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arXiv · 0804.4618

Fleming's bound for the decay of mixed states

Florian Fröwis·Gebhard Grübl·Markus Penz
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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(\Pi \rme^{-\rmi ht}\rho \rme^{\rmi ht}) \geq\cos^{2}((\Delta h)_{\rho}t) $ for all real $t$ with $(\Delta h)_{\rho}| t| \leq\pi/2.$ We show that equality either holds for all $t\in\mathbb{R}$ or it does not hold for a single $t$ with $0<(\Delta h)_{\rho}| t| \leq\pi/2.$ All the density operators saturating the bound for all $t\in\mathbb{R},$ i.e. the mixed intelligent states, are determined.

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Florian Fröwis, Gebhard Grübl, Markus Penz. 2008-04-29. Fleming's bound for the decay of mixed states. https://doi.org/10.1088/1751-8113/41/40/405201

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