Detecting quantum speedup in closed and open systems

TL;DR

This paper introduces a general measure for detecting quantum speedup in both closed and open systems, revealing how quantum coherence, entanglement, and environmental memory effects can accelerate quantum evolution.

Contribution

It proposes a novel speed measure based on Riemannian metrics and distinguishes between longitudinal and transverse speedup mechanisms in quantum systems.

Findings

Quantum coherence and entanglement can enhance speedup.

Environmental memory effects contribute to acceleration.

The measure applies to various quantum systems.

Abstract

We construct a general measure for detecting the quantum speedup in both closed and open systems. The speed measure is based on the changing rate of the position of quantum states on a manifold with appropriate monotone Riemannian metrics. Any increase in speed is a clear signature of dynamical speedup. To clarify the mechanisms for quantum speedup, we first introduce the concept of longitudinal and transverse types of speedup: the former stems from the time evolution process itself with fixed initial conditions, while the latter is a result of adjusting initial conditions. We then apply the proposed measure to several typical closed and open quantum systems, illustrating that quantum coherence (or entanglement) and the memory effect of the environment together can become resources for longitudinally or transversely accelerating dynamical evolution under specific conditions and assumptions.