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Home , Nicolas Gisin, Quantum cloning, Quantum teleportation

H. Deriedmatten, I. Marcikic, R. Thew, W. Tittel, H. Zbinden Groupe de Physique Appliquée-unité d’Optique Université de Genène • The science and the science-fiction of • Intuitive and mathematical introduction • What is teleported ? • Q fax? The no-cloning theorem • The “teleportation channel”: Entanglement • The Geneva experiment Geneva University Geneva • Telecom wavelengths • Time-bin • partial Bell measurement and tests of Bell inequality • Applications: GAP Optique GAP Optique • Simplifications, limitations • Q relays and Q repeaters 1 The Geneva Teleportation experiment over 3x2 km

Photon = particle (atom) of light

Polarized Unpolarized photon ≈ ( structured photon) (≈ unstructured ≈ dust) Geneva University Geneva GAP Optique GAP Optique

2 55 metres

2 km of 2 km of optical fibre optical fibre Geneva University Geneva

Two entangled GAP Optique GAP Optique

3 55 metres

2 km of

Geneva University Geneva optical fibre GAP Optique GAP Optique

4 55 metres

Bell measurement (partial)

the 2 photons Geneva University Geneva interact

4 possible results: 0, 90, 180, 270 degrees GAP Optique GAP Optique

5 55 metres

Bell measurement (partial)

the 2 photons ion Geneva University Geneva at interact rel Cor ect erf 4 possible results: P The correlation is independent of the quantum 0, 90, 180, 270 degrees

GAP Optique GAP Optique state which may be unknown or even entangled with a fourth photon 6 Quantum teleportation ψ 2 U Bell

ψ ⊗ EPR = + ⊗ + (c 0 0 c1 1 ) ( 0,0 1,1 ) / 2 11 = ((00,0,0 ++ 11,1,1 )) ⊗ ( c 0 + c 1 ) 2 0 1 Ψ 2 2 123 1 Geneva University Geneva + ((00,0,0 −− 11,1,1 )) ⊗ ( c 0 − c 1 ) 2 0 1 σ Ψ 2 2 123 z 1 + ((00,1,1 ++ 11,0,0 )) ⊗ ( c 0 + c 1 ) 2 22 1 0 σ Ψ x

GAP Optique GAP Optique 123 1 + ((00,1,1 −− 11,0,0 )) ⊗ ( c 0 − c 1 ) 2 22 1 0 σ Ψ 123 y 7 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 Geneva University Geneva 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 GAP Optique C.H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres and W. Wootters, PRL 70, 1895 (1993) D. Boschi et al., Phys. Rev. Lett. 80, 1121 (1998) Y-K. Kim et al., Phys. Rev. Lett. 86, 1370 (2001) D. Bouwmeester et al., 390, 575 (1997) I. Marcikic et al., Nature 421, 509 (2003) 8 A Quantum Fax ?

During a quantum teleportation process, the original system is destroyed.

According to the basic law of quantum , this is a necessity since it is impossible to clone an unknown . If not: – one could violate Heisenberg’s uncertainty relations

Geneva University Geneva (Quantum Physics would be deterministic !) – one could exploit entanglement and cloning to signal faster than light. (Relativity would have an absolute time). GAP Optique GAP Optique

9 No cloning theorem and the compatibility with relativity No cloning theorem: It is impossible to copy an unknown quantum state, ψ →// ψ ⋅ψ Proof #1: 0 → 0,0 0 + 1 → 0,0 + 1,1 ⇒ 1 → 1,1 ≠ ( 0 + 1 ) ⊗ ( 0 + 1 ) Proof #2: (by contradiction) Alice Source of Bob Geneva University Geneva entangled particules M * }clones GAP Optique GAP Optique

Arbitrary fast signaling ! 10 No cloning theorem and the compatibility with relativity

• The first account on was done by E.P. Wigner in his analysis of earlier work by W.M. Elsasser devoted to a discussion of the origin of life and the multiplication of organisms. Wigner has presented a quantum-mechanical argument according to which ``the probability is zero for existence of self-reproducing states''.

• Today’s standard references are:

Geneva University Geneva W. K. Wootters and W. H. Zurek, Nature 299, 802, 1982. P.W. Milonni and M.L.Hardies, Phys. Lett. A 92, 32, 1982.

• The connection to “no signaling” appeared in: GAP Optique GAP Optique N. Gisin, Phys. Lett. A 242, 1, 1998.

11 The Quantum Teleportation channel ? Geneva University Geneva GAP Optique GAP Optique

12 Entanglement A ρ is separableρ iff it decomposes in product states with probabilité coefficients p >0 : ρ j = A ⊗ ρ B ∑ j p j j j

ρ is entangled iff it is not separable. Given a ρ, one knows of no constructive method to determine wheher ρ is separable or entanglement ! Geneva University Geneva

The partial transpose test : pt If ρ is seprable, then its partial transpose is ρ ≥ 0 ρ αβ GAP Optique GAP Optique pt ≡ ρ β whreab, a ,αb (this test is exhaustive en dim 2x2) 13 Non-locality: definition P(a,b | A, B)

probability Events. Experimental settings. Not under human Under human control control

The correlations P(a,b|An,Bm) are local iff there is a random variable λ such that:

Geneva University Geneva λ λ λ P(a,b|An,Bm, ) = P(a|An, ) ·P(b|Bm, )

Historically λ was called a “local hidden variable”. Today, one measures the amount of nonlocality by the minimum GAP Optique GAP Optique communication required to reproduce P(a,b|An,Bm).

14 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).

Geneva University Geneva Quantum physics offers new ways of processing information. GAP Optique GAP Optique

15 WhatWhat can can carry be the teleported Q info to ? be teleported ? Photon Done 

Atom Probably soon !

Molecule Likely some day

Virus ?? Possibly ?? Geneva University Geneva

GAP Optique GAP Optique Large object Still science-fiction

16 Q communication in optical fibres

Two problems : Losses and decoherence. How to minimize them ?

The transmission depends on the wavelength - Lower attenuation : 1310 nm (0.3 dB/km) and 1550 nm (0.2dB/km) (telecom wavelengths)

 Decoherence due to birefringence : Geneva University Geneva Polarization Mode Dispersion

Time-bin coding with photons at telecom wavelength GAP Optique GAP Optique

17 Time-bin qubits

ψ = + iφ ‰ : c0 0 c1e 1 0

0 − i 1 ‰ 2 any qubit state can be created and 0 + 1 0 − 1 measured in any basis 2 2 0 + i 1 2

ψ = + iφ 1 Alice c0 0 c1e 1 Bob φ ϕ D 1 0 Geneva University Geneva ν 1 0 h 0 D1 switch switch variable coupler variable coupler GAP Optique GAP Optique State preparation Projective measurement

W. Tittel & G. Weihs, Quant. Inf. Comput. 1, Number 2, 3 (2001) 18 Photon pairs source λ λ p s,i nonlinear filtre birefringent crystal Parametric fluorescence Energy and momentum conservation ω = ω + ω r = r + r p s i kp ks ki Phase matching determines the wavelengths and propagation directions of the down-converted photons

Geneva University Geneva Energy conservation: ⇒ each photon from the pair has an uncertain frequency, but the sum of the two frequencies is precisely that of the pump laser ⇒ each photon from the pair has an uncertain age,

GAP Optique GAP Optique but the age’s difference is precisely zero

⇒ similar to the original EPR state 19 Time-bin entanglement α 0 φ 1 A A φ + 2 km + Detectors & optical fibers Coincidence Variable Laser PDC coupler 1 B 0 B ψ = c 0 0 + c e iφ 1 1 β 0 A B 1 A B Photon pair creation in a non-linear crystal 250 V net =96% Parametric down-conversion (PDC) After 2x2km Energy and momentum200 conservation of optical fibers Geneva University Geneva r r r ω =ω +ω150 = + Robust againstp s i k p k s k i

decoherence 100 λ Noise level in optical fibers s=1310nm λ =710nm p 50 λ GAP Optique GAP Optique coincidences [/10s] i=1550nm

0 R. Thew et al., Phys. Rev. A 66, 0623040 (2002) 20406080100 20 phase[arb unit] The interferometers

C FM 1 2 δ 3 FM

single mode fibers Geneva University Geneva Michelson configuration circulator C : second output port Faraday mirrors FM: compensation of birefringence

GAP Optique GAP Optique temperature tuning enables phase change

21 Optical circulator verticalhorizontal -45° pol. pol. PBS@45°

portport 22

Faraday PBS@0° effect

port 1 Geneva University Geneva horizontalvertical +45° pol. pol.pol.

GAP Optique GAP Optique port 3

22 Faraday mirrors

λ • 4 Faraday rotator • standard mirror (⊥ incidence) λ • 4 Faraday rotator

FM

Geneva University Geneva → ω r → − ω r mr R( )mω ( R( )m) − mr ← R−1( )(−R(ω)mr ) ← GAP Optique GAP Optique ω Independent of 23 Partially Entangled Time-Bin Qubits

φ ψ = + i p c0 00 c1e 11

Geneva University Geneva = V 2c0c1

= − 2 2 − 2 2 E c0 log2 c0 c1 log2 c1 GAP Optique GAP Optique

R. Thew et al., Phys. Rev. A 66, 062304 (2002) 24 Geneva 1997 Geneva University Geneva GAP Optique GAP Optique

25 2-υ source of Aspect’s 1982 experiment Geneva University Geneva GAP Optique GAP Optique

26 Photon pairs source (Geneva 1997)

P F L r se La nm 55 6 KNbO3 Energy-time entanglement ‹ λ = 655 nm; λ =1310 nm output 1 output 2 p s,i diode laser

crystal lens simple, compact, handy 40 x 45 x 15 cm3 filter Ipump = 8 mW Geneva University Geneva laser with waveguide in LiNbO3 with quasi phase matching, ≈ µ Ipump 8 W GAP Optique GAP Optique

27 test of Bell inequalities over 10 km

Bellevue

4.5 km FM δ1

l ne Z FM an ch APD1 + tum an qu km Genève 8.1 - APD1

R++ F m r P L R-+ k se la & 9 R+- classical channels . KNbO 0 3 R-- 1

Geneva University Geneva APD 2- 9 .3 k q m ua APD2+ nt um S F ch Z ann δ2 el 7 FS .3 km GAP Optique GAP Optique Bernex

28 results

1.0 15 Hz coincidences

Sraw = 2.41

Snet = 2.7 0.5 violation of Bell

inequalities by 16 t

n (25) standard-

e

i

c i deviations

f 0.0 f

e close to quantum- o

c mechanical

n o

i predictions

t a Geneva University Geneva

l -0.5 same result in the e

r V = (85.3 ± 0.9)%

r raw lab o c V = (95.5 ± 1) % net. 0 1000 4000 7000 10000 13000

GAP Optique GAP Optique time [sec]

29 I. Marcikic et al., Nature, teleportation setup 421, 509-513, 2003

InGaAs C & Creation of a qubit Ge InGaAs β A B

Beam splitter 50:50 Creation of an entangled pair

α Creation of a photon

WDM RG filter WDM RG filter Creation of any qubit to be teleported LBO LBO The Bell measurement Geneva University Geneva

Φ Analysis of the teleported qubit Mode locked Ti:Saphire

GAP Optique GAP Optique Femto-second laser Coincidence electronics Pulse width =150 fs 3-fold 4-fold 30 A B BellBell statestate measurementmeasurement

1 2 0 1 i0 1 +i0 1 +0 1 −1 0 1 0 i0 1 +i0 1 −0 1 +1 0 1 2 a A A B B A B A B 1 2 a A A B B A B A B Geneva University Geneva

0 1 + 1 0 i( 0 1 + 0 1 ) 0 1 − 1 0 0 1 − 1 0 1 2 1 2 a A A B B 1 2 1 2 a A B A B GAP Optique GAP Optique

H. Weinfurter, Europhysics Letters 25, 559-564 (1994) H. de Riedmatten et al., Phys. Rev. A 67, 022301 (2003) 31 Geneva University Geneva GAP Optique GAP Optique

32 Teleportation of a time-bin qubit equatorial states

35 10000 „ 2 photons +laser clock 30 (1310&1550nm) 8000 { 3 photons+laser clock 25

20 6000

15 4000 Raw visibility : 10 Vraw=70 ± 5 % 2000 5 3-fold coindences [/500s] coindences 3-fold 4-fold coincidences [/500 s] [/500 coincidences 4-fold Geneva University Geneva 0 0 4567891011 phase β [a.u]

1+V GAP Optique GAP Optique Fidelity for equatorial states : F = raw =85 ± 2.5 % eq 2 33 Teleportation of a time-bin qubit North&South poles

Initial qubit 300 Time-bin 0 Time-bin 1 prepared in : P()1,0 250 F()0.1 = time-bin0 P()1,0 + P()0,1 time-bin1 200

150

100 F()0,1 = 88% ± 4% coincidences [a.u] coincidences

Geneva University Geneva 50 F()1,0 = 84% ± 4%

0 0123456 delay between start&stop [ns] GAP Optique GAP Optique = 2 + 1 = Ftot Feq Fp 85 % ± 3 % 3 3 34 Bob ExperimentalExperimental setupsetup & Charlie InGaAs Ge fs laser @ 710 nm InGaAs fs laser @ 710 nm

55 m BS AliceAlice:creation:creation of of qubits qubits to to

2 k bebe teleported teleported m

m Alice 2k k m 2 creationcreation of of entangled entangled qubits qubits m µ 1 .3 . 1.5 1 3 µm µ m WDM µm CharlieCharlie:the:the Bell Bell measurementmeasurement 1.5 WDM RG Bob:analysis of the RG Bob:analysis of the LBO LBO teleportedteleported qubit, qubit, 5555 mm fromfrom Geneva University Geneva CharlieCharlie

22 kmkm of of optical fiber

er coincidence electronics GAP Optique GAP Optique coincidence electronics s sync out

fs la I. Marcikic et al., Nature, 421, 509-513, 2003 35 1 resultsresults

C Equatorial states F = correct + 0 Ccorrect Cwrong 40 MeanMean9000FidelityFidelity F()0,1 35 = 78 ± 3% 8000 30 = 2 7000+ 1 F()1,0 = 77 ± 3% 25 Fmean Feq 6000 Fp 5000 20 3 3 4000 15 = mean fidelity: Fpoles=77.5 ± 3 % 77.5 3000±2.5 % 10 2000 North & south poles 5 1000 four-fold coincidences [1/500s] [1/500s] coincidences coincidences four-fold four-fold Three-fold coincidence [/500s] [/500s] Three-fold Three-fold coincidence coincidence 0 » 67 % 0 (no entanglement)

Geneva University Geneva 024681012141618 1.0 Phase [arb. units] 0.8

0.6 Raw visibility : Vraw= 55 ± 5 % + 0.4 =1 Vraw 0.2 eq = 77.5 ± 2.5 % unit] coincidence[arb GAP Optique GAP Optique F 2 0.0 0123456 time between start and stop [ns] 36 Bob ExperimentalExperimental setupsetup & Charlie InGaAs Ge fs laser @ 710 nm InGaAs fs laser @ 710 nm

55 m BS AliceAlice:creation:creation of of qubits qubits to to

2 k bebe teleported teleported m

m Alice 2k k m 2 creationcreation of of entangled entangled qubits qubits m µ 1 .3 . 1.5 1 3 µm µ m WDM µm CharlieCharlie:the:the Bell Bell measurementmeasurement 1.5 WDM RG Bob:analysis of the RG Bob:analysis of the LBO On the LBO teleportedteleported qubit, qubit, 5555 mm fromfrom Geneva University Geneva same CharlieCharlie spool ! 22 kmkm of of optical optical fiber fiber

er coincidence electronics GAP Optique GAP Optique coincidence electronics s sync out

fs la I. Marcikic et al., Nature, 421, 509-513, 2003 37 Tailoring high dimensional time-bin entanglement Rc

TAC Mode-locked fs Ti:Saphire f=75 MHz λ ∆τ = 150 fs =710nm Ge APD InGaAs APD

λ=1310 nm λ AOM =1550 nm WDM

∆τ=13 ns LBO

d pulses train NLC BS δ Bulk interferometer Analysis with 2-arms 1.0 interferometer 0.9 0.8 0.7 Geneva University Geneva − V=Vmaxd 1 0.6 d 0.5 0.4

de Riedmatten et al, Visibility 0.3 Quant. Inf. Comput, 2, 425 (2002) 0.2

GAP Optique GAP Optique 0.1 0.0 5101520 38 Dimension d StabilisationStabilisation ofof thethe interferometersinterferometers

Idea: verify from time to time the phase

Feedback Stabilisation period ~ 5 [s] 5

4 BS PIN 3

Phase 2 WDM Measuring period controler ~ 100 [s] Stabilised laser Switch units] [arb. Intensity 1

FM 0 10800 10820 10840 10860 10880 10900 10920 10940 Time [s] FM

Geneva University Geneva APD EPR Source Every 100 s the phase is brought back to a given value GAP Optique GAP Optique

39 BellBell testtest overover 5050 kmkm

0 = short path Type I NLC ϕ µ 1 = long path Creating photons @ 1.3 & 1.55 m

Φ + = 1 ()0 0 + 1 1 2 A B A B

Bob Alice 25 km SOF 25 km DSF α β A-1 B-1 & A B 1 & 1 0 1 p A 0 p1 B

Geneva University Geneva 1 0 1 0 p A 0 p 0 A 0 B p B 1 1 1 0 p 0 A 1 p1 A p A B 0 p0 B 1 p1 B 0 1 1 p A B 1 0 0 1 1 0 p A B 0 0 1 α β ∝ + α + β p A B p A B Pij ( , ) 1 ijV cos( ) Time arrival on A1 Time arrival on B1 0 1 0 1 0 1 p A B p A B GAP Optique GAP Optique No single photon interference because his twin photon gives information of creation time 40 Coincidence between Ai & Bj BellBell testtest overover 5050 kmkm

‰ Until now no phase control

‰ Correlation function: E(α, β ) = V cos(α + β )

‰ Violation of Bell inequalities depends on visibility: 4 1.0 S = V 0.8

2 0.6 Row visibility after 50 km 0.4 0.2

Geneva University Geneva = ± 0.0 Vraw 78 1.6% -0.2

-0.4

S = 2.21± 0.04 Function Correlation -0.6

-0.8

GAP Optique GAP Optique Violation of Bell inequalities σ -1.0 by more than 4.5 0 20406080100 Phase α+β [a.u] 41 α β BellBell testtest overover 5050 kmkm α ‰ With phase control weβ can choose four different settings α = 0° or 90° and β = α-45° or 45° β ‰ Violation of Bell inequalities: α S = E( = 0° , = −45° ) + E( = 90° , = −45° ) + E( = 0° , = 45° ) − E( = 90° , β = 45° ) α ° ° 1.01.0 = β = − = ± 1.0 E( 0 , 45 ) 0.518 0.006 1.0 1.0 0.80.8 0.8 α 0.8 0.8 0.6 ° ° 0.60.6 = β = − = ± 0.6 0.6 E( 90 , 45 ) 0.554 0.005 0.4 0.40.4 0.4 0.4 α 0.2 0.20.2 Geneva University Geneva ° ° 0.2 0.2 E( = 0 , β = 45 ) = 0.533± 0.006 0.0 0.00.0 0.0 0.0 α -0.2 -0.2 ° ° -0.2 -0.2-0.2 Correlation Function -0.4

= β = = ± Correlation Function Correlation Function E( 90 , 45 ) 0.581 0.007 Correlation Function -0.4 -0.4-0.4 -0.4

-0.6 Correlation Function -0.6 -0.6-0.6 -0.6 -0.8 -0.8 -0.8-0.8 -0.8 = ± -1.0 -1.0 -1.0 0.00.20.40.60.81.01.21.4 GAP Optique GAP Optique S 2.185 0.012 -1.0 -1.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.00.0 0.2 0.2 0.4 0.4 0.6 0.8 0.8 1.0 1.0 1.2 1.2 0.0 0.5 1.0Time 1.5 Time[h] [h] 2.0 2.5 3.0 3.5 Violation of Bell inequalities TimeTime [h] [h] σ by more than 15 42 For what could Q teleportation be useful ? For the ’s fascination ! For teaching Q physics ! For the secure communications of tomorrow !

If the structure to be teleported contains a message, then no adversary can intercept it, since it doesn’t exist anywhere inbetween the emitter and the receiver !

Geneva University Geneva to make the idea practical with today’s technology Let’s exploit this idea

GAP Optique GAP Optique to improve tomorrow’s

43 Geneva University Geneva GAP Optique GAP Optique

44 Experimental QKD with entanglement W. Tittel et al., pulsed source PRL 84, 4737, 2000

to Alice Bob

D D

D NL crystal D Perfect correlation in the time domain

Geneva University Geneva counts counts

t-to t-to GAP Optique GAP Optique

Perfect correlation in the frequency domain 45 SimulationSimulation ofof QKDQKD overover 5050 kmkm 0

BB84 protocol 0 + 1 0 − 1 2 2 ϕ 0 , 1 basis

0 + 1 0 − 1 1 , basis 2 2

Alice Bob 25 km SOF 25 km DSF αβ A0 B0 Geneva University Geneva

A1 CodingCoding B1 0 1 α β 0 1 p A Passiveand suchchoice that p B 1 0 1 0 p A of basis p B always0 0 coincidence1 1 0 0 1 1 0 0 1 1 p A p A p B p B A0B0 = 0 and A1B1 = 1 GAP Optique GAP Optique 01 46 SimulationSimulation ofof QKDQKD overover 5050 kmkm 0 + 1 0 − 1 , basis 10000 9000

2 2 8000

Bit Rate7000 RA0B0+RA1B1 4000 1400 6000 0.5

3500 5000

4000 3000 0.45 Coincidences [arb.unit] 3000 2500 1200

2000 2000 0.4 1000

1500 Coincidences [arb.unit] Coincidences 1000 0 1600 1650 1700 1750 18000.35 1850 1900 1000 Delay between start & stop [arb.unit]

500 R + R 0.3 0 800 A0B1 A1B0 400 450 500 550 600 650 700 750= 800 850 900 Delay between startQBER & stop [arb.unit] Coincidences between A0 and B0 + + + 0.25 R R R R QBER A0B0 A1B1 A0B1 A1B0 Coincidences600 between A1 and B0 12000 Rate [200 Rate s] Bit 0.2

12000 10000 0.15 10000 400 8000 Geneva University Geneva 8000 0.1 6000

6000 200 Coincidences [arb.unit] Coincidences 4000 0.05

Coincidences [arb.unit] Coincidences 4000

2000

2000 0 0 0123456 0 2800 2850 2900 2950 3000 3050 3100 0 Time [h] Delay between start & stop [arb.unit] 4000 4050 4100 4150 4200 4250 4300 Delay between start & stop [arb.unit] GAP Optique GAP Optique Mean value of QBER = 10 % Coincidences between A and B Coincidences between A0 and B1 1 1 47 SimulationSimulation ofof QKDQKD overover 5050 kmkm 0 , 1 basis Wrong counts

6000

5000

4000 Wrong QBER = ∑ =13.3% 3000 ∑(Wright +Wrong)

2000

1000 Geneva University Geneva

0 500 600 700 800 900

Delay between start & stop [arb.unit]

Wright counts Coincidences between A0 and B0 GAP Optique GAP Optique

48 Experimental QKD with entanglement W. Tittel et al., PRL 84, 4737, 2000 pulsed source

to Alice Bob

D D

D NL crystal D Geneva University Geneva GAP Optique GAP Optique

49 Experimental QKD with entanglement

cw source Alice* Bob

NL crystal

Geneva University Geneva J. Franson, PRL 62, 2205, 1989 W. Tittel et al., PRL 81, 3563-3566, 1998 GAP Optique GAP Optique

50 From Bell tests to Quantum cryptography 100% correlation ⇒ perfect key Fragile correlation ⇒ secret key Alice Bob *

Geneva University Geneva W. Tittel et al., PRL 81, 3563-3566, 1998 GAP Optique GAP Optique

51 From Bell tests to Quantum cryptography 100% correlation ⇒ perfect key Fragile correlation ⇒ secret key Alice Bob * * Geneva University Geneva G. Ribordy et al., Phys. Rev. A 63, 012309, 2001 P.D. Townsend et al., Electr. Lett. 30, 809, 1994 R. Hughes et al., J. Modern Opt. 47, 533-547 , 2000 GAP Optique GAP Optique

52 Quantum cryptography below lake Geneva

Alice Bob Att.

PBS * F.M. Geneva University Geneva

Applied Phys. Lett. 70, 793-795, 1997. . Letters 33, 586-588, 1997; 34, 2116-2117, 1998. J. Modern optics 48, 2009-2021, 2001. GAP Optique GAP Optique

53 Pseudo single-photon Q cryptography: the Plug-&-Play configuration

Bob Alice Laser

FR PM APD

D APD A PBS PM

Drawback 1: Drawback 2: PerfectRayleigh interference backscattering (V≥99%) withoutTrojan any adjustments horse attacks, since: Geneva University Geneva • both pulses travel the same path in inverse order • both pulses have exactly the same polarisation thanks to FM GAP Optique GAP Optique

54 RMP 74, 145-195, 2002, QC over 67 km, QBER ≈ 5% Quant-ph/0101098 Geneva University Geneva GAP Optique GAP Optique + aerial cable (in Ste Croix, Jura) ! D. Stucki et al., New Journal of Physics 4, 41.1-41.8, 2002. Quant-ph/0203118 55 Company established in 2001 – -off from the

Products – Quantum Cryptography (optical fiber system) – Quantum Random Number Generator – Single-photon detector module (1.3 µm and 1.55 µm) Geneva University Geneva

Contact information email: [email protected] GAP Optique GAP Optique web: http://www.idquantique.com 56 1.0 = − I AB 1 H(QBER) 0.8 ≤ IAE 1-IAB

0.6

IAE 0.4

Geneva University Geneva 0.2 Shannon Information Bell inequ. violated Bell inequ. not violated 0.0 0.0 0.1 0.2 QBER GAP Optique GAP Optique

57 Limits of Q crypto

n ≈ η ≈ 0.1 -distance

-2 -bit rate

10 Q c ha nn el l oss ≈ I AB I Eve (optical noise) Secret bit per pulse Geneva University Geneva

-6 Detector noise 10

GAP Optique GAP Optique ≈ 100 km distance

58 PNS Attack: the idea

90,5% 9% 0.5% Alice 0 ph 1 ph 2 ph 0 ph 0 ph 1 ph Bob

LossesEve!!! Lossless channel QND (e.g. measurement of teleportation) photon number Geneva University Geneva ÎPNS (photon-number splitting): ‹The photons that reach Bob are unperturbed

GAP Optique GAP Optique ‹Constraint for Eve: do not introduce more losses than expected (PNS important for long-distance QKD). 59 Limits of Q crypto

-distance

-2 -bit rate Q

10 ch a nn el los s ≈ − I AB I Eve (multi photon pulse)

≈ I AB I Eve (optical noise) Secret bit per pulse Geneva University Geneva

-6 Detector noise 10

GAP Optique GAP Optique ≈ 50 km ≈ 100 km distance

60 How to improve Q crypto ?

Effect on Effect on Feasibility distance bit rate Detectors 1-υsource Q channel Protocols

Geneva University Geneva Q relays Q repeater GAP Optique GAP Optique

61 A new protocol: SARG

The quantum protol is identical to the BB84

During the public discussion phase of the new protocol Alice doesn’t announce bases but sets of non-orthogonal states ⇒ even if Eve hold a copy, she Geneva University Geneva can’t find out the bit with certainty ⇒ More robust against PNS attacks ! GAP Optique GAP Optique Joint patent UniGE + id Quantique pending Phys. Rev. A, 2003; quant-ph/0211131& 0302037 62 SARG vs BB84 PNS, optimal µ, detector efficiency η, dark counts D

Perfect detectors η=1, D=0

µ = 0.335 Typical detector η=0.1, D=10-5 µ = 0.014 Geneva University Geneva SARG BB84 Secret key rate, log10 [bits/pulse] GAP Optique GAP Optique Distance [km] 67km = Geneva-Lausanne 63 3-photon: Q teleportation & Q relays ψ 2 bits U Bell

ψ ⊗ EPR Classical channel Alice Charlie Bob

1.00 132 0.98 ψ 0.96 BSM EPR source ψ 0.94 Geneva University Geneva 0.92 0.90 y 0.88 n=1 n=2 n=3 n=4 0.86 Fidelit 0.84

GAP Optique GAP Optique 0.82 0.80 0 50 100 150 200 250 300 350 64 Distance [km] Q repeaters & relays J. D. Franson et al, PRA 66,052307,2002 Bell measurement * . . * entanglement entanglement

entanglement

Bell measurement

Geneva University Geneva . * ?? * entanglement entanglement

REPEATER RELAY REPEATER QND measurement GAP Optique GAP Optique + Q memory

65 Conclusions

‰ Q teleportation = the possibility to teleport the "ultimate structure" of an object from one place to with: another, without the object ever being

‰ telecom wavelength anywhere in between

‰ two different crystals (spatially separated sources)

‰ from one wavelength (1300 nm) to another (1550 nm)

‰ first time with time-bins (ie insensitive to polarization fluctuations)

‰ over 3x2 km of fiber and 55 meters of physical distance

‰ mean fidelity : ≈ 85% both in the lab and at a distance of 2 km Geneva University Geneva

‰ mean fideity 77.5% in a 3x2km quantum relay configuration

‰ Q teleportation raises questions about the meaning of basic concepts like: object, information, space & time. GAP Optique GAP Optique

‰ Elementary Q processor can extend today’s Q crypto systems 66 1.0 = − I AB 1 H(QBER)

0.8 individual IAE

0.6

1-way 2-way Alice 0.4 class. Inf. Proc. quantum. Inf. Proc. and suffice suffice Bob

Geneva University Geneva separated 0.2 Shannon Information Bell inequality: or can be never classical violated violated 0.0 GAP Optique GAP Optique 0.0 0.1D0 0.2 0.3QBER 0.4

67 Bell’s inequality: (D. Mermin, Am. J. Phys. 49, 940-943, 1981)

Bob Left Middle Right Alice same different same different same different

Left 100 % 0 % 1/4 3/4 1/4 3/4 Middle1/4 3/4 100 % 0 % 1/4 3/4 Right 1/4 3/4 1/4 3/4 100 % 0 %

LMR if ≠ settings Prob(results =) GGG 100 % GGR 1/3 GRG 1/3 RGG 1/3 Geneva University Geneva GRR 1/3 Alice RGR 1/3 Bob RRG 1/3 RRR 100 % Arbitr. mixture ≥ 1/3 Bell Inequality GAP Optique GAP Optique

Quantum = 1 / 4 Quantum non-locality 68