Quantum Speed Limit and Divisibility of the Dynamical Map

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 behaviour 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.

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

“…Mixed states are relevant also when estimating the speed limit bound in the classical limit [78]. While for specific classes of dynamical evolutions and initial states, a link between non-Markovianity of the dynamics and the qsl exists, this is not true in general [557,558]. The qsl has been connected to thermodynamic quantities such as energy fluctuations or the entropy production rate for Markovian and non-Markovian dynamics [174,239].…”

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

“…Mixed states are relevant also when estimating the speed limit bound in the classical limit [75]. While for specific classes of dynamical evolutions and initial states, a link between non-Markovianity of the dynamics and the qsl exists, this is not true in general [551,552]. The qsl has been connected to thermodynamic quantities such as energy fluctuations or the entropy production rate for Markovian and non-Markovian dynamics [170,237].…”

“…While progress on quantum speed limits for open quantum systems in general [177,461] and their relation to non-Markovianity in particular [551,552] has been remarkable, their identification in many-body systems continues to be an open challenge. Here, the qsl is intimately connected to controllability.…”

Phase covariant channel: Quantum speed limit of evolution

“…This channel can be thought of as an approximation of the general spin-Boson problem and involves both unital and non-unital components [31]. A work on similar lines was initiated recently in [32]. Here, in addition to the impact of various processes like heating, dissipation and dephasing on τ QSL , we also consider the role of coherence and mixing, as well as mixed initial states.…”