Additivity of quantum capacities in simple non-degradable quantum channels

TL;DR

This paper identifies new classes of non-degradable quantum channels with additive coherent information, providing insights into quantum capacity additivity and offering tractable examples for understanding quantum communication limits.

Contribution

It introduces two families of non-degradable channels with additive coherent information, expanding the understanding of capacity additivity beyond degradable channels.

Findings

Channels outperforming their environment can have additive coherent information.

Structural constraints can guarantee strong additivity.

Relaxing constraints may lead to loss of strong additivity, with weak additivity possibly remaining.

Abstract

Quantum channel capacities give the fundamental performance limits for information flow over a communication channel. However, the prevalence of superadditivity is a major obstacle to understanding capacities, both quantitatively and conceptually. In contrast, examples exhibiting additivity, though relatively rare, offer crucial insights into the origins of nonadditivity and form the basis of our strongest upper bounds on capacity. Degradable channels, whose coherent information is provably additive, stand out as among the few classes of channels for which the quantum capacity is exactly computable. In this paper, we introduce two families of non-degradable channels whose coherent information remains additive, making their quantum capacities tractable. First, we demonstrate that channels capable of ``outperforming" their environment, under conditions weaker than degradability, can exhibit either strong or weak additivity of coherent information. Second, we explore a complementary construction that modifies a channel to preserve coherent information additivity while destroying the ``outperforming" property. We analyze how structural constraints guarantee strong and weak additivity and investigate how relaxing these constraints leads to the failure of strong additivity, with weak additivity potentially persisting.