Extensive nonadditivity of privacy

TL;DR

This paper demonstrates the extensive nonadditivity of private capacity in quantum channels, showing that combining channels can significantly increase overall privacy capabilities beyond individual limits.

Contribution

It introduces a natural setting where the nonadditivity of quantum privacy capacity is maximized, contrasting with prior work that showed limited or conditional nonadditivity.

Findings

A channel with 2 log d input qubits has private capacity less than 2.

Combining a zero private capacity channel with another increases joint capacity to (1/2)log d.

The work reveals the strongest form of nonadditivity in quantum privacy capacities.

Abstract

Quantum information theory establishes the ultimate limits on communication and cryptography in terms of channel capacities for various types of information. The private capacity is particularly important because it quantifies achievable rates of quantum key distribution. We study the power of quantum channels with limited private capacity, focusing on channels that dephase in random bases. These display extensive nonadditivity of private capacity: a channel with 2 log d input qubits has a private capacity less than 2, but when used together with a second channel with zero private capacity the joint capacity jumps to (1/2)log d. In contrast to earlier work which found nonadditivity vanishing as a fraction of input size or conditional on unproven mathematical assumptions, this provides a natural setting manifesting nonadditivity of privacy of the strongest possible sort.