Problem
Research questions and friction points this paper is trying to address.
strong converse exponent
private communication
quantum wiretap channel
secret-key transmission
private capacity
The exact strong converse exponent for private communication over quantum channels
🤖 AI Summary
This study addresses the exact determination of the strong converse exponent for secret key transmission over quantum wiretap channels. To this end, it introduces the novel concepts of Rényi private information and its regularization, which jointly quantify reliability and secrecy, and establishes precise integral representations alongside continuity bounds. The primary contribution lies in achieving an exact characterization of the strong converse exponent and proving its convergence to the private capacity. Furthermore, this work rigorously demonstrates that the fidelity decays exponentially at any rate exceeding the private capacity, thereby establishing definitive theoretical limits for this problem.
📝 Abstract
We determine the exact strong converse exponent for secret-key transmission and generation over general finite-dimensional quantum wiretap channels, measuring reliability and secrecy jointly by squared fidelity to an ideal secret key. We introduce a novel Renyi private information whose regularization characterizes this exponent. An exact integral representation in terms of ordinary private information gives a uniform continuity bound, showing that the regularized quantity converges to private capacity as the Renyi order approaches one. This establishes for any wiretap channel an exponential fidelity decay at every rate above private capacity.
Innovation
Methods, ideas, or system contributions that make the work stand out.
strong converse exponent
quantum wiretap channels
Renyi private information
private capacity
squared fidelity
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