Bounds to unitary evolution

TL;DR

This paper derives bounds on the survival probability of a quantum state over time using energy moments, with improvements achieved through energy cut-offs, applicable even when exact moments are unavailable.

Contribution

It introduces a method to bound quantum state survival probabilities using energy moments, enhanced by energy cut-offs for broader applicability.

Findings

Established upper and lower bounds for survival probability.

Energy cut-offs improve bounds where exact moments are unavailable.

Method applicable to a wider class of quantum states.

Abstract

Upper and lower bounds are established for the survival probability $|<\psi(0)|\psi(t)>|^{2}$ of a quantum state, in terms of the energy moments $<\psi(0)|H^{n}|\psi(0)>$. Introducing a cut-off in the energy generally enables considerable improvement in these bounds and allows the method to be used where the exact energy moments do not exist.