Defining Security in Quantum Key Distribution

2025-09-16

AI Summary

This work addresses the physical interpretation and rigorous characterization of the fundamental security parameter ε in quantum key distribution (QKD). Motivated by longstanding conceptual ambiguities and criticisms surrounding the standard ε-security definition in the literature, we adopt an axiomatic approach grounded in basic security postulates to formally prove that ε admits a precise probabilistic interpretation: it quantifies the maximum probability that the generated key fails to satisfy the required security criteria. Integrating non-asymptotic quantum information theory, we establish a unified mathematical framework for ε-security. Our analysis resolves persistent conceptual confusions, directly responds to foundational critiques, and—crucially—provides a quantifiable, experimentally verifiable foundation for practical security assessment. By anchoring ε in well-defined operational semantics, this work significantly strengthens the rigor, coherence, and explanatory power of QKD’s theoretical security guarantees.

Technology Category

• Machine Learning: Quantum Machine Learning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Application Domains: Security

Application Category

• Security and Privacy: Large-scale security measurements
• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

The security of quantum key distribution (QKD) is quantified by a parameter $varepsilon>0$, which -- under well-defined physical assumptions -- can be bounded explicitly. This contrasts with computationally secure schemes, where security claims are only asymptotic (i.e., under standard complexity assumptions, one only knows that $varepsilon o 0$ as the key size grows, but has no explicit bound). Here we explain the definition and interpretation of $varepsilon$-security. Adopting an axiomatic approach, we show that $varepsilon$ can be understood as the maximum probability of a security failure. Finally, we review and address several criticisms of this definition that have appeared in the literature.

Problem

• Defining and quantifying security in quantum key distribution
• Contrasting QKD's explicit security bounds with asymptotic computational schemes
• Interpreting epsilon-security as maximum probability of failure

Innovation

• Quantifies security with explicit epsilon bound
• Uses axiomatic approach for probability interpretation
• Addresses criticisms of epsilon-security definition