Quantum decoherence is the suppression of observable phase coherence when a system becomes entangled with unobserved environmental degrees of freedom. In a preferred basis, tracing out the environment damps off-diagonal entries of the system's reduced density matrix while leaving the corresponding populations unchanged.
If a joint pure state is , the off-diagonal entry of the system's reduced density matrix is multiplied by the environmental overlap . Independent repeated interactions multiply these overlaps.
Quantum recoherence is a later restoration of phase coherence. It can occur when a finite environment revisits a state having substantial overlap with its initial conditional state.
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