Quantum capacity analysis of finite-dimensional lossy channels

TL;DR

This paper investigates the quantum capacity of 4-dimensional MAD channels, a qudit generalization of amplitude damping channels, using new techniques beyond degradability conditions.

Contribution

It introduces methods to compute quantum capacity for MAD channels outside traditional degradable regimes and characterizes their degradability regions.

Findings

Quantum capacity of 4-dimensional MAD channels was computed.

Complete degradability and antidegradability regions were characterized.

New analytical and semi-numerical methods were developed for d-dimensional MAD channels.

Abstract

Traditionally, Quantum Information, and Quantum Communication specifically, have been focused on qubit-based architectures. Recent results, however, highlighted that higher dimensional architectures (qudit-based) may present advantages both in terms of communication and computation; a family of channels called Multi-level Amplitude Damping (MAD) channels, which are a possible qudit generalization of the well known Amplitude Damping Channels, is able to model energy decay processes that may happen during signal transmission. In this work, the Quantum Capacity of 4-dimensional MAD's is studied, relying on a technique for computing it even outside of degradable and antidegradable conditions. We also characterized the complete region of antidegradability and degradability in the parameter space for a generic d-dimensional MAD using both analytical and semi-numerical methods.