The Structure and Quantum Capacity of a Partially Degradable Quantum Channel

TL;DR

This paper introduces partially degradable quantum channels, proving their quantum capacity is additive and showing they can outperform standard channels in quantum data transmission.

Contribution

The paper defines partially degradable channels, proves their quantum capacity is additive, and demonstrates their advantage in quantum communication.

Findings

Quantum capacity of PD channels is additive.

PD channels can achieve higher data rates than non-PD channels.

Partial degradability can be exploited for improved quantum communication.

Abstract

The quantum capacity of degradable quantum channels has been proven to be additive. On the other hand, there is no general rule for the behavior of quantum capacity for non-degradable quantum channels. We introduce the set of partially degradable (PD) quantum channels to answer the question of additivity of quantum capacity for a well-separable subset of non-degradable channels. A quantum channel is partially degradable if the channel output can be used to simulate the degraded environment state. PD channels could exist both in the degradable, non-degradable and conjugate degradable family. We define the term partial simulation, which is a clear benefit that arises from the structure of the complementary channel of a PD channel. We prove that the quantum capacity of an arbitrary dimensional PD channel is additive. We also demonstrate that better quantum data rates can be achieved over a PD channel in comparison to standard (non-PD) channels. Our results indicate that the partial degradability property can be exploited and yet still hold many benefits for quantum communications.