For a qubit with fixed relaxation time

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

For a qubit with fixed relaxation time T1T_1, the decoherence time is 1T2=12T1+1Tϕ.\frac{1}{T_2} = \frac{1}{2T_1} + \frac{1}{T_\phi}. ((a)) Calculate T2T_2, as a multiple of T1T_1, for pure dephasing times Tϕ=T1/10T_\phi = T_1/10, T1/2T_1/2, T1T_1, 2T12T_1 and 10T110T_1. ((b)) State the value T2/T1T_2/T_1 approaches as Tϕ→∞T_\phi \to \infty, and explain in one sentence why T2T_2 never reaches it.

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