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arXiv:1212.1862 · IEEE Transactions on Automatic Control

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

Guofeng Zhang, M. R. James

Published Nov 30, 2012• 64 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1109/tac.2012.2230816

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Abstract : The proposed work attempted to establish a theoretical framework for the analysis and control of quantum linear systems and their interactions with non-classical quantum fields by developing control theoretic concepts exploiting special features of quantum systems. The research aimed to continue developing a new mathematical framework for robust control of quantum linear systems and extend results to quantum linear systems subject to non-classical quantum fields. The major outcomes of this project are (i) derivation of quantum filtering equations for systems non-classical input states including single photon states, (ii) determination of how linear quantum systems respond to multichannel non-classical states, (iii) linear quantum models for quantum memories and the zero dynamics principle for perfect information transfer, (iv) development of new structured uncertainty methods that ensure robust stability of quantum systems based on nominal linear models, and (v) physical realizability results for finite level quantum systems.
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