|ψ⟩
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|ψ⟩ = α|0⟩ + β|1⟩  •  iℏ ∂|ψ⟩/∂t = Ĥ|ψ⟩
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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.

Related Topics & Quantum Guides:

Lindblad Master EquationSuperconducting Transmon Qubits