= Solution
<Quantum decoherence> arises when different system alternatives correlate with distinguishable environmental states. For an initially uncorrelated state, a measurement-like <unitary time evolution> can produce
$$
(\alpha|0\rangle+\beta|1\rangle)|E_0\rangle
\longmapsto\alpha|0\rangle|E_0(t)\rangle+\beta|1\rangle|E_1(t)\rangle.
$$
Taking the environmental <partial trace> gives
$$
\rho_S(t)=\begin{pmatrix}
|\alpha|^2&\alpha\beta^*\langle E_1(t)|E_0(t)\rangle\\
\alpha^*\beta\langle E_0(t)|E_1(t)\rangle&|\beta|^2
\end{pmatrix}.
$$
The environmental overlap suppresses locally observable <quantum coherence>. Scattered <photons>, surrounding gas and uncontrolled apparatus variables can carry away such records. The interaction often singles out robust states forming a <pointer basis>. Decoherence can be much faster than thermal <energy> relaxation because recording a macroscopic distinction need not transfer much <energy>.
The overall state can remain pure and evolve unitarily even when the system alone looks like a classical mixture. Discarding environmental information is therefore not, by itself, a proof of fundamental <wavefunction> collapse or a solution to the definite-outcome <measurement problem>. A small controlled environment can return coherence, as in the <single-qubit environment dephasing model>; practical irreversibility arises when recovering the many dispersed records becomes inaccessible. In an interferometer, varying gas <pressure> or an independently controllable path marker tests the dependence of fringe contrast on this environmental coupling. Quantum computation must suppress or correct such unwanted system–environment entanglement to preserve the intended <interference>.
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