On the Response of Quantum Linear Systems to Single Photon Input Fields

Zhang, Guofeng; James, M. R.

doi:10.1109/tac.2012.2230816

Cited by 65 publications

(98 citation statements)

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“…If |1 ξ is taken as an input field state for a passive system that initially set to the ground state, then, in the long time limit the system returns to the ground state and the output is a single photon field state with pulse shape ξ ′ (ω) = Ξ(−iω)ξ(ω) [45]. That is, as in the coherent input case, the output field state is completely characterized by the transfer function as follows:…”

Section: Discussionmentioning

confidence: 99%

“…Note that limiting to a special class of linear systems does not mean straightforward applicability of the general identification theory for classical systems, but we need to take into account the essential feature of the focused system. Another specifically quantum aspect of the present theory is that all our results apply also to non-classical input states such as a single photon field; indeed, the transfer function can be used to describe the input-output relation even in such strong quantum scenarios [45], which is one of the advantages of the linear setup.…”

Section: Introductionmentioning

confidence: 91%

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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: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 91%

System Identification for Passive Linear Quantum Systems

Guţǎ

Yamamoto

2016

IEEE Trans. Automat. Contr.

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“…As pointed out in [12], a photon must exist as a pulse in both waveguide and free-space. The analytical approach proposed in this paper is thus directly applicable to temporal pulse shaping [39], as compared to the previous frequency-domain approaches. Moreover, the QSDE approach is extremely powerful in modelling a network of quantum systems, which has also been demonstrated in section 4.…”

Section: Resultsmentioning

confidence: 99%

Exact analysis of the response of quantum systems to two-photons using a QSDE approach

Pan

Dong

2016

New J. Phys.

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We introduce the quantum stochastic differential equation (QSDE) approach to exactly analyze the response of quantum systems to a continuous-mode two-photon input. The QSDE description of the two-photon process allows us to integrate the input-output analysis with the quantum network theory, and so the analytical computability of the output state of a general quantum system can be addressed within this framework. We show that the time-domain two-photon output states can be exactly calculated for a large class of quantum systems including passive linear networks, optomechanical oscillators and two-level emitter in waveguide systems. In particular, we propose to utilise the results for the exact simulation of the stimulated emission as well as the study of the scattering of two-mode photon wave packets.

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“…. , b n ) [2], [10]. The noise processes can be represented as annihilation operators on an appropriate Fock space [2], but from the system theory viewpoint they can be treated as quantum stochastic processes.…”

Section: Communication Channelmentioning

confidence: 99%

“…Here we introduced the notation for the impulse response, associated with the annihilation part of the system [10],…”

Section: Communication Channelmentioning

confidence: 99%

Active versus Passive Coherent Equalization of Passive Linear Quantum Systems

Ugrinovskii

James

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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The paper considers the problem of equalization of passive linear quantum systems. While our previous work was concerned with the analysis and synthesis of passive equalizers, in this paper we analyze coherent quantum equalizers whose annihilation (respectively, creation) operator dynamics in the Heisenberg picture are driven by both quadratures of the channel output field. We show that the characteristics of the input field must be taken into consideration when choosing the type of the equalizing filter. In particular, we show that for thermal fields allowing the filter to process both quadratures of the channel output may not improve mean square accuracy of the input field estimate, in comparison with passive filters. This situation changes when the input field is 'squeezed'.

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On the Response of Quantum Linear Systems to Single Photon Input Fields

Cited by 65 publications

References 40 publications

System Identification for Passive Linear Quantum Systems

System Identification for Passive Linear Quantum Systems

Exact analysis of the response of quantum systems to two-photons using a QSDE approach

Active versus Passive Coherent Equalization of Passive Linear Quantum Systems

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