Problem
Research questions and friction points this paper is trying to address.
private communication
zero private capacity
quantum channels
Private communication via zero-private-capacity quantum channels
๐ค AI Summary
็ ็ฉถ่งฃๅณไบ้่ฟ้ถ็งๅฏๅฎน้้ๅญไฟก้ๅฎ็ฐ็งไบบ้ไฟก็้ฎ้ข๏ผ้่ฟ็ปๅไฝฟ็จๅ่ฝ็บงไฟก้ๅๅๆฆ้คๆฆ็็้ๅญๆฏ็นๆฆ้คไฟก้๏ผๅฎ็ฐไบ่ถ
่ฟ0.0001903็็งๅฏๆฏ็นไผ ่พใ
๐ 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
zero-private-capacity quantum channels
superactivation
secure communication
joint measurement
classical coding
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