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 $\rho$ on a finite dimensional Hilbert space with the orthogonal projection $\Pi$ onto the range of $\rho$ there holds the estimate $\Tr(Π\rme^{-\rmi ht}ρ\rme^{\rmi ht}) \geq\cos^{2}((Δh)_ρt) $ for all real $t$ with $(\Delta h{)}_{\rho }|t|\le \pi /2.$ We show that equality either holds for all $t\in \mathbb{R}$ or it does not hold for a single $t$ with $0<(\Delta h{)}_{\rho }|t|\le \pi /2.$ All the density operators saturating the bound for all $t\in \mathbb{R},$ i.e. the mixed intelligent states, are determined.

12 pages

References in corpus (4)

• Quantum limits to dynamical evolution
• Elementary Derivation for Passage Times
• Elementary proof of the bound on the speed of quantum evolution
• Bounds to unitary evolution

Cited by in corpus (2)

• Macroscopic quantum states: measures, fragility and implementations
• Kind of entanglement that speeds up quantum evolution