Transmission of coherent information at the onset of interactions

TL;DR

This paper explores how quantum information, especially entanglement, is transmitted at the start of interactions between systems, introducing the concept of $n$-coherent information and the $n$-exposure to better understand early-time quantum channel behavior.

Contribution

It introduces the $n$-coherent information and $n$-exposure concepts, providing a new framework to analyze initial quantum information transmission and address divergences in coherent information.

Findings

First-order change in coherent information can be zero for certain initial states.

Divergences in second-order change can be regulated using $n$-coherent information.

The $n$-exposure quantifies how initial entanglement is affected by interactions.

Abstract

In this work, we investigate the parameters governing the rate at which a quantum channel arises at the onset of an interaction between two systems, $A$ and $B$. In particular, when system $A$ is pre-entangled with an ancilla, $\tilde{A}$, we quantify the early-time transmission of pre-existing entanglement by calculating the leading order change in coherent information of the complementary channel ($A\rightarrow B'$). We show that, when $A$ and $B$ are initially unentangled and $B$ is pure, there is no change in coherent information to first order, while the leading (second) order change is divergent. However, this divergence may be regulated by embedding the conventional notion of coherent information into what we call the family of $n$-coherent informations, defined using $n$-R\'enyi entropies. We find that the rate of change of the $n$-coherent information at the onset of the interaction is governed by a quantity, which we call the $n$-exposure, which captures the extent to which the initial coherent information of $A$ with $\tilde{A}$ is exposed to or `seen by' the interaction Hamiltonian between $A$ and $B$. We give examples in qubit systems and in the light-matter interaction.