The European Physical Journal D

, Volume 41, Issue 3, pp 579–587 | Cite as

Engineering multiphoton states for linear optics computation

  • P. Aniello
  • C. LupoEmail author
  • M. Napolitano
  • M. G.A. Paris
Quantum Optics and Quantum Information


Transformations achievable by linear optical components allow to generate the whole unitary group only when restricted to the one-photon subspace of a multimode Fock space. In this paper, we address the more general problem of encoding quantum information by multiphoton states, and elaborating it via ancillary extensions, linear optical passive devices and photodetection. Our scheme stems in a natural way from the mathematical structures underlying the physics of linear optical passive devices. In particular, we analyze an economical procedure for mapping a fiducial 2-photon 2-mode state into an arbitrary 2-photon 2-mode state using ancillary resources and linear optical passive N-ports assisted by post-selection. We found that adding a single ancilla mode is enough to generate any desired target state. The effect of imperfect photodetection in post-selection is considered and a simple trade-off between success probability and fidelity is derived.


03.67.-a Quantum information 03.67.Lx Quantum computation 42.50.Dv Nonclassical states of the electromagnetic field, including entangled photon states; quantum state engineering and measurements 


01.30.+r Quantum states and dynamics as a resource for information processing 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. M. Nielsen, I. Chuang, Quantum Information and Quantum Computation (Cambridge University Press, Cambridge, 2000) Google Scholar
  2. E. Knill, R. Laflamme, G. Milburn, Nature 409, 46 (2001) CrossRefADSGoogle Scholar
  3. U. Leonhardt, Rep. Prog. Phys. 66, 1207 (2003) CrossRefADSGoogle Scholar
  4. P. Kok, W.J. Munro, K. Nemoto, T.C. Ralph, J.P. Dowling, G.J. Milburn, arXiv:quant-ph/0512071 (2005) Google Scholar
  5. C.R. Myers, R. Laflamme, arXiv:quant-ph/0512104 (2005) Google Scholar
  6. N.J. Cerf, C. Adami, P.G. Kwiat, Phys. Rev. A 57, R1477 (1998) Google Scholar
  7. S. Scheel, N. Lütkenhaus, New J. Phys. 6 51 (2004); see also J. Eisert, Phys. Rev. Lett. 95, 04052 (2005) Google Scholar
  8. P. Aniello, R. Coen Cagli, J. Opt. B: Quantum Semiclass. Opt. 7, S711 (2005) Google Scholar
  9. P. Aniello, C. Lupo, M. Napolitano, Open Sys. & Information Dyn. 13, 415 (2006) zbMATHCrossRefGoogle Scholar
  10. P. Jordan, Z. Phys. 94, 531 (1935) zbMATHCrossRefGoogle Scholar
  11. J. Schwinger, in Quantum theory of angular momentum, edited by L.C. Biedenharn, H. van Dam (Academic Press, New York, 1965) Google Scholar
  12. M.H. Stone, Proc. Nat. Acd. Scie. USA 16, 172 (1930) CrossRefADSGoogle Scholar
  13. J. von Neumann, Math. Ann. 194, 570 (1931) CrossRefGoogle Scholar
  14. D. DiVincenzo, Fortschr. Phys. 48, 771 (2000) zbMATHCrossRefGoogle Scholar
  15. S. Scheel, K. Nemoto, W.J. Munro, P.L. Knight, Phys. Rev. A 68, 032310 (2003) CrossRefADSMathSciNetGoogle Scholar
  16. G.G. Lapaire, P. Kok, J.P. Dowling, J.E. Sipe, Phys. Rev. A 68, 04234 (2003) CrossRefGoogle Scholar
  17. E. Knill, Phys. Rev. A 66, 052306 (2002) CrossRefADSMathSciNetGoogle Scholar
  18. S.A. Gaal, Linear Analysis and Representation Theory (Springer-Verlag, Berlin, 1973) Google Scholar
  19. E. Knill, Phys. Rev. A 68, 064303 (2003) CrossRefADSGoogle Scholar
  20. A. Ferraro, S. Olivares, M.G.A. Paris, “Gaussian States in Quantum Information”, Napoli Series on Physics and Astrophysics (Bibliopolis, Napoli, 2005) Google Scholar
  21. M. Bondani, G. Zambra, A. Andreoni, M. Gramegna, M. Genovese, G. Brida, A. Rossi, M.G.A. Paris, Phys. Rev. Lett. 95, 063602 (2005) CrossRefADSGoogle Scholar
  22. G. Zambra, M.G.A. Paris, Reconstruction of photon statistics using low performance photon counters, arXiv:quant-ph/0607052 Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Authors and Affiliations

  • P. Aniello
    • 1
  • C. Lupo
    • 1
    Email author
  • M. Napolitano
    • 1
  • M. G.A. Paris
    • 2
  1. 1.INFN Sezione di Napoli and Dipartimento di Scienze Fisiche dell'Università di Napoli `Federico II'NapoliItalia
  2. 2.Dipartimento di Fisica dell'Università di MilanoMilanoItalia

Personalised recommendations