Evolution equation for entanglement of assistance

TL;DR

This paper derives a universal evolution equation for the entanglement of assistance under local noisy channels, simplifying the analysis of entanglement dynamics in quantum systems.

Contribution

It introduces a general factorization law that relates the entanglement of assistance evolution to the action of noisy channels on maximally entangled states.

Findings

Entanglement of assistance dynamics are universally determined by noisy channel effects.

The evolution equation simplifies the characterization of entanglement in experimental setups.

The results facilitate understanding entanglement behavior under unknown noise processes.

Abstract

We investigate the time evolution of the entanglement of assistance when one subsystem undergoes the action of local noisy channels. A general factorization law is presented for the evolution equation of entanglement of assistance. Our results demonstrate that the dynamics of the entanglement of assistance is determined by the action of a noisy channel on the pure maximally entangled state, in which the entanglement reduction turns out to be universal for all quantum states entering the channel. This single quantity will make it easy to characterize the entanglement dynamics of entanglement of assistance under unknown channels in the experimental process of producing entangled states by assisted entanglement.