Quantum speed limits for adiabatic evolution, Loschmidt echo and beyond

TL;DR

This paper derives new quantum speed limits for time-dependent target subspaces, providing bounds on adiabatic fidelity and Loschmidt echo, which are crucial for understanding quantum evolution speed and stability.

Contribution

It introduces a general quantum speed limit for time-dependent target subspaces and compares evolving states under different Hamiltonians, extending existing bounds.

Findings

Bounds on adiabatic fidelity for time-dependent Hamiltonians

Quantum speed limits for general target subspaces

Bounds on Loschmidt echo for different Hamiltonian evolutions

Abstract

One often needs to estimate how fast an evolving state of a quantum system can depart from some target state or target subspace of a Hilbert space. Such estimates are known as quantum speed limits. We derive a quantum speed limit for a general time-dependent target subspace. When the target subspace is an instantaneous invariant subspace of a time-dependent Hamiltonian, the obtained quantum speed limit bounds the adiabatic fidelity, which is a figure of merit of quantum adiabaticity. We also compare two states evolving under two different Hamiltonians and derive a bound on the Loschmidt echo.