Bounding quantum capacities via partial orders and complementarity

TL;DR

This paper introduces operationally motivated bounds on quantum capacities using partial orders and complementarity, providing new insights into capacity limitations and aiding numerical estimation.

Contribution

It presents a novel approach to bounding quantum capacities through partial orders and complementarity, enhancing understanding of capacity relationships and superadditivity.

Findings

Bounds relate capacities to properties of complementary channels or states

Partial orders help understand superadditivity and capacity differences

Examples demonstrate the bounds' usefulness in numerical estimation

Abstract

Quantum capacities are fundamental quantities that are notoriously hard to compute and can exhibit surprising properties such as superadditivity. Thus, a vast amount of literature is devoted to finding tight and computable bounds on these capacities. We add a new viewpoint by giving operationally motivated bounds on several capacities, including the quantum capacity and private capacity of a quantum channel and the one-way distillable entanglement and private key of a quantum state. These bounds are generally phrased in terms of capacity quantities involving the complementary channel or state. As a tool to obtain these bounds, we discuss partial orders on quantum channels and states, such as the less noisy and the more capable order. Our bounds help to further understand the interplay between different capacities, as they give operational limitations on superadditivity and the difference between capacities in terms of the information-theoretic properties of the complementary channel or state. They can also be used as a new approach towards numerically bounding capacities, as discussed with some examples.