Quantum Speed Limit From Tighter Uncertainty Relation

TL;DR

This paper introduces a new quantum speed limit derived from tighter uncertainty relations, providing a more accurate bound on the evolution speed of quantum systems, applicable to both pure and mixed states, and outperforming the traditional Mandelstam-Tamm bound.

Contribution

It presents a novel quantum speed limit based on tighter uncertainty relations, extending the bound to mixed states and demonstrating improvements over the Mandelstam-Tamm bound.

Findings

New speed limit outperforms MT bound in examples

Tighter uncertainty relations derived for pure and mixed states

Optimization over basis sets further improves the bound

Abstract

The quantum speed limit provides a fundamental bound on how fast a quantum system can evolve between the initial and the final states under any physical operation. The celebrated Mandelstam-Tamm (MT) bound has been widely studied for various quantum systems undergoing unitary time evolution. Here, we prove a new quantum speed limit using the tighter uncertainty relations for pure quantum systems undergoing arbitrary unitary evolution. We also derive a tighter uncertainty relation for mixed quantum states and then derive a new quantum speed limit for mixed quantum states from it such that it reduces to that of the pure quantum states derived from tighter uncertainty relations. We show that the MT bound is a special case of the tighter quantum speed limit derived here. We also show that this bound can be improved when optimized over many different sets of basis vectors. We illustrate the tighter speed limit for pure states with examples using random Hamiltonians and show that the new quantum speed limit outperforms the MT bound.