Increasing quantum speed limit via non-uniform magnetic field

TL;DR

This paper demonstrates that using non-uniform magnetic fields can surpass the traditional quantum speed limit for relativistic electrons, enabling faster quantum information processing and bridging relativistic and non-relativistic quantum dynamics.

Contribution

It introduces a method to exceed the established quantum speed limit by employing variable magnetic fields and analyzes the resulting energy redistribution effects.

Findings

QSL increases with magnetic field strength up to saturation in uniform fields.

Variable magnetic fields can push QSL beyond the saturation limit, reaching 0.4-0.6c.

Energy levels become non-degenerate in non-uniform fields, enabling higher QSL.

Abstract

Quantum speed limit (QSL) defines the theoretical upper bound on how fast a quantum system can evolve between states. It imposes a fundamental constraint on the rate of quantum information processing. For a relativistic spin-up electron in a uniform magnetic field, QSL increased with the magnetic field strength till around $10^{15}$ Gauss, before saturating at a saturated QSL (SQSL) of 0.2407c, where c is the speed of light. We show that by using variable magnetic fields, it is possible to surpass this limit, achieving SQSL upto 0.4-0.6c. To attain this quantum phenomenon, we solve the evolution equation of relativistic electron in spatially varying magnetic fields and find that the energies of various electron states become non-degenerate as opposed to the constant magnetic field case. This redistribution of energy is the key ingredient to accomplish higher QSL and, thus, a high information processing speed. We further explore how QSL can serve as a bridge between relativistic and non-relativistic quantum dynamics, providing insights via the Bremermann-Bekenstein bound, a quantity which constrains the maximal rate of information production. We also propose a practical experimental setup to realize these advancements. These results hold immense potential for propelling fields of quantum computation, thermodynamics and metrology.