Quantum Kolmogorov Complexity and Quantum Key Distribution

TL;DR

This paper applies quantum algorithmic information theory, specifically quantum Kolmogorov complexity, to analyze the security of the BB84 quantum key distribution protocol, demonstrating its effectiveness in generating nearly random keys.

Contribution

It introduces a security criterion for quantum key distribution based on quantum Kolmogorov complexity, linking algorithmic information theory with quantum cryptography.

Findings

BB84 protocol produces keys that appear almost random to eavesdroppers

Quantum Kolmogorov complexity provides a new security measure

High probability of secure key distribution close to 1

Abstract

We discuss the Bennett-Brassard 1984 (BB84) quantum key distribution protocol in the light of quantum algorithmic information. While Shannon's information theory needs a probability to define a notion of information, algorithmic information theory does not need it and can assign a notion of information to an individual object. The program length necessary to describe an object, Kolmogorov complexity, plays the most fundamental role in the theory. In the context of algorithmic information theory, we formulate a security criterion for the quantum key distribution by using the quantum Kolmogorov complexity that was recently defined by Vit\'anyi. We show that a simple BB84 protocol indeed distribute a binary sequence between Alice and Bob that looks almost random for Eve with a probability exponentially close to 1.