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Quantum engineered optical pulses

Unconditional quantum cloning of coherent states with linear optics Gerd Leuchs, Vincent Josse, Ulrik L. Andersen Institut für Optik, Information und Photonik, Max-Planck Forschungsgruppe, Universität Erlangen-Nürnberg. Quantum engineered optical pulses.

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Quantum engineered optical pulses

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  1. Unconditional quantum cloning of coherent states with linear opticsGerd Leuchs, Vincent Josse, Ulrik L. AndersenInstitut für Optik, Information und Photonik, Max-Planck Forschungsgruppe, Universität Erlangen-Nürnberg Quantum Optics VI Krynica 2005

  2. Quantum engineered optical pulses comparison discrete  continuous variables linear optics c.v. quantum information optimal quantum cloning of coherent states Quantum Optics VI Krynica 2005

  3. discrete vs. continuous discrete dichotomic variable continuous variables  dim Hilbert space alternatively : continuous variables x , p phase space p x W(x,p) types of continuous quantum variables • field quadratures • Stokes variables (polarization) Quantum Optics VI Krynica 2005

  4. Entanglement generation Quantum Optics VI Krynica 2005

  5. Entanglement ?!? Christus Mansionem Benedicat Caspar Melchior Balthasar Quantum Optics VI Krynica 2005

  6. Continuous Variables and Beam Splitters >>> coherent state cryptography (post selection)  not correlated ‘ >>> -teleportation, -secret sharing -quantum erasing -etc. nonlin  entangled nonlin ‘  nonlin entangled ‘ Quantum Optics VI Krynica 2005

  7. Continuous Variables and Beam Splitters (2) nonlin  detection of 1 Photon cat like state (J. Wenger, R.T. Brouri, P. Grangier, PRL92_153601 (2004)) 0 nonlin no detection (average loss 1 photon)  degradation of non-classical properties 0 in discrete case: Knill, Laflamme, Milburn Nature 409, 46 (2001) Quantum Optics VI Krynica 2005

  8. linear optics – detection – feed forward feed forward amplitude and/or phase detector ô Modulator â â‘‘ â‘ • feed forward used in: • teleportation • quantum memory • here • … ê Quantum Optics VI Krynica 2005

  9. quantum memory (Copenhagen,Garching/ Paris) quantum eraser (Erlangen, Olomouc) quantum cloner (Erlangen) teleportation (Pasadena / Canberra / Taiyuan / Tokyo / …) dense coding (Taiyuan) key distribution (Orsay / Erlangen / Canberra, Brisbane / North Western/Oregon/…) quantum interferometry(Erlangen / Stockholm) secret sharing (Canberra) purification(Erlangen) … continuous variable protocols - experiments Quantum Optics VI Krynica 2005

  10. quantum cloning no cloning theorem (Wootters and Zurek, 1982) approximate cloning of single qubits (Buzek, Hillery, 1996) approximate cloning of coherent states: theory: Cerf et al, PRL 85, 1751 (2000), experiment: here Quantum Optics VI Krynica 2005

  11. quantum cloning quantum cloning of coherent states fundamental aspects distribution of (partial) quantum information possible attack in quantum cryptography Quantum Optics VI Krynica 2005

  12. “classical“ cloning of coherent state xclone xin (a) p p pin p pclone p in clone x x x x in clone Clones Input a Copying clone 1 p a Copying clone 2 a in x Copying a clone N 12 cloner: 2 extra units of quantum uncertainty  F=1/2 Quantum Optics VI Krynica 2005

  13. quantum cloning of a coherent state N. Cerf other proposals: D’Ariano et al., PRL86, 914 (2001) Braunstein et al., PRL86, 4938 (2001) Fiurasek, PRL86, 4942 (2001) xclone xin (a) p p pin p pclone p in clone x x x x in clone Clones Input p x a  Clone 1 a a disp D in D a clone 2 12 cloner: 1 extra units of quantum uncertainty scheme using linear optics and feed forward: experiment: U.L.Andersen, V.Josse, G.L., PRL 2005 to appear Quantum Optics VI Krynica 2005

  14. Heisenberg description g aout,clone aout v3 v2 v1 ain x p Quantum Optics VI Krynica 2005

  15. Quantum description of feed forward action v2 after displacement D: v1 after measurement of x and p II I III III‘ projection operator for sub-system III‘ summing over all possible measurment outcomes  density matrix (III‘) in Heisenberg representation: B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, and E.S. Polzik, Nature 432, 482 (2004) Quantum Optics VI Krynica 2005

  16. Quantum approach p x a  clone 1 a a in disp D D a clone 2 Quantum Optics VI Krynica 2005

  17. quantum cloning of coherent side bands Ulrik L. Andersen, Vincent Josse and G. L., quant-ph / 0501005, PRL ‘05 Quantum Optics VI Krynica 2005

  18. quantum cloning of coherent side band (2) added noise: 3.15 3.28 dB close to quantum limit of 3 dB observed fidelity 64% theoretical limit: 66.67% Gaussian 68.26% non Gaussian N.Cerf et al quant-ph0410058 Ulrik L. Andersen, Vincent Josse and G. L., quant-ph / 0501005, PRL ‘05 Quantum Optics VI Krynica 2005

  19. A B theory group N. Lütkenhaus U. L. Andersen (N. Korolkova) R. Filip T.C. Ralph O. Glöckl (Ch. Silberhorn)V. Josse S. LorenzR. Loudon J. Heersink M.D. Reid Ch. Marquardt P.D. Drummond J. Schneider E.H. Huntington D. ElserH.A. Bachor M. SabuncuN. Cerf J. Milanovic Quantum Optics VI Krynica 2005

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