Abstract
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.
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Albert Einstein-Hedwig and Max Born, Briefwechsel 1916–1955. Nymphenburger Verlagshandlung GmbH (1935)
Einstein, A., Podolski, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)
Schrodinger, E.: Die gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften 23, 807 (1935)
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)
Zurek, W.H.: Decoherence and the transition from quantum to classical. Phys. Today 44, 36 (1991)
Zurek, W.H.: Quantum decoherence, Poincarè seminar 2005. Prog. Math. Phys. 48, 1 (2007)
Dur, W., Simon, C., Cirac, J.I.: Effective size of certain macroscopic quantum superpositions. Phys. Rev. Lett. 89, 210402 (2002)
Dur, W., Briegel, H.J.: Stability of macroscopic entanglement under decoherence. Phys. Rev. Lett. 92, 180403 (2004)
Gorin, T., Pineda, C., Seligman, T.H.: Decoherence of an n-qubit quantum memory. Phys. Rev. Lett. 99, 240405 (2007)
Schleich, W.: Schrödinger cat states. In: Quantum Optics in Phase Space, pp. 306–313. Wiley, New York (2001)
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)
Raimond, J.M., Brune, M., Haroche, S.: Manipulating quantum entanglement with atoms and photons in a cavity. Rev. Mod. Phys. 73, 565 (2001)
Ourjoumtsev, A., Tualle-Bruori, R., Laurat, J., Grangier, P.: Generating optical Schrödinger kittens for quantum information processing. Science 312, 83 (2006)
Ourjoumtsev, A., Jeong, H., Tualle-Bruori, R., Grangier, P.: Generation of optical ‘Schrödinger cats’ from photon number states. Nature 448, 784 (2007)
De Martini, F., Sciarrino, F., Vitelli, C.: Entanglement test on a microscopic-macroscopic system. Phys. Rev. Lett. 100, 253601 (2008)
Sciarrino, F., De Martini, F.: Realization of the optimal phase-covariant quantum cloning machine. Phys. Rev. A 72, 062313 (2005)
Sciarrino, F., De Martini, F.: Implementation of optimal phase-covariant cloning machines. Phys. Rev. A 76, 012330 (2007)
De Martini, F.: Amplification of quantum entanglement. Phys. Rev. Lett. 81, 2842 (1998)
De Martini, F.: Quantum superposition of parametrically amplified multiphoton pure states. Phys. Lett. A 250, 15 (1998)
De Martini, F., Sciarrino, F., Secondi, V.: Realization of an optimally distinguishable multiphoton quantum superposition. Phys. Rev. Lett. 95, 240401 (2005)
De Martini, F., Sciarrino, F.: Non-linear parametric processes in quantum information. Progr. Quantum Electron. 29, 165 (2005)
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)
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)
De Martini, F., Sciarrino, F., Vitelli, C.: Entanglement and non-locality in a micro-macroscopic system. arXiv:0804.0341 (2008)
Zurek, W.H.: Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 75, 715 (2003)
Zurek, W.H.: Environment-assisted invariance, entanglement, and probabilities in quantum physics. Phys. Rev. Lett. 90, 120404 (2003)
Jozsa, R.: Fidelity for mixed quantum states. J. Mod. Opt. 41, 2315 (1994)
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)
Hubner, M.: Explicit computation of the Bures distance for density matrices. Phys. Lett. A 163, 239 (1992)
Braunstein, S.L., Caves, C.M.: Statistical distance and the geometry of quantum states. Phys. Rev. Lett. 72, 3439 (1994)
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)
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)
Loudon, R.: Travelling-wave attenuation. In: The Quantum Theory of Light, pp. 310–318. Oxford University Press, London (2000)
Leonhardt, U.: Quantum statistics of a lossless beam splitter: SU(2) symmetry in phase space. Phys. Rev. A 48, 3265 (1993)
Schleich, W., Pernigo, M., Le Kien, F.: Nonclassical state from two pseudoclassical states. Phys. Rev. A 44, 2172 (1991)
Björk, G.: Private communication
Jacobson, J., Bjork, G., Chuang, I., Yamamoto, Y.: Photonic de Broglie waves. Phys. Rev. Lett. 74, 4835 (1995)
Kapale, K.T., Dowling, J.P.: Bootstrapping approach for generating maximally path-entangled photon states. Phys. Rev. Lett. 99, 053602 (2007)
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)
Slater, L.J.: The Gauss function. In: Generalized Hypergeometric Functions, pp. 1–39. Cambridge University Press, Cambridge (1966)
Peres, A.: The measuring process. In: Quantum Theory: Methods and Concepts, pp. 373–429. Kluwer Academic, Norwell (1995)
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)
Huttner, B., Muller, A., Gautier, J.D., Zbinden, H., Gisin, N.: Unambiguous quantum measurement of nonorthogonal states. Phys. Rev. A 54, 3783 (1996)
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)
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De Martini, F., Sciarrino, F., Spagnolo, N. et al. Generation of Highly Resilient to Decoherence Macroscopic Quantum Superpositions via Phase-covariant Quantum Cloning. Found Phys 41, 492–508 (2011). https://doi.org/10.1007/s10701-010-9445-z
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DOI: https://doi.org/10.1007/s10701-010-9445-z