Quantum channels with zero privacy enable secure communication together
Private communication via zero-private-capacity quantum channels
Information Theory
Summary
In quantum communication, some channels are considered useless for sending private messages. This paper shows that combining two such 'zero privacy' channels can actually allow private communication. The authors found a specific example where using these channels together enables sending secret bits, which was thought impossible before. This finding challenges previous ideas about how quantum channels provide security.
What this means in practice
- •For quantum communication engineers: Design secure quantum communication protocols using combined zero-capacity channels to achieve private data transfer previously considered impossible.
- •For quantum cryptography developers: Develop new quantum encryption systems exploiting superactivation effects to enhance security beyond individual channel limitations.
Authors
Chengkai Zhu, Xin Wang
Abstract
Private communication over a noisy quantum channel requires reliable transmission to the receiver and secrecy from the environment. Whether two channels with zero private capacity can jointly enable private communication is a longstanding open problem in quantum information theory. Here we resolve this problem by exhibiting a four-level channel and a qubit erasure channel with half erasure probability, each with zero private capacity, whose joint use achieves more than 0.0001903 private bits per product use. The encoding gives the receiver a linear information gain with at most quadratic environmental leakage, enabling privacy through a fixed joint measurement and classical coding. This superactivation, impossible for independent classical memoryless wiretap channels, shows that a channel's private capacity alone does not determine its value for secure communication. The initial activation example was identified through interactions with large language models, and the result has been formalized in Lean 4.