Asymptotic inference in system identification for the atom maser

Catana, Catalin; Horssen, Merlijn van; Guţǎ, Mădălin

doi:10.1098/rsta.2011.0528

Cited by 15 publications

(27 citation statements)

References 25 publications

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“…[8], [9], [10], [11], [12], [13], [14], [15], [16] for a shortlist of recent results. Further, detailed statistical analysis for some dynamical quantum identification problems have been demonstrated [17], [18], [19], [20].…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

System Identification for Passive Linear Quantum Systems

Guţǎ

Yamamoto

2016

IEEE Trans. Automat. Contr.

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“…We should also mention the other contributions to this volume on important problems such as system identification [53,54], preparation and stabilization of target states using only local dissipation [55,56] and quantum dynamical programming [57].…”

Section: Discussionmentioning

confidence: 99%

Principles and applications of quantum control engineering

Gough

2012

Phil. Trans. R. Soc. A.

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“…For sufficiently long times, the cavity reaches its unique steady state, and the measurement process is stationary. In this regime one can compute the Fisher information for certain statistics of the measurement data and prove their asymptotic normality [15]. Here we complete this analysis by investigating and comparing the maximum likelihood estimator based on the full measurement record, and the alternative likelihoodfree method of approximate Bayesian computation, based on a set of measurement statistics.…”

Section: Input Excited Atomsmentioning

confidence: 99%

“…[14] for a more general treatment). In continuous-time, a similar analysis was undertaken in [15] for the particular model of the atom maser: a cavity interacting with incoming identically prepared two-levels atoms which are subsequently measured to produce a continuous-time counting process, as illustrate in Figure 1. One of the intriguing findings was that for certain values of the unknown parameter (the Rabi angle φ), the total atom counts are poor statistics (zero classical Fisher information), while the quantum Fisher information of the output attains its maximum.…”

Section: Introductionmentioning

confidence: 99%

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Maximum likelihood versus likelihood-free quantum system identification in the atom maser

Catana¹,

Kypraios²,

Guţǎ³

2014

J. Phys. A: Math. Theor.

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We consider the system identification problem of estimating a dynamical parameter of a Markovian quantum open system (the atom maser), by performing continuous time measurements in the system's output (outgoing atoms). Two estimation methods are investigated and compared. On the one hand, the maximum likelihood estimator (MLE) takes into account the full measurement data and is asymptotically optimal in terms of its mean square error. On the other hand, the 'likelihood-free' method of approximate Bayesian computation (ABC) produces an approximation of the posterior distribution for a given set of summary statistics, by sampling trajectories at different parameter values and comparing them with the measurement data via chosen statistics.Our analysis is performed on the atom maser model, which exhibits interesting features such as bistability and dynamical phase transitions, and has connections with the classical theory of hidden Markov processes. Building on previous results which showed that atom counts are poor statistics for certain values of the Rabi angle, we apply MLE to the full measurement data and estimate its Fisher information. We then select several correlation statistics such as waiting times, distribution of successive identical detections, and use them as input of the ABC algorithm. The resulting posterior distribution follows closely the data likelihood, showing that the selected statistics contain 'most' statistical information about the Rabi angle.

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Asymptotic inference in system identification for the atom maser

Cited by 15 publications

References 25 publications

System Identification for Passive Linear Quantum Systems

System Identification for Passive Linear Quantum Systems

Principles and applications of quantum control engineering

Maximum likelihood versus likelihood-free quantum system identification in the atom maser

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