A qubit undergoes a Ramsey sequence with free-precession time

PHYSICS · Multi-part · Fermi University Physics · Quantum Information & Technology · Open quantum systems, decoherence and error correction · Physical realizations and quantum technologies

Quantum Information and Technology, Ch Quantum metrology and sensing

Problem

A qubit undergoes a Ramsey sequence with free-precession time τ=20 μs\tau = 20\,\mu\mathrm{s}. Pure dephasing acts during the free evolution with dephasing time T2=50 μsT_2 = 50\,\mu\mathrm{s}, and the resulting fringe has visibility V(τ)=e−τ/T2V(\tau) = e^{-\tau/T_2}, as follows from the phase-damping channel. The Ramsey sequence is operated at the working point φ=π/2\varphi = \pi/2, where a fringe of visibility VV has classical Fisher information F(π/2)=V2F(\pi/2) = V^2. ((a)) Find the visibility V(τ)V(\tau). ((b)) Using the Cramer-Rao bound, find the number of shots ν\nu needed to determine the phase φ\varphi to Δφ=5×10−3 rad\Delta\varphi = 5\times10^{-3}\,\mathrm{rad}.

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