Fleming's bound for the decay of mixed states
Abstract
Fleming's inequality is generalized to the decay function of mixed states. We show that for any symmetric hamiltonian h and for any density operator on a finite dimensional Hilbert space with the orthogonal projection onto the range of there holds the estimate ( - ht ht) ≥2(( h)t) for all real t with ( h)| t| ≤π/2. We show that equality either holds for all t∈R or it does not hold for a single t with 0<( h)| t| ≤π/2. All the density operators saturating the bound for all t∈R, i.e. the mixed intelligent states, are determined.
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