# Evolution speed of open quantum dynamics

## TL;DR

This paper derives a formula for the speed of open quantum system evolution using Euclidean norms, linking it to skew information and analyzing its properties through examples.

## Contribution

It introduces a novel approach to quantify the evolution speed of open quantum systems using Euclidean embedding and skew information, providing new insights into their dynamics.

## Key findings

- Evolution speed is connected to modified skew information of Hamiltonian and Lindblad operators.
- The speed can increase or decrease over time, not necessarily decreasing.
- An open-system quantum navigation problem is formulated and analyzed.

## Abstract

The space of density matrices is embedded in a Euclidean space to deduce the dynamical equation satisfied by the state of an open quantum system. The Euclidean norm is used to obtain an explicit expression for the speed of the evolution of the state. The unitary contribution to the evolution speed is given by the modified skew information of the Hamiltonian, while the radial component of the evolution speed, connected to the rate at which the purity of the state changes, is shown to be determined by the modified skew information of the Lindblad operators. An open-system analogue of the quantum navigation problem is posed, and a perturbative analysis is presented to identify the amount of change on the speed. Properties of the evolution speed are examined further through example systems, showing that the evolution speed need not be a decreasing function of time.