Generalised quantum speed limit for arbitrary time-continuous evolution

TL;DR

This paper derives a comprehensive quantum speed limit applicable to various quantum dynamics, including non-Hermitian and relativistic systems, extending the standard bounds and providing new insights into quantum evolution rates.

Contribution

It introduces a generalized quantum speed limit formalism for arbitrary time-continuous evolution, encompassing unitary, non-unitary, and non-Hermitian dynamics, unifying and extending existing bounds.

Findings

Derived a GQSL applicable to diverse quantum dynamics.

Estimated speed limits for non-Hermitian systems.

Extended the QSL to time-dependent and relativistic quantum systems.

Abstract

The quantum speed limit describes how quickly a quantum system can evolve in time from an initial state to a final state under a given dynamics. Here, we derive a generalised quantum speed limit (GQSL) for arbitrary time-continuous evolution using the geometrical approach of quantum mechanics. The GQSL is applicable for quantum systems undergoing unitary, non-unitary, completely positive, non-completely positive and relativistic quantum dynamics. This reduces to the well known standard quantum speed limit (QSL), i.e., the Mandelstam-Tamm bound when the quantum system undergoes unitary time evolution. Using our formalism, we then obtain a quantum speed limit for non-Hermitian quantum systems. To illustrate our findings, we have estimated the quantum speed limit for a time-independent non-Hermitian system as well as for a time-dependent non-Hermitian system namely the Bethe-Lamb Hamiltonian for general two-level system.