Skip to main content

Advertisement

Log in

Quantum interference of photons in simple networks

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

A theoretical investigation of quantum interference of photonic multistates in simple devices like beam splitters, Mach–Zehnder interferometers and double-loop devices are presented. Variable transmission and reflection coefficients as well as variable phase shifts are included in order to calculate quantum states and mean photon numbers at the outputs. Various input states like Fock states and coherent states and a combination of both are considered as well as squeezed states. Two methods are applied: The direct matrix method and the method of unitary representation. Remarkable results appear in a double-loop interferometer where for special phase shifts equal mean photon numbers in the three output ports are obtained provided certain input states are given. A computerized simulation of general networks using various input Fock states is presented. Multistate devices will be used in future linear quantum computation and quantum information processing schemes.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Nielsen M.A., Chuang I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  2. Knill E., Laflamme R., Milburn G.J.: A scheme for efficient quantum computation with linear optics. Nature 409, 46 (2001)

    Article  ADS  Google Scholar 

  3. Ralph T.C., White A.G., Munro W.J., Milburn G.J.: Simple scheme for efficient linear optics quantum gates. Phys. Rev. A 65, 012314–1 (2001)

    Google Scholar 

  4. O’Brien, J.L.: Optical quantum computing. Science 318, 1567–1570 arXiv:0803.1554 (2007)

    Google Scholar 

  5. Politi, A., Cryan, M.J., Rarity, J.G., Yu, S., O’Brien, J.L.: Silica-on silicon waveguide quantum circuits. Science 320, 646 (2008) arXiv:0802.0136

  6. Kok P., Munro W.J., Nemoto K., Ralph T.C., Dowling J.P., Milburn G.J.: Linear optical quantum computing with photonic qubits. Rev. Mod. Phys. 79, 135 (2007)

    Article  ADS  Google Scholar 

  7. Ralph, T.C., Pryde, G.J.: Quantum optical computation. pp. 1–70 (2011) arXiv:1103.6071

  8. Skaar J., Escartín J.C.G., Landro H.: Quantum mechanical description of linear optics. Am. J. Phys. 72, 1385 (2004)

    Article  ADS  Google Scholar 

  9. Gerry C.C., Knight P.L.: Introductory Quantum Optics. Cambridge University Press, Cambridge (2005)

    Google Scholar 

  10. Schleich W.P.: Quantum Optics in Phase Space. Wiley, Berlin (2001)

    Book  MATH  Google Scholar 

  11. Loudon R.: The Quantum Theory of Light. Oxford University Press, Oxford (2000)

    MATH  Google Scholar 

  12. Reck M., Zeilinger A.: Experimental realization of any discrete unitary operator. Phys. Rev. Lett. 73, 58 (1994)

    Article  ADS  Google Scholar 

  13. Reck, M., Zeilinger, A.: Quantum phase tracing of correlated photons in optical multiports. In: DeMartini, F., Denardo, G., Zeilinger, A. (eds) Proceedings of the Adriatico Workshop on Quantum Interferometry (pp. 171–178). World Scientific, Singapore (1993)

  14. Weihs G., Reck M., Weinfurter H., Zeilinger A.: Two-photon interference in optical fiber multiports. Phys. Rev. A 54, 893 (1996)

    Article  ADS  Google Scholar 

  15. Hong C.K., Ou Z.Y., Mandel L.: Measurement of subpicosecond time intervals between two photons by interference. Phys. Rev. Lett. 59, 2044 (1987)

    Article  ADS  Google Scholar 

  16. Kim M.S., Son W., Bužek V., Knight P.L.: Entanglement by a beam splitter: nonclassicality as a prerequisite for entanglement. Phys. Rev. A 65, 032323 (2002)

    Article  ADS  Google Scholar 

  17. Stokes G.G.: On attractions and on Clairaut’s theorem. Camb. Dublin Math. J. 4, 1 (1849)

    Google Scholar 

  18. Holbrow C.H., Galvez E., Parks M.E.: Photon quantum mechanics and beam splitters. Am. J. Phys. 70, 260 (2002)

    Article  ADS  Google Scholar 

  19. Jauch J.M., Rohrlich F.: The Theory of Photons and Electrons. Springer, Berlin (1976)

    Book  Google Scholar 

  20. Biedenharn L.C., Louck J.D.: Angular Momentum in Quantum Physics. Addison-Wesley, USA (1981)

    MATH  Google Scholar 

  21. Leonhardt U.: Measuring the Quantum State of Light. Cambridge University Press, Cambridge (1997)

    Google Scholar 

  22. Mandel L., Wolf E.: Optical Coherence and Quantum Optics. Cambridge University Press, Cambridge (1995)

    Google Scholar 

  23. Windhager, A., Suda, M., Pacher, C., Peev, M.,Poppe, A.: Quantum interference between a single- photon Fock state and a coherent state. Opt. Commun. 284, 1907–1912 (2011) arXiv:1009.1844

    Google Scholar 

  24. Hendrych M., Dušek M., Haderka O.: The effect of beam-splitter imperfections and losses on fringe visibility in a Mach–Zehnder interferometer. Acta Physica Slovaka 46, 393 (1996)

    Google Scholar 

  25. Paris, M.G.A.: Entanglement and visibility at the output of a Mach-Zehnder interferometer. Phys. Rev. A 59, 1615–1621 (1999) quant-ph/9811078

    Google Scholar 

  26. Paris, M.G.A.: Optical qubit by conditional interferometry. Phys. Rev. A 62, 033813 1–8 (2000) quant-ph/9909075

  27. Soubusta J., Bartůšková L., Černoch A., Fiurášek J., Dušek M.: Several experimental realizations of symmetric phase-covariant quantum cloners of single-photon qubits. Phys. Rev. A 76, 042318–1 (2007)

    Google Scholar 

  28. Hradil Z., Dušek M.: Analogy between optimal spin estimation and interferometry. Opt. Commun. 182, 361 (2000)

    Article  ADS  Google Scholar 

  29. Walls D.F.: Squeezed states of light. Nature 306, 141 (1983)

    Article  ADS  Google Scholar 

  30. Paris M.G.A.: Joint generation of identical squeezed states. Phys. Lett. A 225, 28 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  31. Hillery M.: An introduction to the quantum theory of nonlinear optics. Acta Phys. Slov. 59, 1 (2009)

    Article  ADS  Google Scholar 

  32. Andreoni A., Bondani M., D’Ariano G.M., Paris M.G.A.: Dichromatic squeezing generation. Eur. Phys. J. D 13, 415 (2001)

    Article  ADS  Google Scholar 

  33. Paris M.G.A., Chizhov A.V., Steuernagel O.: Phase space distributions from three-port couplers. Opt. Commun. 134, 117 (1997)

    Article  ADS  Google Scholar 

  34. Duer W., Vidal G., Cirac J.I.: Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 062314 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  35. Simon, D.S., Sergienko, A.V., Bahder, T.B.: Dispersion and fidelity in quantum interferometry. Phys. Rev. A 78, 053829 1–12 (2008) arXiv:0810.4501

  36. Bartůšková L., Černoch A., Filip R., Fiuráśek J., Soubusta J., Dušek M.: Optical implementation of the encoding of two qubits to a single qutrit. Phys. Rev. A 74, 022325 (2006)

    Article  ADS  Google Scholar 

  37. Miková M., Fikerová H., Straka I., Mičuda M., Fiurášek J., Ježek M., Dušek M.: Increasing efficiency of a linear-optical quantum gate using electronic feed-forward. Phys. Rev. A 85, 012305 (2012)

    Article  ADS  Google Scholar 

  38. Hübel H., Hamel D.R., Fedrizzi A., Ramelow S., Resch K.J., Jennewein T.: Direct generation of photon triplets using cascaded photon-pair sources. Nature 466, 601 (2010)

    Article  ADS  Google Scholar 

  39. Weihs G., Reck M., Weinfurter H., Zeilinger A.: All-fiber three-path Mach-Zehnder interferometer. Opt. Lett. 21, 302 (1996)

    Article  ADS  Google Scholar 

  40. Bartůšková L., Černoch A., Soubusta J., Dušek M.: Programmable discriminator of coherent states: experimantal realization. Phys. Rev. A 77, 034306–1 (2008)

    Google Scholar 

  41. Reinsch, M.W.: A simple expression for the terms in the Baker–Campbell–Hausdorff series. pp. 1–12 (1999) arXiv:math-ph/9905012

  42. Dakna M., Knöll L., Welsch D.-G.: Photon-added state preparation via conditional measurement on a beam splitter. Opt. Commun. 145, 309 (1998)

    Article  ADS  Google Scholar 

  43. Zavatta A., Viciani S., Bellini M.: Quantum-to-classical transition with single-photon-added coherent states of light. Science 306, 660 (2004)

    Article  ADS  Google Scholar 

  44. Zavatta A., Parigi V., King M.S., Bellini M.: Subtracting photons from arbitrary light fields: experimental test of coherent state invariance by single-photon annihilation. New J. Phys. 10, 123006 (2008)

    Article  ADS  Google Scholar 

  45. Lee S.-Y., Nha H.: Quantum state engineering by a coherent superposition of photon subtraction and addition. Phys. Rev. A 82, 053812 (2010)

    Article  ADS  Google Scholar 

  46. Gerrits T., Glancy S., Clement T.S., Calkins B., Lita A.E., Miller A.J., Migdal A.L., Nam S.W., Mirin R.P., Knill E.: Generation of optical coherent state superpositions by number-resolved photon subtraction from squeezed vacuum. Phys. Rev. A 82, 031802 (2010)

    Article  ADS  Google Scholar 

  47. Xiang G.Y., Ralph T.C., Lund A.P., Walk N., Pryde G.J.: Noiseless linear amplification and distillation of entanglement. Nat. Photonics 4, 316 (2010)

    Article  Google Scholar 

  48. Zavatta A., Fiurášek J., Bellini M.: A high-fidelity noisless amplifier for quantum light states. Nat. Photonics 5, 52 (2011)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Suda.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Suda, M., Pacher, C., Peev, M. et al. Quantum interference of photons in simple networks. Quantum Inf Process 12, 1915–1945 (2013). https://doi.org/10.1007/s11128-012-0479-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-012-0479-3

Keywords

Navigation