A courier network wants to send a confidential message of bits using a one-time pad
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 courier network wants to send a confidential message of L=106 bits using a one-time pad, which needs a key of the same length L shared secretly in advance. The key is generated by BB84 over a fibre link whose sifted key has an asymptotic quantum bit error rate Q=4% after all corrections, so the Shor-Preskill/CSS argument gives a net secret-key rate r=1−2h(Q) secret bits per sifted bit, where h is the binary entropy in bits.
((a)) Derive an expression for the number of sifted bits n needed to supply a one-time-pad key of length L, in terms of L, h and Q.
((b)) Given that on average only half of the qubits Alice sends survive the public basis comparison (sifting), derive an expression for the number of qubits N she must transmit.
((c)) Evaluate n and N for L=106 bits and Q=4%.