= Quantum decoherence
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= Environmental decoherence
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= Decoherence
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<Quantum decoherence> is the suppression of observable <quantum phase> relations through interaction with unobserved degrees of freedom. A simple model starts with $(a|0\rangle+b|1\rangle)|E\rangle$ and correlates the alternatives with environmental states:
$$
a|0\rangle|E_0\rangle+b|1\rangle|E_1\rangle.
$$
Taking the <partial trace> multiplies the off-diagonal entry of the <reduced density matrix> by $\langle E_1|E_0\rangle$. If the environmental records become nearly orthogonal, <interference> between the two alternatives becomes locally inaccessible even though the joint state can remain pure.
Preserving diagonal populations is a property of <dephasing>, not a general requirement for <quantum decoherence>. An <amplitude damping channel>, for example, changes an excited-state population as $\rho_{11}\mapsto(1-p)\rho_{11}$ while suppressing coherence as $\rho_{01}\mapsto\sqrt{1-p}\rho_{01}$. Thus <energy> relaxation and <quantum decoherence> can occur together, with different rates. Pure <dephasing> instead preserves populations in its selected <pointer basis>.<Foundations II: Measurement and Evolution by John Preskill>[Sections 3.4.2–3.4.3, equations (3.125)–(3.132), phase damping and spontaneous-emission amplitude damping]{ref}
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