Quantum channels with zero privacy can secure messages together
Private communication via zero-private-capacity quantum channels
Information Theory
Summary
Sending secret messages over noisy channels is tricky because the information needs to reach the receiver but stay hidden from others. The paper shows that two channels which individually cannot keep messages private can actually work together to send private information. This surprising effect, called superactivation, means that just looking at a channel's ability alone doesn't tell us its full power for secure communication. The authors used advanced computer tools including AI and formal verification to confirm their findings.
quantum channelprivate capacitynoisy channelsuperactivationquantum information theoryquantum erasure channelsecure communicationquantum encodingclassical codingformal verification
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.