Lower bound on the life-time of quantum states based on the mean energy, and its relationship with quantum entanglement

Abstract

An uncertainty relationship between the mean energy and lifetime of a state is derived. States which minimize the average lifetime, also optimize the linear entropy. The connection between this inequality and entanglement is explored. In the case of factorizable, symmetric states of two non-interacting systems, entanglement is needed in order to reach the minimum possible lifetime. States with a given mean energy and discrete energy spectra that exhibit the most varied possible evolution as measured by their overlap, also have an optimal linear entropy. We show that this is not the same for states with continuous energy spectra and discuss the implications in the context of the meaning of linear entropy.