1. Quantum Optics VI Krynica 20051 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

2. Quantum Optics VI Krynica 20052 Quantum engineered optical pulses comparison discrete  continuous variables linear optics c.v. quantum information optimal quantum cloning of coherent states

3. Quantum Optics VI Krynica 20053 discrete vs. continuous types of continuous quantum variables field quadratures Stokes variables (polarization) x p phase space W(x,p) discrete dichotomic variable continuous variables  dim Hilbert space alternatively : continuous variables x, p

4. Quantum Optics VI Krynica 20054 Entanglement generation

5. Quantum Optics VI Krynica 20055 Christus Mansionem Benedicat Caspar Melchior Balthasar Entanglement ?!?

6. Quantum Optics VI Krynica 20056   ‘   not correlated non lin entangled non lin  ‘  entangled >>> coherent state cryptography (post selection) >>>-teleportation, -secret sharing -quantum erasing -etc. Continuous Variables and Beam Splitters

7. Quantum Optics VI Krynica 20057  00 no detection (average loss 1 photon) degradation of non- classical properties non lin detection of 1 Photon  00 non lin cat like state (J. Wenger, R.T. Brouri, P. Grangier, PRL92_153601 (2004)) Continuous Variables and Beam Splitters (2) in discrete case: Knill, Laflamme, Milburn Nature 409, 46 (2001)

8. Quantum Optics VI Krynica 20058 linear optics – detection – feed forward Modulator detector â ê â‘‘ ô â‘ feed forward amplitude and/or phase feed forward used in: teleportation quantum memory here  …

9. Quantum Optics VI Krynica 20059 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

10. Quantum Optics VI Krynica 200510 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

11. Quantum Optics VI Krynica 200511 quantum cloning quantum cloning of coherent states –fundamental aspects –distribution of (partial) quantum information –possible attack in quantum cryptography

12. Quantum Optics VI Krynica 200512 “classical“ cloning of coherent state Copying a clone 1 x p a clone N a in a clone 2 Copying  x clone  p clone x p x clone p Clones  x in  p in Input x p x in p (a) 1  2 cloner: 2 extra units of quantum uncertainty  F=1/2

13. Quantum Optics VI Krynica 200513 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) experiment: U.L.Andersen, V.Josse, G.L., PRL 2005 to appear D D a Clone 1 a disp x p a clone 2 a in  x in  p in Input x p x in p (a)  x clone  p clone x p x clone p Clones 1  2 cloner: 1 extra units of quantum uncertainty scheme using linear optics and feed forward:

14. Quantum Optics VI Krynica 200514 Heisenberg description g v2v2 a out,clone v1v1 a in a out v3v3 xp

15. Quantum Optics VI Krynica 200515 Quantum description of feed forward action v1v1 v2v2 II I III‘ after measurement of x and p after displacement D: projection operator for sub-system III‘ summing over all possible measurment outcomes  density matrix (III‘) in Heisenberg representation: III B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, and E.S. Polzik, Nature 432, 482 (2004)

16. Quantum Optics VI Krynica 200516 Quantum approach D D a clone 1 a disp x p a clone 2 a in

17. Quantum Optics VI Krynica 200517 quantum cloning of coherent side bands Ulrik L. Andersen, Vincent Josse and G. L., quant-ph / 0501005, PRL ‘05

18. Quantum Optics VI Krynica 200518 quantum cloning of coherent side band (2) Ulrik L. Andersen, Vincent Josse and G. L., quant-ph / 0501005, PRL ‘05 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

19. Quantum Optics VI Krynica 200519 theory group N. Lütkenhaus U. L. Andersen (N. Korolkova) R. Filip T.C. Ralph O. Glöckl (Ch. Silberhorn) V. Josse S. Lorenz R. Loudon J. Heersink M.D. Reid Ch. Marquardt P.D. Drummond J. Schneider E.H. Huntington D. Elser H.A. Bachor M. Sabuncu N. Cerf J. Milanovic A B