini Ann Henri Poincarémentioning

confidence: 99%

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Poisson and Diffusion Approximation of Stochastic Master Equations with Control

Pellegrini

2009

Ann. Henri Poincaré

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“…This motivates the study of robust quantum control, in which the quantum systems to be controlled are modeled as uncertain quantum systems, e.g., see Mabuchi and Khaneja (2005). A related problem is the problem of robust estimation and filtering for uncertain quantum systems, e.g., see Yamamoto and Bouten (2009). The issue of robust stability is particularly important in the case of quantum feedback control since in this case, there is always the possibility of instability.…”

Section: Introductionmentioning

confidence: 99%

Robustness Issues in Quantum Control

Petersen

2013

Encyclopedia of Systems and Control

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Robust quantum control theory is concerned with the design of controllers for quantum systems taking into account uncertainty is the model of the system. The robust open-loop control of quantum systems is discussed in this entry. Also discussed is the robust stability analysis problem for quantum systems, and two forms of quantum small gain theorem are presented. In addition, the entry discusses the design of robust quantum feedback control systems.

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“…[52] and Eq. (20), the dynamical equation of the evolution operator U t (ǫ) of the total system can be expressed as:…”

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confidence: 99%

Quantum Coherent Nonlinear Feedback With Applications to Quantum Optics on Chip

Zhang

Liu

et al. 2012

IEEE Trans. Automat. Contr.

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Abstract-In the control of classical mechanical systems, feedback has been applied to the generation of desired nonlinear dynamics, e.g., in chaos control. However, how much this can be done is still an open problem in quantum mechanical systems. This paper presents a scheme of enhancing nonlinear quantum effects via the recently developed coherent feedback techniques, which can be shown to outperform the measurementbased quantum feedback scheme that can only generate pseudononlinear quantum effects. Apart from the advantages of our method, an unsolved problem is that the decoherence rate is also increased by the quantum amplifier, which may be solved by introducing, e.g., an integral device or an nonlinear quantum amplifier. Such a proposal is demonstrated via two application examples in quantum optics on chip. In the first example, we show that nonlinear Kerr effect can be generated and amplified to be comparable with the linear effect in a transmission line resonator (TLR). In the second example, we show that by tuning the gains of the quantum amplifiers in a TLR coherent feedback network, the resulting nonlinear effects can generate and manipulate nonGaussian "light" (microwave field) which exhibits fully quantum sub-Poisson photoncount statistics and photon antibunching phenomenon. The scheme opens up broad applications in engineering nonlinear quantum optics on chip. Particularly, in this study, the concept of feedback nonlinearization which is very useful for quantum feedback control systems is introduced. This is in contrast to the feedback linearization concept used in classical nonlinear feedback control systems.Index Terms-Feedback nonlinearization, quantum coherent feedback control, nonlinear quantum optics, on-chip quantum optics, quantum control.

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Quantum Risk-Sensitive Estimation and Robustness

Cited by 62 publications

References 53 publications

Poisson and Diffusion Approximation of Stochastic Master Equations with Control

Poisson and Diffusion Approximation of Stochastic Master Equations with Control

Robustness Issues in Quantum Control

Quantum Coherent Nonlinear Feedback With Applications to Quantum Optics on Chip

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