Simple proof of confidentiality for private quantum channels in noisy environments

TL;DR

This paper presents a simplified and robust proof of confidentiality for noisy quantum channels using entanglement distillation, enhancing security levels and applicable even under full eavesdropper control, with implications for secure quantum networks.

Contribution

It provides a straightforward proof of confidentiality for noisy quantum channels via hashing, improving security guarantees from linear to exponential levels and extending to multiparty quantum networks.

Findings

Confidentiality can be guaranteed even when entanglement distillation fails.

Security levels are exponentially improved for hashing protocols.

The proof applies under full eavesdropper control and noisy environments.

Abstract

Complete security proofs for quantum communication protocols can be notoriously involved, which convolutes their verification, and obfuscates the key physical insights the security finally relies on. In such cases, for the majority of the community, the utility of such proofs may be restricted. Here we provide a simple proof of confidentiality for parallel quantum channels established via entanglement distillation based on hashing, in the presence of noise, and a malicious eavesdropper who is restricted only by the laws of quantum mechanics. The direct contribution lies in improving the linear confidentiality levels of recurrence-type entanglement distillation protocols to exponential levels for hashing protocols. The proof directly exploits the security relevant physical properties: measurement-based quantum computation with resource states and the separation of Bell-pairs from an eavesdropper. The proof also holds for situations where Eve has full control over the input states, and obtains all information about the operations and noise applied by the parties. The resulting state after hashing is private, i.e., disentangled from the eavesdropper. Moreover, the noise regimes for entanglement distillation and confidentiality do not coincide: Confidentiality can be guaranteed even in situation where entanglement distillation fails. We extend our results to multiparty situations which are of special interest for secure quantum networks.