Skip to main content
SpringerLink
Log in

Single-photon coherent feedback control and filtering

  • Living reference work entry
  • First Online:
Encyclopedia of Systems and Control

Abstract

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.)

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

References

  • 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):043820

    Article  Google Scholar 

  • Gao Q, Zhang GF, Petersen IR (2019) An exponential quantum projection filter for open quantum systems. Automatica 99:59–68

    Article  MathSciNet  Google Scholar 

  • Gardiner C, Zoller P (2004) Quantum noise: a handbook of Markovian and non-Markovian Quantum stochastic methods with applications to quantum optics. Springer, Berlin

    MATH  Google Scholar 

  • 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):043819

    Article  Google Scholar 

  • Song HT, Zhang GF, Xi ZR (2016) Continuous-mode multiphoton filtering. SIAM J Control Optim 54(3):1602–1632

    Article  MathSciNet  Google Scholar 

  • Wiseman HM, Milburn GJ (2009) Quantum measurement and control. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Zhang GF, Grivopoulos S, Petersen IR, Gough JE (2018) The Kalman decomposition for linear quantum systems. IEEE Trans Autom Control 63(2):331–346

    Article  MathSciNet  Google Scholar 

  • Zhang GF, James MR (2013) On the response of quantum linear systems to single photon input fields. IEEE Trans Autom Control 58(5):1221–1235

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

I wish to thank financial support from the Hong Kong Research Grant Council under grants 15206915, 15208418, and 15203619.

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China

    Guofeng Zhang

Authors
  1. Guofeng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guofeng Zhang .

Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, MA, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, MN, USA

    Tariq Samad

Section Editor information

  1. Research School of Electrical, Energy and Materials Engineering, Australian National University, Canberra, ACT, Australia

    Ian R. Petersen

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer-Verlag London Ltd., part of Springer Nature

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Zhang, G. (2020). Single-photon coherent feedback control and filtering. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_100156-1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_100156-1

  • Published:

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5102-9

  • Online ISBN: 978-1-4471-5102-9

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Search

Navigation