A key-distribution link between two data centres delivers a sifted key from which a…

PHYSICS · Multi-part · Fermi University Physics · Quantum Information & Technology · Quantum information theory and communication · Quantum information theory and communication

Quantum Information and Technology, Ch Quantum key distribution and quantum networks

Problem

A key-distribution link between two data centres delivers a sifted key from which a random sample of m=2000m = 2000 bits has already been removed for error estimation, leaving n=48000n = 48000 sifted bits for the final key. The sample gives a measured error rate Q^=1.5%\hat Q = 1.5\%. Security uses a z=4z = 4 standard-error upper bound on QQ, information reconciliation with efficiency fEC=1.10f_{\rm EC} = 1.10, the Shor-Preskill phase-error term h(Qbound)h(Q_{\rm bound}), and a privacy-amplification security parameter ϵ=10−8\epsilon = 10^{-8}. ((a)) Compute the upper confidence bound Qbound=Q^+zQ^(1−Q^)/mQ_{\rm bound} = \hat Q + z\sqrt{\hat Q(1-\hat Q)/m}. ((b)) Compute the reconciliation leak per key bit, fEC h(Qbound)f_{\rm EC}\,h(Q_{\rm bound}), and the phase-error term h(Qbound)h(Q_{\rm bound}). ((c)) Using the leftover hash correction 2log⁡2(1/ϵ)2\log_2(1/\epsilon) bits, compute the final secret key length ℓ=n[1−fEC h(Qbound)−h(Qbound)]−2log⁡2(1/ϵ).\ell = n\left[1-f_{\rm EC}\,h(Q_{\rm bound})-h(Q_{\rm bound})\right]-2\log_2(1/\epsilon).

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