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Coherent state is one thing and decoherence is something else. The coherent state has the form $(\text I) \ |\alpha \rangle = e^{-\alpha ^2/2} \sum _n \frac {\alpha ^n}{\sqrt {n!}} |n \rangle.$ where $|n \rangle$ is a Fock state of n identical particles. This state is a coherent superposition of Fock states, and its density matrix has diagonal and ...