Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Single-photon coherent feedback control and filtering

Living reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5102-9_100156-1


A light field is in a k-photon state if it contains exactlyk photons. Due to their highly quantum nature, photon states hold promising applications in quantum communication, computing, metrology, and simulations. Recently, there has been rapidly growing interest in the generation and manipulation of various photon states. A new and important problem in the field of control engineering is: How to analyze and synthesize quantum systems driven by photon states to achieve pre-specified control performance? In this survey, we introduce single-photon states and show how a quantum linear system processes a single-photon input and how to use linear coherent feedback networks to shape the temporal pulse of a single photon. A single-photon filter is also presented. (An extended version of this survey can be found at arXiv:1902.10961.)


Quantum control systems Filtering Coherent feedback control 
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I wish to thank financial support from the Hong Kong Research Grant Council under grants 15206915, 15208418, and 15203619.


  1. Bartley TJ, Donati G, Spring JB, Jin X-M, Barbieri M, Datta A, Smith B.J. and Walmsley IA (2012) Multiphoton state engineering by heralded interference between single photons and coherent states. Physl Rev A 86(4):043820CrossRefGoogle Scholar
  2. Gao Q, Zhang GF, Petersen IR (2019) An exponential quantum projection filter for open quantum systems. Automatica 99:59–68MathSciNetCrossRefGoogle Scholar
  3. Gardiner C, Zoller P (2004) Quantum noise: a handbook of Markovian and non-Markovian Quantum stochastic methods with applications to quantum optics. Springer, BerlinzbMATHGoogle Scholar
  4. Gough JE, James MR, Nurdin HI and Combes J (2012) Quantum filtering for systems driven by fields in single-photon states or superposition of coherent states. Phys Rev A 86(4):043819CrossRefGoogle Scholar
  5. Song HT, Zhang GF, Xi ZR (2016) Continuous-mode multiphoton filtering. SIAM J Control Optim 54(3):1602–1632MathSciNetCrossRefGoogle Scholar
  6. Wiseman HM, Milburn GJ (2009) Quantum measurement and control. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  7. Zhang GF, Grivopoulos S, Petersen IR, Gough JE (2018) The Kalman decomposition for linear quantum systems. IEEE Trans Autom Control 63(2):331–346MathSciNetCrossRefGoogle Scholar
  8. Zhang GF, James MR (2013) On the response of quantum linear systems to single photon input fields. IEEE Trans Autom Control 58(5):1221–1235MathSciNetCrossRefGoogle Scholar

Authors and Affiliations

  1. 1.Department of Applied MathematicsThe Hong Kong Polytechnic UniversityHong KongChina

Section editors and affiliations

  • Ian R. Petersen
    • 1
  1. 1.Research School of Electrical, Energy and Materials EngineeringAustralian National UniversityCanberraAustralia