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

Quantum Optics VI Krynica 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

Quantum Optics VI Krynica Entanglement generation

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

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

Quantum Optics VI Krynica  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_ (2004)) Continuous Variables and Beam Splitters (2) in discrete case: Knill, Laflamme, Milburn Nature 409, 46 (2001)

Quantum Optics VI Krynica 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  …

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

Quantum Optics VI Krynica “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

Quantum Optics VI Krynica 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:

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

Quantum Optics VI Krynica 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)

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

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

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

Quantum Optics VI Krynica 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