Quantum communication through a partially reflecting accelerating mirror

TL;DR

This paper models quantum communication through a semi-transparent, accelerating mirror, deriving analytical expressions for particle production and analyzing the channel's capacity for transmitting classical and quantum information.

Contribution

It extends the black hole mirror analogy to semi-transparent mirrors, providing explicit formulas for Bogoliubov coefficients and quantum channel capacities.

Findings

Derived explicit Bogoliubov coefficients for semi-transparent accelerating mirrors.

Analyzed the quantum channel properties and capacities for information transmission.

Connected mirror dynamics to quantum communication performance.

Abstract

Motivated by the fact that the null-shell of a collapsing black hole can be described by a perfectly reflecting accelerating mirror, we investigate an extension of this model to mirror semi-transparency and derive a general implicit expression for the corresponding Bogoliubov coefficients. Then, we turn this into an explicit analytical form by focusing on mirrors that are accelerated via an impulsive force. From the so-obtained Bogoliubov coefficients we derive the particle production. Finally, we realize the field coming from left-past spacetime region, passing through the semitransparent moving mirror and ending up to right-future spacetime region as undergoing the action of a Gaussian quantum channel. We study the transmission and noisy generation properties of this channel, relating them to the Bogoliubov coefficients of the mirror's motion, through which we evaluate capacities in transmitting classical and quantum information.