GAP Optique 1 Quantum Communication  Quantum cryptography: a beautiful idea!  Quantum cryptography on a “black-board”  Quantum cryptography below lake Geneva  Quantum cryptography on noisy channels  Quantum teleportation  quantum memories Nicolas Gisin GAP-Optique, University of Geneva S. Fasel, J.-D. Gautier, Ivan Marcikic, G. Ribordy, H. de Riedmatten, V. Scarani, A. Stefanov, D. Stücki, S. Tanzilli, W. Tittel, H. Zbinden

GAP Optique 2 What is quantum communication  Quantum Communication is the art of transferring a quantum state from one location, Alice, to a distant one, Bob. Alice Bob  A quantum state can’t be copied, hence the original is necessarily destroyed and there remains no copy.  Copying quantum states would violate both Heisenberg’s uncertainty relations and the impossibility of faster than light signalling. Hence, the impossibility of “Q cloning” is one of the best established facts in Science.

GAP Optique 3 What is quantum communication  Quantum Communication is the art of transferring a quantum state from one location, Alice, to a distant one, Bob. photon splitter detectors The photon explores both paths Quantum randomness Quantum nonlocality (entanglement)

GAP Optique 4 Quantum cryptography: a beautiful idea Basic Quantum Mechanics: A quantum measurement perturbs the system QM  limitations However, QM gave us the laser, micro- electronics, superconductivity, etc. New Idea: Let's exploit QM for secure communications

GAP Optique 5  If Eve tries to eavesdrop a "quantum communication channel", she has to perform some measurements on individual quanta (single photon pulses).  But, quantum mechanics tells us: every measurement perturbs the quantum system.  Hence the "reading" of the "quantum signal" by a third party reduces the correlation between Alice's and Bob's data.  Alice and Bob can thus detect any undesired third party by comparing (on a public channel) part of their "quantum signal".

GAP Optique 6  The "quantum communication channel" is not used to transmit a message (information), only a "key" is transmitted (no information).  If it turns out that the key is corrupted, they simply disregard this key (no information is lost).  If the key passes successfully the control, Alice and Bob can use it safely.  Confidentiality of the key is checked before the message is send.  The safety of Quantum Cryptography is based on the root of Quantum Physics.

GAP Optique 7 Modern Cryptology Secrecy is based on: Information theory The key is secrete The key contains the decoding key: Only the two partners have a copy ! The security is proven (Shannon theorem) Example: Message: Key: Coded message: Complexity theory The key is public The public key contains the decoding key, but it is very difficult to find (one way functions) The security is not proven (no one knows whether one way functions exist) Example: 127 x 229 = 29083

GAP Optique 8 BB84 protocol: Eve  25% errors

GAP Optique 9

10 Experimental Realization  Single photon source  Polarization or phase control during the single photon propagation  Single photon detection avalanche photodiode (Germanium or InGaAs) in Geiger mode  dark counts based on supraconductors  requires cryostats laser pulses strongly attenuated (  0.1 photon/pulse) photon pair source (parametric downconversion) true single-photon source parallel transport of the polarization state (Berry topological phase)  no vibrations fluctuations of the birefringence  thermal and mechanical stability depolarization  polarization mode dispersion smaller than the source coherence Stability of the interferometers coding for the phase

GAP Optique 11 Single Photon Generation (1) Attenuated Laser Pulse Simple, handy, uses reliable technology  today’s best solution Poissonian Distribution 0% 20% 40% 60% 80% 100% Number of photons per pulse Probability Mean = 1 Mean = 0.1 Attenuating Medium 1nrather tha or..." 2or 1 0"

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GAP Optique 13 Polarization effects in optical fibers:  Polarization encoding is a bad choice !

GAP Optique 14 Phase Coding  Single-photon interference Basis 1:  A = 0;  Basis 2:  A =  Basis:  B = 0;  Compatible:Alice  A  D i BobD i  A (  A -  B = n  ) Incompatible:Alice and Bob ?? (  A -  B =  ) Bases

GAP Optique 15 Difficulties with Phase Coding  Stability of a 20 km long interferometer? Problems: stabilization of the path difference  active feedback control stability of the interfering polarization states Time (ns) Coincidences long -long 0 Time Window short -short short - long + long - short 

GAP Optique 16 The plug&play setup Perfect interference (V  99%) without any adjustments, since: both pulses travel the same path in inverse order both pulses have exactly the same polarisation thanks to FM Alice Bob Drawback 1: Rayleigh backscattering Drawback 2: Trojan horse attacks

GAP Optique 17 Faraday mirrors Faraday rotator standard mirror (  incidence) Faraday rotator FM Independent of 

GAP Optique 18 Avalanche photodiodes  Single-photon detection with avalanches in Geiger mode  macroscopic avalanche triggered by single-photon Silicon:1000 nm Germanium:1450 nm InGaAs/InP:1600 nm Typical value for InGaAs at -50 C o :  =10%, D=10 -5

GAP Optique 19 QC over 67 km, QBER  5% + aerial cable (in Ste Croix, Jura) ! D. Stucki et al., New Journal of Physics 4, , Quant-ph/ RMP 74, , 2002, Quant-ph/

GAP Optique 20 + aerial cable (in Ste Croix, Jura) ! Rev.Mod.Phys. 74, 145, 2002 New Journal of Physics 4, , 2002 Quantum Cryptography under lake Geneva km + aerial cable (in Ste Croix, Jura) !

GAP Optique 21 Used daily by some commercial customers Spin-off from the University of Geneva, km Installed multiplexed quantum channel for commercial users.

GAP Optique 22Eavesdropping  incoherent attacks : Eve attaches independent probes to each qubit and measures them individually after basis reconciliation  coherent attacks : process several probes coherently after privacy amplification  finite attacks  infinite attacks AliceBob EveU perturbationinformation

GAP Optique 23 Before using the key Alice and Bob must:  Evaluate QBER (Quantum Bit error Rate = Disturbance)  Apply a classical error correction protocol: e.g. compare b k +b n. If Alice and Bob agree, they keep b k and drop b n. If Alice and Bob disagree they drop both bits.  Apply a classical privacy amplification protocol: e.g. replace b k with b k +b n.  Alice and Bob must evaluate how much information Eve may have !

GAP Optique 24 From raw to net key AliceBob error correction XOR=1 00 Quantum channel Public channel (loss) transmission basis reconciliation estimation of QBER Sifted key, sifted bit-rate Raw key XOR=0XOR=1 – 0 – XOR=1 – 0 – 1 – 1 0 – 1 0 Eve 0 XOR 0 = 0 0 XOR 1 = 1 privacy amplification secure key, net rate secure key I(  ) > I max (  ) distillation of a secure key how to find I(  )? how to find I(  )?

GAP Optique 25 Alice Eavedropping (cloning) machine U Bob Eve Bell states Error operator:

GAP Optique 26 Where: N. Cerf et al., PRL 84,4497,2000 & 88,127902,2002

GAP Optique 27 individual, symmetrical attacks and BB’84 - R net =R sifted ( I (  ) - I max (  ) ) secret-key rate one way communication Bob's information Eve's information Information [bit] QBER (Disturbance) QBER max classical error correction and privacy amplification Individual/finite collective, symmetric attacks: QBER Max  15 % infinite collective attacks: QBER Max  11 % (lower bound)

GAP Optique 28 I AE 2-wayAlice quantum. Inf. Proc.and sufficeBob separated Bell inequality: can be never violated or classical 1-way class. Inf. Proc. suffice D0D0

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GAP Optique 30 Quantum Hacking 1.There is nothing like “unconditional security” ! (as emphasized in our 2002 RMP) 2.But it should not obscure the fact that there is nothing like cracking QKD ! In contrast, in classical crypto both the principle and the implementation can be attacked. If the principle of classical crypto gets broken, then -All electronic money looses all value -All past communications can be read The principle of QKD will never be attacked, only the implementation.

GAP Optique 31 Long distance QKD: World records 150 km of installed fibers, Optics Express 17, (2009) Lausanne 250 km in the lab. NJP 11, (2009)

GAP Optique 32 P2P + WDM Today Commercial Today Lab +4 Years kHz 100kHz Distance [km] Rate 1Hz MHz 10kHz 1MHz There is a hard wall around 400 km ! Secret Key Rate With the best optical fibers, perfect noise-free detectors and ideal 10 GHz single-photon sources, it would take centuries to send 1 qubit over 1000 km ! How far can one send a photon ?

GAP Optique 33 Beating the hard wall: Teleportation of entanglement Entanglement Q teleportation Entanglement over twice the distance  Entanglement between photons that never interacted PRA 71, 05302, 2005

GAP Optique 34 The Geneva Teleportation experiment over 3x2 km Photon = particle (atom) of light Polarized photon (  structured photon) Unpolarized photon (  unstructured  dust)

GAP Optique metres 2 km of optical fibre 2 km of optical fibre Two entangled photons

GAP Optique metres 2 km of optical fibre

GAP Optique metres Bell measurement (partial) the 2 photons interact 4 possible results: 0, 90, 180, 270 degrees

GAP Optique metres Bell measurement (partial) the 2 photons interact 4 possible results: 0, 90, 180, 270 degrees Perfect Correlation The correlation is independent of the quantum state which may be unknown or even entangled with a fourth photon

GAP Optique 39 Quantum teleportation     z    x    y  Bell 2 bits U 

GAP Optique 40 What is teleported ?  According to Aristotle, objects are constituted by matter and form, ie by elementary particles and quantum states.  Matter and energy can not be teleported from one place to another: they can not be transferred from one place to another without passing through intermediate locations.  However, quantum states, the ultimate structure of objects, can be teleported. Accordingly, objects can be transferred from one place to another without ever existing anywhere in between! But only the structure is teleported, the matter stays at the source and has to be already present at the final location.

GAP Optique 41 Implications of entanglement  The world can’t be understood in terms of “little billiard balls”.  The world is nonlocal (but the nonlocality can’t be used to signal faster than light).  Quantum physics offers new ways of processing information.

GAP Optique 42 Photon pairs source laser nonlinear birefringent crystal filtre l s,i lplp  Parametric fluorescence  Energy and momentum conservation  Phase matching determines the wavelengths and propagation directions of the down-converted photons

GAP Optique  source of Aspect’s 1982 experiment

GAP Optique 44 Photon pairs source (Geneva 1997)  Energy-time entanglement  diode laser  simple, compact, handy  40 x 45 x 15 cm 3  I pump = 8 mW  with waveguide in LiNbO 3 with quasi phase matching, I pump  8  W KNbO 3 F Laser L P  655nm output 1 output 2 lens filter crystal laser

GAP Optique 45 The qubit sphere and the time-bin qubit  qubit :  different properties : spin, polarization, time-bins  any qubit state can be created and measured in any basis variable coupler variable coupler les i   1 0   h AliceBob D 0 D 1 switch 1 0

GAP Optique 46 entangled time-bin qubit  variable coupler B s A s l B l A  depending on coupling ratio and phase , maximally and non-maximally entangled states can be created non-linear crystal  extension to entanglement in higher dimensions is possible  robustness (bit-flip and phase errors) depends on separation of time-bins

GAP Optique 47 2-photon Q cryptography: Franson interferometer Two unbalanced interferometers  no first order interferences One can not distinguish between "long-long" and "short-short" Hence, according to QM, one should add the probability amplitudes  interferences (of second order) photon pairs  possibility to measure coincidences

GAP Optique 48 test of Bell inequalities over 10 km d 1 KNbO km 9.3 km Genève Bellevue Bernex quantum channel classical channels F laser LP R++ R-+ R+- R-- d 2 APD & FS Z FM Z 4.5 km 7.3 km 10.9 km

GAP Optique 49 results  15 Hz coincidences  S raw = 2.41  S net = 2.7  violation of Bell inequalities by 16 (25) standard- deviations  close to quantum- mechanical predictions  same result in the lab

GAP Optique 50 le labo

GAP Optique 51 2 km of optical fiber Alice Alice:creation of qubits to be teleported Alice 55 m Bob Bob:analysis of the teleported qubit, 55 m from Charlie Bob Charlie Charlie:the Bell measurement Charlie fs 710 nm Experimental setup creation of entangled qubits coincidence electronics & LBO RG WDM RG WDM Ge InGaAs LBO BS InGaAs f s l a s e r sync out 1. 3 m  1. 3 m  1. 5 m  1. 5 m  2km

GAP Optique 52 Bell measurement

GAP Optique 53results Equatorial states Raw visibility : V raw = 55 ± 5 % = 77.5 ± 2.5 % = 78 ± 3% = 77 ± 3% North & south poles mean fidelity: F poles =77.5 ± 3 % 77.5 ±2.5 % Mean Fidelity » 67 % (no entanglement)

GAP Optique 54 Requirements for Quantum Repeaters 1.Distribution of entanglement over long distances 2.Multi-mode quantum memories 3.Entanglement telecom C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden and N. Gisin Phys. Rev. Lett. 98, (2007)

GAP Optique 55 Δ continuous  Dephasing Δ periodic  Rephasing Absorption Frequency Absorption Frequency Rephasing after Controlling the Dephasing! Atomic Frequency Comb

GAP Optique 56 Atomic detuning  Atomic density Output mode Input mode State after absorption Atomic Frequency Comb (AFC) Quantum Memory Ensemble of inhomogeneously broadened atoms Intensity Time Input mode Output mode Control fields Storage state Intensity Time Input mode Output mode  (superradiant Dicke state) M.Afzelius, C.Simon, H. de Riedmatten and N.Gisin, Phys Rev A 79, (2009) BACKWARD Dephasing Periodic structure => Rephasing after a time Collective emission in the forward mode. Photon echo like emission

GAP Optique 57 AFC echo input transmitted echo 20%

GAP Optique 58 Multi-mode storage in Nd 3+ :Y 2 SiO 5 Mapping 64 input modes onto one crystal  n  < 1 per mode 64 time modes can be used to code 32 time-bin qubits! I. Usmani et al., Nature Communications 1,12 (2010)

GAP Optique 59 Probing the coherence of the storage By preparing two gratings, it is possible to read out twice:   Atomic density Atomic detuning     time Preparation sequence Spectral gratings Storage pulses Echoes      M. Staudt et al, PRL 98, (2007) Light Intensity

GAP Optique 60 Visibility : 95 ±3 % Probing the coherence of the storage Incident pulses: 0.8 photon per pulse on average Storage times: 200 ns and 300 ns H. De Riedmatten, M. Afzelius et al, Nature 456, 773, 2008

GAP Optique 61 Nd 3+ :YSO crystal Demonstration of entanglement between a telecom photon and an excitation stored in a crystal Clausen, Usmani et al, Nature 469, , 2011

GAP Optique 62 Filtering Frequency Absorption ~ 6 GHz ~ 100 MHz  Photon from guide  Diffraction grating  Fabry-Perot Cavity  2 Etalons 883 nm 1.5 THz 90GHz FSR = 42, 50 GHz Γ = 600 MHz 1338 nm 1.5 THz 60 GHz FSR = 24 GHz Γ = 45 MHz

GAP Optique 63 Photon – Crystal Entanglement Photon-Crystal entanglement with a violation of the CHSH-Bell inequality: S=2.64 > 2 V raw  80% Clausen, Usmani et al, Nature 469, , 2011

GAP Optique 64 Nature Photonics 6, 234-7, 2012 Heralded quantum entanglement between two crystals

GAP Optique 65 Nature Photonics 6, 234-7, 2012 Heralded quantum entanglement between two crystals

GAP Optique 66 Bit rate of the 1 st transatlantic telegram How long did it take to transmit this congratulation in 1858 ? "The Queen desires to congratulate the President upon the successful completion of this great international work, in which the Queen has taken the deepest interest. The Queen is convinced that the President will join with her in fervently hoping that the electric cable, which now connects Great Britain with the United States, will prove an additional link between the two places whose friendship is founded upon their common interests and reciprocal esteem. The Queen has much pleasure in thus directly communicating with the President, and in renewing to him her best wishes for the prosperity of the United States." 17 hours ! (1 letter took 2 minutes)

GAP Optique 67 Conclusions  Quantum cryptography is a beautiful idea ! (RMP 74, , 2002)  Quantum cryptography exists: you can buy it !  Quantum cryptography relates basic physics to the telecom industry: –from quantum correlations to optical fibers, –from Bell inequalities to security, –from optimal cloning to Shannon information, etc.  Q teleportation with: (Nature 421, 509, 2003)  Q memories for quantum repeaters = the possibility to teleport the "ultimate structure" of an object from one place to another, without the object ever being anywhere in between