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Quantum Teleportation Nicolas Gisin H Quantum teleportation Nicolas Gisin 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 quantum teleportation • Intuitive and mathematical introduction • What is teleported ? • Q fax? The no-cloning theorem • The “teleportation channel”: Entanglement • The Geneva experiment Geneva University • Telecom wavelengths • Time-bin qubits • partial Bell measurement and tests of Bell inequality • Applications: Quantum Key Distribution GAP Optique • Simplifications, limitations • Q relays and Q repeaters 1 The Geneva Teleportation experiment over 3x2 km Photon = particle (atom) of light Polarized photon Unpolarized photon ≈ ( structured photon) (≈ unstructured ≈ dust) Geneva University GAP Optique 2 55 metres 2 km of 2 km of optical fibre optical fibre Geneva University Two entangled photons GAP Optique 3 55 metres 2 km of Geneva University optical fibre GAP Optique 4 55 metres Bell measurement (partial) the 2 photons Geneva University interact 4 possible results: 0, 90, 180, 270 degrees GAP Optique 5 55 metres Bell measurement (partial) the 2 photons ion Geneva University at interact rel Cor ect erf 4 possible results: P The correlation is independent of the quantum 0, 90, 180, 270 degrees GAP Optique state which may be unknown or even entangled with a fourth photon 6 Quantum teleportation ψ 2 bits 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 + ((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 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 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 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., Nature 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 physics, this is a necessity since it is impossible to clone an unknown quantum state. If not: – one could violate Heisenberg’s uncertainty relations Geneva University (Quantum Physics would be deterministic !) – one could exploit entanglement and cloning to signal faster than light. (Relativity would have an absolute time). 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 entangled particules M * }clones GAP Optique Arbitrary fast signaling ! 10 No cloning theorem and the compatibility with relativity • The first account on quantum cloning 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 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 N. Gisin, Phys. Lett. A 242, 1, 1998. 11 The Quantum Teleportation channel ? Geneva University GAP Optique 12 Entanglement A density matrix ρ is separable iff it decomposes in product states with probabilité coefficients pj>0 : ρ = ρ 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 The partial transpose test : pt If ρ is seprable, then its partial transpose is ρ ≥ 0 GAP Optique ρ pt ≡ ρ whreab,αβ aβ ,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 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 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 Quantum physics offers new ways of processing information. 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 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 Polarization Mode Dispersion Time-bin coding with photons at telecom wavelength GAP Optique 17 Time-bin qubits ψ = + iφ qubit : 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 ν 1 0 h 0 D1 switch switch variable coupler variable coupler 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 laser 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 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 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 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 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 Michelson configuration circulator C : second output port Faraday mirrors FM: compensation of birefringence 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 horizontalvertical +45° pol. pol.pol. GAP Optique port 3 22 Faraday mirrors λ • 4 Faraday rotator • standard mirror (⊥ incidence) λ • 4 Faraday rotator FM Geneva University mr → R(ω )mr → (−R(ω)mr ) − mr ← R−1(ω)(−R(ω)mr ) ← GAP Optique ω Independent of 23 Partially Entangled Time-Bin Qubits φ ψ = + i p c0 00 c1e 11 Geneva University = V 2c0c1 = − 2 2 − 2 2 E c0 log2 c0 c1 log2 c1 GAP Optique R. Thew et al., Phys. Rev. A 66, 062304 (2002) 24 Geneva 1997 Geneva University GAP Optique 25 2-υ source of Aspect’s 1982 experiment Geneva University 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 laser with waveguide in LiNbO3 with quasi phase matching, ≈ µ Ipump 8 W 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 APD 2- 9 .3 k q m ua APD2+ nt um S F ch Z ann δ2 el 7 FS .3 km 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 l -0.5 same result in the e r V = (85.3 ± 0.9)% r raw lab o c V = (95.5 ± 1) % net.
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