A qubit with relaxation time has Bloch vector at

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

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Problem

A qubit with relaxation time T1=100 μsT_1 = 100\,\mu\mathrm{s} has Bloch vector r⃗=(0.5,0.5,−0.5)\vec r = (0.5, 0.5, -0.5) at t=0t=0. Amplitude damping acts for t=50 μst = 50\,\mu\mathrm{s}. ((a)) Find the damping parameter γ=1−e−t/T1\gamma = 1 - e^{-t/T_1}. ((b)) Find the Bloch vector at time tt, using rz→γ+(1−γ)rzr_z \to \gamma + (1-\gamma)r_z and rx,y→1−γ rx,yr_{x,y} \to \sqrt{1-\gamma}\,r_{x,y}.

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