Foundations of Physics

, Volume 41, Issue 3, pp 492–508 | Cite as

Generation of Highly Resilient to Decoherence Macroscopic Quantum Superpositions via Phase-covariant Quantum Cloning

  • Francesco De MartiniEmail author
  • Fabio Sciarrino
  • Nicolò Spagnolo
  • Chiara Vitelli


In this paper we analyze the resilience to decoherence of the Macroscopic Quantum Superpositions (MQS) generated by optimal phase-covariant quantum cloning according to two coherence criteria, both based on the concept of Bures distance in Hilbert spaces. We show that all MQS generated by this system are characterized by a high resilience to decoherence processes. This analysis is supported by the results of recent MQS experiments of N=3.5×104 particles.


Macroscopic quantum superposition Decoherence Phase-covariant cloning 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Albert Einstein-Hedwig and Max Born, Briefwechsel 1916–1955. Nymphenburger Verlagshandlung GmbH (1935) Google Scholar
  2. 2.
    Einstein, A., Podolski, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935) zbMATHCrossRefADSGoogle Scholar
  3. 3.
    Schrodinger, E.: Die gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften 23, 807 (1935) CrossRefADSGoogle Scholar
  4. 4.
    Nielsen, M.A., Chuang, I.L.: Quantum noise and quantum operations. In: Quantum Information and Quantum Computation, pp. 353–398. Cambridge University Press, Cambridge (2000) Google Scholar
  5. 5.
    Zurek, W.H.: Decoherence and the transition from quantum to classical. Phys. Today 44, 36 (1991) CrossRefGoogle Scholar
  6. 6.
    Zurek, W.H.: Quantum decoherence, Poincarè seminar 2005. Prog. Math. Phys. 48, 1 (2007) CrossRefMathSciNetGoogle Scholar
  7. 7.
    Dur, W., Simon, C., Cirac, J.I.: Effective size of certain macroscopic quantum superpositions. Phys. Rev. Lett. 89, 210402 (2002) CrossRefADSGoogle Scholar
  8. 8.
    Dur, W., Briegel, H.J.: Stability of macroscopic entanglement under decoherence. Phys. Rev. Lett. 92, 180403 (2004) CrossRefADSGoogle Scholar
  9. 9.
    Gorin, T., Pineda, C., Seligman, T.H.: Decoherence of an n-qubit quantum memory. Phys. Rev. Lett. 99, 240405 (2007) CrossRefMathSciNetADSGoogle Scholar
  10. 10.
    Schleich, W.: Schrödinger cat states. In: Quantum Optics in Phase Space, pp. 306–313. Wiley, New York (2001) CrossRefGoogle Scholar
  11. 11.
    Brune, M., Haroche, S., Raimond, J.M., Davidovich, L., Zagury, N.: Manipulation of photons in a cavity by dispersive atom-field coupling: Quantumnondemolition measurements and generation of “Schrödinger cat” states. Phys. Rev. A 45, 5193 (1992) CrossRefADSGoogle Scholar
  12. 12.
    Raimond, J.M., Brune, M., Haroche, S.: Manipulating quantum entanglement with atoms and photons in a cavity. Rev. Mod. Phys. 73, 565 (2001) CrossRefMathSciNetADSzbMATHGoogle Scholar
  13. 13.
    Ourjoumtsev, A., Tualle-Bruori, R., Laurat, J., Grangier, P.: Generating optical Schrödinger kittens for quantum information processing. Science 312, 83 (2006) CrossRefADSGoogle Scholar
  14. 14.
    Ourjoumtsev, A., Jeong, H., Tualle-Bruori, R., Grangier, P.: Generation of optical ‘Schrödinger cats’ from photon number states. Nature 448, 784 (2007) CrossRefADSGoogle Scholar
  15. 15.
    De Martini, F., Sciarrino, F., Vitelli, C.: Entanglement test on a microscopic-macroscopic system. Phys. Rev. Lett. 100, 253601 (2008) CrossRefADSGoogle Scholar
  16. 16.
    Sciarrino, F., De Martini, F.: Realization of the optimal phase-covariant quantum cloning machine. Phys. Rev. A 72, 062313 (2005) CrossRefADSGoogle Scholar
  17. 17.
    Sciarrino, F., De Martini, F.: Implementation of optimal phase-covariant cloning machines. Phys. Rev. A 76, 012330 (2007) CrossRefADSGoogle Scholar
  18. 18.
    De Martini, F.: Amplification of quantum entanglement. Phys. Rev. Lett. 81, 2842 (1998) zbMATHCrossRefMathSciNetADSGoogle Scholar
  19. 19.
    De Martini, F.: Quantum superposition of parametrically amplified multiphoton pure states. Phys. Lett. A 250, 15 (1998) CrossRefADSGoogle Scholar
  20. 20.
    De Martini, F., Sciarrino, F., Secondi, V.: Realization of an optimally distinguishable multiphoton quantum superposition. Phys. Rev. Lett. 95, 240401 (2005) CrossRefGoogle Scholar
  21. 21.
    De Martini, F., Sciarrino, F.: Non-linear parametric processes in quantum information. Progr. Quantum Electron. 29, 165 (2005) CrossRefADSGoogle Scholar
  22. 22.
    Nagali, E., De Angelis, T., Sciarrino, F., De Martini, F.: Experimental realization of macroscopic coherence by phase-covariant cloning of a single photon. Phys. Rev. A 76, 042126 (2007) CrossRefADSGoogle Scholar
  23. 23.
    Ricci, M., Sciarrino, F., Cerf, N.J., Filip, R., Fiurasek, J., De Martini, F.: Separating the classical and quantum information via quantum cloning. Phys. Rev. Lett. 95, 090504 (2005) CrossRefADSGoogle Scholar
  24. 24.
    De Martini, F., Sciarrino, F., Vitelli, C.: Entanglement and non-locality in a micro-macroscopic system. arXiv:0804.0341 (2008)
  25. 25.
    Zurek, W.H.: Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 75, 715 (2003) CrossRefMathSciNetADSzbMATHGoogle Scholar
  26. 26.
    Zurek, W.H.: Environment-assisted invariance, entanglement, and probabilities in quantum physics. Phys. Rev. Lett. 90, 120404 (2003) CrossRefMathSciNetADSGoogle Scholar
  27. 27.
    Jozsa, R.: Fidelity for mixed quantum states. J. Mod. Opt. 41, 2315 (1994) zbMATHCrossRefMathSciNetADSGoogle Scholar
  28. 28.
    Bures, D.: An extension of Kakutani’s theorem on infinite product measures to the tensor product of semiinfinite w *algebras. Trans. Am. Math. Soc. 135, 199 (1969) zbMATHMathSciNetGoogle Scholar
  29. 29.
    Hubner, M.: Explicit computation of the Bures distance for density matrices. Phys. Lett. A 163, 239 (1992) CrossRefMathSciNetADSGoogle Scholar
  30. 30.
    Braunstein, S.L., Caves, C.M.: Statistical distance and the geometry of quantum states. Phys. Rev. Lett. 72, 3439 (1994) zbMATHCrossRefMathSciNetADSGoogle Scholar
  31. 31.
    De Martini, F., Sciarrino, F., Spagnolo, N.: Decoherence, environment-induced superselection, and classicality of a macroscopic quantum superposition generated by quantum cloning. Phys. Rev. A 79, 052305 (2009) CrossRefADSGoogle Scholar
  32. 32.
    De Martini, F., Sciarrino, F., Spagnolo, N.: Anomalous lack of decoherence of the macroscopic quantum superpositions based on phase-covariant quantum cloning. Phys. Rev. Lett. 103, 100501 (2009) CrossRefGoogle Scholar
  33. 33.
    Loudon, R.: Travelling-wave attenuation. In: The Quantum Theory of Light, pp. 310–318. Oxford University Press, London (2000) Google Scholar
  34. 34.
    Leonhardt, U.: Quantum statistics of a lossless beam splitter: SU(2) symmetry in phase space. Phys. Rev. A 48, 3265 (1993) CrossRefADSGoogle Scholar
  35. 35.
    Schleich, W., Pernigo, M., Le Kien, F.: Nonclassical state from two pseudoclassical states. Phys. Rev. A 44, 2172 (1991) CrossRefADSGoogle Scholar
  36. 36.
    Björk, G.: Private communication Google Scholar
  37. 37.
    Jacobson, J., Bjork, G., Chuang, I., Yamamoto, Y.: Photonic de Broglie waves. Phys. Rev. Lett. 74, 4835 (1995) CrossRefADSGoogle Scholar
  38. 38.
    Kapale, K.T., Dowling, J.P.: Bootstrapping approach for generating maximally path-entangled photon states. Phys. Rev. Lett. 99, 053602 (2007) CrossRefADSGoogle Scholar
  39. 39.
    Sciarrino, F., Vitelli, C., De Martini, F., Glasser, R.T., Cable, H., Dowling, J.P.: Experimental sub-Rayleigh resolution by an unseeded high-gain optical parametric amplifier for quantum lithography. Phys. Rev. A 77, 012324 (2008) CrossRefADSGoogle Scholar
  40. 40.
    Slater, L.J.: The Gauss function. In: Generalized Hypergeometric Functions, pp. 1–39. Cambridge University Press, Cambridge (1966) Google Scholar
  41. 41.
    Peres, A.: The measuring process. In: Quantum Theory: Methods and Concepts, pp. 373–429. Kluwer Academic, Norwell (1995) Google Scholar
  42. 42.
    Spagnolo, N., Vitelli, C., Giacomini, S., Sciarrino, F., De Martini, F.: Polarization preserving ultra fast optical shutter for quantum information processing. Opt. Express 16, 17609 (2008) CrossRefADSGoogle Scholar
  43. 43.
    Huttner, B., Muller, A., Gautier, J.D., Zbinden, H., Gisin, N.: Unambiguous quantum measurement of nonorthogonal states. Phys. Rev. A 54, 3783 (1996) CrossRefMathSciNetADSGoogle Scholar
  44. 44.
    Spagnolo, N., Vitelli, C., De Angelis, T., Sciarrino, F., De Martini, F.: Wigner-function theory and decoherence of the quantuminjected optical parametric amplifier. Phys. Rev. A 80, 032318 (2009) CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Francesco De Martini
    • 1
    • 2
    Email author
  • Fabio Sciarrino
    • 1
    • 3
  • Nicolò Spagnolo
    • 1
    • 4
  • Chiara Vitelli
    • 1
    • 4
  1. 1.Dipartimento di Fisica“Sapienza” Università di RomaRomeItaly
  2. 2.Accademia Nazionale dei LinceiRomeItaly
  3. 3.Istituto Nazionale di Ottica ApplicataFirenzeItaly
  4. 4.Consorzio Nazionale Interuniversitario per le Scienze Fisiche della MateriaRomeItaly

Personalised recommendations