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alberliu

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In every single textbook I've read, decoherence has always been explained by (1) introduce density matrix and (2) explain that interactions with environment cause off-diagonal terms (coherences) to decay exponentially. However, I've been wondering how to connect the density matrix back to the Hilbert space wavefunction of the original system after decoherence. It kind of makes sense that this is not possible, since after the environment interacts with the system enough, the system's density matrix becomes a mixed state that cannot be represented by a wavefunction.

However, if I consider a single 2-level system that has suffered decoherence, it really bugs me how the density matrix of this single 2-level system becomes a mixed state, since to me a mixed state is synonymous with statistical mixture. Physically, if the environment is constantly perturbing the phases of each state in the superposition, it makes sense that in an ensemble the interference terms average to zero over time, but if there is only a single 2-level system won't there still be quantum interference phenomena?