Linear Circuit Models for On-Chip Quantum Electrodynamics

The purpose of this paper is to extend linear systems and signals theory to include single photon quantum signals. We provide detailed results describing how quantum linear systems respond to multichannel single photon quantum signals. In particular, we characterize the class of states (which we call photon-Gaussian states) that result when multichannel photons are input to a quantum linear system.We show that this class of quantum states is preserved by quantum linear systems. Multichannel photon-Gaussian states are defined via the action of certain creation and annihilation operators on Gaussian states. Our results show how the output states are determined from the input states through a pair of transfer function relations. We also provide equations from which output signal intensities can be computed. Examples from quantum optics are provided to illustrate the results.

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“…They also appear in circuit quantum electrodynamics (circuit QED) systems, e.g., Eqs. ( 18)- (21) in Reference [28].…”

Section: A Dynamicsmentioning

confidence: 99%

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

Zhang

James

2013

IEEE Trans. Automat. Contr.

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“…In recent years there has been a rapid growth in the study of quantum linear systems. Quantum linear systems and signals theory has been proven very effective in the study of many quantum systems including quantum optical systems, optomechanical systems, cavity quantum electro-magnetic dynamical systems, atomic ensembles and quantum memories, see, e.g., [Gardiner & Zoller, 2000]; [Wall & Milburn, 2008]; [Wiseman & Milburn, 2010]; [Stockton, van Handel & Mabuchi, 2004]; [Zhang, Chen, Bhattacharya, & Meystre, 2010]; [Massel, et al, 2011]; [Matyas, et al, 2011]; [Tian, 2012]; ; [Hush, Carvalho, Hedges & James, 2013]. Because of its analytical and computational advantages, the linear setting always serves as an essential starting point for development of a more general theory.…”

Section: Introductionmentioning

confidence: 99%

On realization theory of quantum linear systems

Gough

Zhang

2015

Automatica

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The purpose of this paper is to study the realization theory of quantum linear systems. It is shown that for a general quantum linear system its controllability and observability are equivalent and they can be checked by means of a simple matrix rank condition. Based on controllability and observability a specific realization is proposed for general quantum linear systems in which an uncontrollable and unobservable subspace is identified. When restricted to the passive case, it is found that a realization is minimal if and only if it is Hurwitz stable. Computational methods are proposed to find the cardinality of minimal realizations of a quantum linear passive system. It is found that the transfer function of a quantum linear passive system G can be written as a fractional form in terms of a matrix function Σ; moreover, G is lossless bounded real if and only if Σ is lossless positive real. A type of realization for multi-inputmulti-output quantum linear passive systems is derived, which is closely related to its controllability and observability decomposition. Two realizations, namely the independent-oscillator realization and the chain-mode realization, are proposed for single-input-single-output quantum linear passive systems, and it is shown that under the assumption of minimal realization, the independent-oscillator realization is unique, and these two realizations are related to the lossless positive real matrix function Σ.

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“…The fact that Q and T 0 are of full rank was used in the above derivation. If we partition the states as in (6),…”

Section: B Linear Quantum Stochastic Systemsmentioning

confidence: 99%

“…Linear Quantum Stochastic Systems (LQSSs) are a class of models used in linear quantum optics [3], [4], [5], circuit QED systems [6], [7], quantum opto-mechanical systems [8], [9], [10], [11], and elsewhere. The mathematical framework for these models is provided by the theory of quantum Wiener processes, and the associated Quantum Stochastic Differential Equations [12], [13], [14].…”

Section: Introductionmentioning

confidence: 99%