Capacity Estimates via comparison with TRO channels

TL;DR

This paper introduces a method to estimate the capacities of a broad class of quantum channels by comparing them to TRO channels, which have simple capacity formulas, using operator space and interpolation techniques.

Contribution

It provides perturbative capacity estimates for quantum channels via comparison with TRO channels, extending capacity analysis to non-degradable channels.

Findings

Capacity estimates mainly for quantum and private capacities.

Applicable to non-degradable channels like random unitary channels.

Uses operator space and complex interpolation methods.

Abstract

A ternary ring of operators (TRO) in finite dimensions is a diagonal sum of spaces of rectangular matrices. TRO as operator space corresponds to quantum channels that are diagonal sums of partial traces, which we call TRO channels. TRO channels admits simple, single-letter capacity formula. Using operator space and complex interpolation techniques, we give perturbative capacities estimates for a wider class of quantum channels by comparison to TRO channels. Our estimates applies mainly for quantum and private capacity and also strong converse rates. The examples includes random unitary from group representations which in general are non-degradable channels.