Speed limits in Liouville space for open quantum systems

TL;DR

This paper derives tighter speed limits on the rate of purity change in open quantum systems using Liouville space, applicable to various decoherence and thermalization processes, and demonstrates their attainability.

Contribution

It introduces novel, state-independent speed limits in Liouville space for open quantum systems, improving upon previous bounds in Hilbert space.

Findings

Speed limits are tighter in Liouville space than in Hilbert space.

Bounds depend only on the generators of nonunitary dynamics.

Speed limits are shown to be attainable, confirming their tightness.

Abstract

One of the defining properties of an open quantum system is the variation of its purity in time. We derive speed limits on the rate of purity change for systems coupled to a Markovian environment. Our speed limits are based on Liouville space where density matrices are represented as vectors. This approach leads to speed limits that are always tighter compared to their parallel speed limits in Hilbert space. These bounds depend solely on the generators of the nonunitary dynamics and are independent of the particular states of the systems. Thus, they are perfectly suited to investigate dephasing, thermalization, and decorrelation processes of arbitrary states. We show that our speed limits can be attained and are therefore tight. As an application of our results we study correlation loss, and the speed of classical and quantum correlation erasure in multi-particle system.