T1 Relaxation & T2 Dephasing | Quantum Decoherence Time Constants
Quick Technical Answer:
T1 (longitudinal relaxation time) is the timescale over which a qubit decays from |1⟩ to |0⟩ due to energy dissipation, while T2 (transverse coherence time) is the timescale over which quantum superposition phase coherence is lost: 1/T2 = 1/(2T1) + 1/T_φ.
Formula / Unitary:
\frac{1}{T_2} = \frac{1}{2T_1} + \frac{1}{T_\phi}, \quad \rho_{01}(t) = \rho_{01}(0) e^{-t/T_2}, \quad \rho_{11}(t) = \rho_{11}(0) e^{-t/T_1}
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Frequently Asked Questions
What is the theoretical upper limit for T2?
The fundamental upper bound on transverse coherence is T2 ≤ 2 · T1. When pure dephasing is eliminated (T_φ → ∞), coherence is strictly limited by energy relaxation.