Tight Upper Bound Of The Maximum Speed Of Evolution Of A Quantum State

TL;DR

This paper establishes a precise upper limit on how quickly a quantum state can evolve into another with a certain fidelity under a fixed Hamiltonian, linking the speed to the energy deviation.

Contribution

It introduces a tight upper bound on the evolution speed of quantum states based on energy deviation, providing a new measure for quantum information processing capacity.

Findings

Bound is proportional to the average energy deviation from the median.

Provides a fundamental limit on quantum state evolution speed.

Links energy deviation to information processing capability.

Abstract

I report a tight upper bound of the maximum speed of evolution from one quantum state $\rho$ to another $\rho'$ with fidelity $F(\rho,\rho')$ less than or equal to an arbitrary but fixed value under the action of a time-independent Hamiltonian. Since the bound is directly proportional to the average absolute deviation from the median of the energy of the state ${\mathscr D}E$, one may interpret ${\mathscr D}E$ as a meaningful measure of the maximum information processing capability of a system.