# Toward Undetectable Quantum Key Distribution over Bosonic Channels

## TL;DR

This paper demonstrates the possibility of covert quantum key distribution over bosonic channels using a novel protocol that ensures undetectability from an adversary, with theoretical bounds and practical implications for secure communication.

## Contribution

It introduces a protocol combining pulse-position modulation and multi-level coding for covert QKD, along with a new bound on Eve's information for bosonic channels.

## Key findings

- Covert key expansion is feasible over quantum channels with limited adversary control.
- The protocol achieves undetectability, making communication indistinguishable from random noise.
- A new bound on Eve's information enables positive throughput in bosonic channels.

## Abstract

We show that covert secret key expansion is possible using a public authenticated classical channel and a quantum channel largely under control of an adversary, which we precisely define. We also prove a converse result showing that, under the golden standard of quantum key distribution by which the adversary completely controls the quantum channel, no covert key generation is possible. We propose a protocol based on pulse-position modulation and multi-level coding that allows one to use traditional quantum key distribution (QKD) protocols while ensuring covertness, in the sense that no statistical test by the adversary can detect the presence of communication better than a random guess. When run over a bosonic channel, our protocol can leverage existing discrete-modulated continuous variable protocols. Since existing techniques to bound Eve's information do not directly apply, we develop a new bound that results in positive throughput for a range of channel parameters.