Entanglement rates for bipartite open systems

TL;DR

This paper establishes upper bounds on how quickly bipartite open quantum systems can generate entanglement, considering both irreversible dynamics and mutual information, with bounds depending on system dimensions.

Contribution

It introduces new upper bounds on entanglement generation rates for bipartite open systems, accounting for Hamiltonian and dissipative effects, with bounds that depend logarithmically on system size.

Findings

Upper bound on entanglement rate with logarithmic dependence on smaller system dimension

Upper bound on mutual information change independent of ancilla dimension

Analysis applicable to Lindblad-form quantum dynamics

Abstract

We provide upper bound on the maximal rate at which irreversible quantum dynamics can generate entanglement in a bipartite system. The generator of irreversible dynamics consists of a Hamiltonian and dissipative terms in Lindblad form. The relative entropy of entanglement is chosen as a measure of entanglement in an ancilla-free system. We provide an upper bound on the entangling rate which has a logarithmic dependence on a dimension of a smaller system in a bipartite cut. We also investigate the rate of change of quantum mutual information in an ancilla-assisted system and provide an upper bound independent of dimension of ancillas.