Judge each claim by whether the stated device's noise allows it
PHYSICS · Multi-part · Fermi University Physics · Quantum Information & Technology · Physical realizations and quantum technologies · Physical realizations and quantum technologies
Quantum Information and Technology, Ch Quantum metrology and sensing
Problem
Judge each claim by whether the stated device's noise allows it. Idealisations: for the computing claim, gate errors act independently and identically on every gate, with no correlations; for the sensing claim, atoms dephase independently at the stated rate.
((a)) Computing. A team runs Shor's algorithm on 50 physical qubits with no error correction, each two-qubit gate having average infidelity r=5×10−3, and claims it can factor a 2048-bit RSA modulus because Shor's algorithm needs only O(L3) gates, here about L3≈8.6×109 gates for L=2048. Estimate the probability that every gate in such a circuit succeeds, and say whether the claim survives.
((b)) Key distribution. A team runs BB84 over 200km of fibre attenuating at 0.2dB/km, sending weak coherent pulses with mean photon number μ=1 and no decoy states, and claims the resulting key is "secure against any eavesdropper permitted by quantum mechanics." Give the fibre transmission in decibels and as a fraction, and say what standard attack this claim ignores and why it matters at this loss.
((c)) Sensing. A team prepares N=104 atoms, each with independent dephasing time T2=1s, either as independent atoms or as one N-atom GHZ state, averages for T=1000s, and optimises the free-precession time for each scheme, then claims "entanglement gives us a hundredfold better frequency sensitivity." Using Δωopt=2e/(NTT2), valid for both optimised schemes, evaluate the claim.