Additive Extensions of a Quantum Channel

TL;DR

This paper introduces a method for extending quantum channels to derive upper bounds on their capacities, with applications to depolarizing and phase-amplitude noise channels, impacting quantum cryptography protocols.

Contribution

It presents a new technique for extending quantum channels to obtain single-letter capacity bounds, simplifying capacity estimation for complex channels.

Findings

Upper bounds on quantum channel capacities derived from extensions.

Application to depolarizing and phase-amplitude noise channels.

Key rate of BB84 limited by derived entropy bounds.

Abstract

We study extensions of a quantum channel whose one-way capacities are described by a single-letter formula. This provides a simple technique for generating powerful upper bounds on the capacities of a general quantum channel. We apply this technique to two qubit channels of particular interest--the depolarizing channel and the channel with independent phase and amplitude noise. Our study of the latter demonstrates that the key rate of BB84 with one-way post-processing and quantum bit error rate q cannot exceed H(1/2-2q(1-q)) - H(2q(1-q)).