Bounded Real Properties for a Class of Annihilation-Operator Linear Quantum Systems

Maalouf, Aline I.; Petersen, Ian R.

doi:10.1109/tac.2010.2060970

Cited by 80 publications

(123 citation statements)

References 32 publications

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“…Hence, the following theorem holds. Note that a similar result is found in [56]. Theorem 5.1: Let A 0 and C 0 be matrices directly obtained from the transfer function Ξ(s), e.g.…”

Section: A Reconstruction Of System Matricessupporting

confidence: 55%

System Identification for Passive Linear Quantum Systems

Guţǎ

Yamamoto

2016

IEEE Trans. Automat. Contr.

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Abstract-System identification is a key enabling component for the implementation of quantum technologies, including quantum control. In this paper, we consider the class of passive linear input-output systems, and investigate several basic questions: (1) which parameters can be identified? (2) Given sufficient inputoutput data, how do we reconstruct the system parameters? (3) How can we optimize the estimation precision by preparing appropriate input states and performing measurements on the output? We show that minimal systems can be identified up to a unitary transformation on the modes, and systems satisfying a Hamiltonian connectivity condition called "infecting" are completely identifiable. We propose a frequency domain design based on a Fisher information criterion, for optimizing the estimation precision for coherent input state. As a consequence of the unitarity of the transfer function, we show that the Heisenberg limit with respect to the input energy can be achieved using non-classical input states.Index Terms-Quantum information and control; System identification; Linear systems; Estimation; Stochastic systems I. INTRODUCTION We are currently witnessing the beginning of a quantum engineering revolution [1], marking a shift from "classical devices" which are macroscopic systems described by deterministic or stochastic equations, to "quantum devices" which exploit fundamental properties of quantum mechanics, with applications ranging from computation to secure communication and metrology [2], [3]. While control theory was developed from the need for predictability in the behavior of "classical" dynamical systems, quantum filtering and quantum feedback control theory [4], [5], [6] deal with similar questions in the mathematical framework of quantum dynamical systems.System identification is an essential component of control theory, which deals with the estimation of unknown dynamical parameters of input-output systems; in particular, the identification of linear systems is a well studied subject in classical systems theory [7]. A similar task arises in the quantum setup, and various aspects of the quantum system identification problem have been considered in the recent literature, cf.

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“…Hence, the following theorem holds. Note that a similar result is found in [56]. Theorem 5.1: Let A 0 and C 0 be matrices directly obtained from the transfer function Ξ(s), e.g.…”

Section: A Reconstruction Of System Matricessupporting

confidence: 55%

System Identification for Passive Linear Quantum Systems

Guţǎ

Yamamoto

2016

IEEE Trans. Automat. Contr.

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“…Clearly this condition is satisfied in the case of an annihilation only system P in the light of the identity (7). Hence the annihilation only system (9) is passive with respect to performance output Z = −Ca, with the storage function V = a † a.…”

Section: Passive Annihilation Only Quantum Systemsmentioning

confidence: 96%

“…The statement of the proposition then follows by contraposition, after noting that being passive, the system (5) cannot have eigenvalues in the open right hand-side of the complex plane due to (7).…”

Section: Decoherence Free Subsystemsmentioning

confidence: 97%

“…(7). Recall [7] that a quantum stochastic differential equation of the form (14) is said to be (canonically) physically realizable if it preserves the canonical commutation relations, Theorem 1 Suppose (−iM, B 1 ) is controllable. Then a DFS cannot be created by coupling the system to an engineered environment.…”

Section: Open Loop Reservoir Engineering For Dfs Generationmentioning

confidence: 99%

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Pole placement approach to coherent passive reservoir engineering for storing quantum information

Nguyen

Zhang

Pan

et al. 2017

2017 American Control Conference (ACC)

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Reservoir engineering is the term used in quantum control and information technologies to describe manipulating the environment within which an open quantum system operates. Reservoir engineering is essential in applications where storing quantum information is required. From the control theory perspective, a quantum system is capable of storing quantum information if it possesses a so-called decoherence free subsystem (DFS). This paper explores pole placement techniques to facilitate synthesis of decoherence free subsystems via coherent quantum feedback control. We discuss limitations of the conventional 'open loop' approach and propose a constructive feedback design methodology for decoherence free subsystem engineering. It captures a quite general dynamic coherent feedback structure which allows systems with decoherence free modes to be synthesized from components which do not have such modes.

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“…In recent years, a number of papers have considered the feedback control of systems whose dynamics are governed by the laws of quantum mechanics rather than classical mechanics [3][4][5][6][7][8][9][10][11][12][13][14][15][16]. In particular, Gough & James [5] and James & Gough [17] consider a framework for quantum systems defined in terms of a triple (S , L, H ), where S is a scattering matrix, L is a vector of coupling operators and H is a Hamiltonian operator.…”

Section: Introductionmentioning

confidence: 99%