Finite-time dynamics of an entanglement engine: current, fluctuations and kinetic uncertainty relations

TL;DR

This paper explores the finite-time behavior of a quantum entanglement engine, analyzing current, fluctuations, and uncertainty relations, revealing critical currents and multiple finite-time KUR definitions.

Contribution

It extends the understanding of entanglement engines beyond steady state by deriving time-dependent dynamics and examining finite-time kinetic uncertainty relations.

Findings

Identifies a critical current as an entanglement indicator.

Derives time-dependent states and currents using a master equation.

Shows multiple finite-time KUR definitions with different violation regimes.

Abstract

Entanglement engines are autonomous quantum thermal machines designed to generate entanglement from the presence of a particle current flowing through the device. In this work, we investigate the functioning of a two-qubit entanglement engine beyond the steady-state regime. Within a master equation approach, we derive the time-dependent state, the particle current, as well as the associated current correlation functions. Our findings establish a direct connection between coherence and internal current, elucidating the existence of a critical current that serves as an indicator for entanglement in the steady state. We then apply our results to investigate kinetic uncertainty relations (KURs) at finite times. We demonstrate that there are more than one possible definitions for KURs at finite times. While the two definitions agree in the steady-state regime, they lead to different parameter's ranges for violating KUR at finite times.