A simulated BB84 exchange sends single-photon pulses

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 simulated BB84 exchange sends N=2×105N = 2\times10^5 single-photon pulses, each with a random bit and a random basis (ZZ or XX); Bob measures each pulse in a randomly chosen basis. An eavesdropper intercepts a fraction f=0.30f = 0.30 of the pulses, measures each intercepted photon in a randomly chosen basis, and resends the state she obtained. ((a)) State the expected sifted key length after Alice and Bob discard the rounds where their bases disagree. ((b)) State the expected quantum bit error rate QQ this attack causes, using the intercept-resend result Q=f/4Q = f/4. ((c)) Alice and Bob randomly reveal m=5000m = 5000 sifted bits to estimate QQ; treating the measured rate as equal to the value from part (b), compute the upper bound Qbound=Q^+5Q^(1−Q^)/mQ_{\rm bound} = \hat Q + 5\sqrt{\hat Q(1-\hat Q)/m} (a five-standard-error bound). ((d)) Using QboundQ_{\rm bound} in the asymptotic BB84 rate r=1−2h(Qbound)r = 1-2h(Q_{\rm bound}), compute rr. ((e)) Estimate the final secret key length obtainable from the remaining n−mn-m sifted bits (the sifted key not used for the error sample), at rate rr.

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