Quantum speed limit and divisibility of the dynamical map

TL;DR

This paper explores how the divisibility properties of quantum dynamical maps influence the quantum speed limit, revealing that speed-up can occur even in divisible (Markovian) dynamics, challenging previous assumptions.

Contribution

It demonstrates that quantum speed-up is possible under P- and CP-divisible dynamics, expanding understanding of the relationship between divisibility and quantum evolution speed.

Findings

Speed-up occurs in P- and CP-divisible dynamics.

Quantum speed limit can be lowered without non-divisibility.

Speed-up is not solely linked to non-Markovianity.

Abstract

The quantum speed limit (QSL) is the theoretical lower limit of the time for a quantum system to evolve from a given state to another one. Interestingly, it has been shown that non-Markovianity can be used to speed-up the dynamics and to lower the QSL time, although this behavior is not universal. In this paper we further carry on the investigation on the connection between QSL and non-Markovianity by looking at the effects of P- and CP-divisibility of the dynamical map to the quantum speed limit. We show that the speed-up can also be observed under P- and CP-divisible dynamics, and that the speed-up is not necessarily tied to the transition from P-divisible to non-P-divisible dynamics.