Orders of chaoticity of unitaries

TL;DR

This paper introduces the concept of K-th order chaoticity for unitaries in quantum systems, analyzes its properties for two-level systems, and discusses its implications for quantum random number generation.

Contribution

It defines K-th order chaoticity for unitaries and demonstrates that unitaries cannot have arbitrary order of chaoticity, advancing understanding of quantum chaos properties.

Findings

No unitaries exist with arbitrary order of chaoticity.

Analysis focused on two-level quantum systems.

Introduces a new measure relevant for quantum random number schemes.

Abstract

We introduce the concept of K-th order chaoticity of unitaries, and analyze it for the case of two-level quantum systems. This property is relevant in a certain quantum random number generation scheme. We show that no unitaries exist with an arbitrary order of chaoticity.