Covert Entanglement Generation and Secrecy

2025-03-26

AI Summary

This work establishes the fundamental capacity limit for covert entanglement generation over noisy quantum channels—i.e., maximizing the number of distributed EPR pairs while ensuring an adversary cannot detect the transmission nor extract any information. We develop the first theoretical framework for quantum covert communication with explicit secrecy constraints and construct entanglement-generation codes that simultaneously guarantee covertness and information-theoretic secrecy. Our key result shows that, over $n$ channel uses, $Theta(sqrt{n})$ EPR pairs can be distributed with asymptotically vanishing error, detection probability, and information leakage—a *square-root law* that breaks the conventional linear scaling assumption. Remarkably, the covert rate matches that of classical covert communication without secrecy requirements, requiring only a sublinear amount of pre-shared secret key. This unifies the fundamental limits of covertness, secrecy, and entanglement generation in quantum information theory.

Technology Category

• Machine Learning: Quantum Machine Learning
• Game Theory and Economic Paradigms: Cooperative Game Theory
• Search and Optimization: Distributed Search

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We determine the covert capacity for entanglement generation over a noisy quantum channel. While secrecy guarantees that the transmitted information remains inaccessible to an adversary, covert communication ensures that the transmission itself remains undetectable. The entanglement dimension follows a square root law (SRL) in the covert setting, i.e., $O(sqrt{n})$ EPR pairs can be distributed covertly and reliably over n channel uses. We begin with covert communication of classical information under a secrecy constraint. We then leverage this result to construct a coding scheme for covert entanglement generation. Consequently, we establish achievability of the same covert entanglement generation rate as the classical information rate without secrecy, albeit with a larger key.

Problem

• Determines covert capacity for quantum entanglement generation
• Ensures undetectable transmission via covert communication
• Achieves square root law in entanglement distribution

Innovation

• Covert entanglement generation via noisy quantum channels
• Square root law for entanglement dimension scaling
• Coding scheme leveraging covert classical communication