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Continuous-variable QKD over long distances. Anthony Leverrier, Télécom ParisTech. joint work with Philippe Grangier, Institut d’Optique. Feynman Festival, June 2009. Outline of the talk. Continuous-variable QKD - quick overview – Towards long distance CVQKD
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Continuous-variable QKD over long distances Anthony Leverrier, Télécom ParisTech joint work with Philippe Grangier, Institut d’Optique Feynman Festival, June 2009
Outline of the talk • Continuous-variable QKD - quick overview – • Towards long distance CVQKD - with a discrete modulation –
Continuous-variable QKD - Quick overview -
Quantum Key Distribution • QKD Alice & Bob can share a secret key. • This key can be used for classical cryptography (one-time pad, AES) • If IAB > IAE (or IAB > IBE) then A & B can distill a secret key • QM imposes tradeoffs between IAB, IAE & IBE
QKD with coherent states • Alice encodes information onto the quadratures of the EM field • Coherent states with a Gaussian modulation • Bob detects this state with an homodyne (interferometric) detection Continuous-Variable QKD. F. Grosshans et al., Nature 421 238 (2003)
Gaussian channel model The coherent states sent in the quantum channel can be altered by: • Losses 1-T • decrease the signal amplitude • « vacuum » added noise 1/T-1 • Excess noise ε • Above the shot noise limit • Equivalent to errors in BB84 • Total noise 1/T-1+ ε
Security proofs (1/2) • Prepare & measure protocol • Used in practice • Alice sends coherent states with a Gaussian modulation • Equivalent entanglement-based • protocol • Used for security proofs • Alice measures one half of an EPR pair and projects the other half on a coherent state F. Grosshans, et al, Quantum Inf. Comput. 3, 535 (2003)
Security proofs (2/2) K = β IAB - IBE Directly observed Upper bound for IBE ? Extremality of Gaussian states R. García-Patrón and N. Cerf, PRL 97, 190503 (2006) • State of Alice and Bob: ρAB • IBE = f(ρAB) • f is unknown but is such that: • For any state ρ,f(ρ) ≤ f(ρG) where ρG is the Gaussian state with the same covariance matrix Γ as ρ • IBE≤ f’(ΓAB), which only depends on T and ε (=accessible experimental parameters)
Pros & Cons • No need to produce nor detect single photons • Uses only fast and standard telecom components • High key rate achievable in principle • but … V. Scarani et al., arxiv 0802.4155 (Review of Modern Physics) Why ? Because of error-correction
Towards long distance CVQKD - With a discrete modulation -
Impact of reconciliation efficiency K = β IAB – IBE Impact almost negligeable while β ≈ 80% Long distance one needs to work at low SNR Gaussian variables are difficult to reconcile at low SNR that’s why CVQKD with Gaussian modulation is limited to short distances
Gaussian or discrete modulation ? • K = β IAB - IBE • One wants to maximize β IAB • A Gaussian modulation maximizes IAB … but not β IAB At low SNR, IAB(discrete) ≈ IAB(Gaussian).
Binary variables are easy to reconcile Gaussian modulation discrete modulation A discrete modulation takes care of the reconciliation problem !
The new Prepare & Measure protocol P Alice’s modulation A N0 P 1 = /4 -A A Q Q -A After the channel • Bob measures a random quadrature • Raw key • Bob sends the absolute value to Alice • Works well, even for VERY noisy data
What about the security of the new protocol ? Entanglement based version of the protocol: Coherent states Orthogonal states Alice performs a projective measurement on the first half of . This projects the second half on one of the four coherent states. • There exist s. t. • For small variance • Hence, IBE(discrete) ≈ IBE(Gaussian)
Performances • For small variance: • IAB(discrete) ≈ IAB(Gaussian) • IBE(discrete) ≈ IBE(Gaussian) • But β(discrete) ≈ 80% • K = βIAB-IBE > 0, even at long distance ! A.L and P. Grangier, PRL 102, 180504 (2009) same as discrete-variable QKD !!
Perspectives: CV vs DV protocols • Homodyne detection vs photon counting • DV: lots of erasures, but small QBER (< 10%) • CV: no erasure high error rate (manageable with discrete modulation, not with a Gaussian modulation) • Same performances (long distance ! ) • Same support of information: coherent states with less than one photon per pulse Differences Similarities