Quantum Kolmogorov Complexity and Information-Disturbance Theorem

TL;DR

This paper explores the relationship between information gain and disturbance in quantum systems using quantum Kolmogorov complexity, providing a new perspective on the fundamental trade-offs in quantum information theory.

Contribution

It introduces a representation of the information-disturbance theorem based on quantum Kolmogorov complexity, linking complexity measures to quantum cryptographic principles.

Findings

Derived quantitative relationships between complexities and disturbance

Linked quantum Kolmogorov complexity to the information-disturbance trade-off

Provided a complexity-based formulation of the theorem

Abstract

In this paper, a representation of the information-disturbance theorem based on the quantum Kolmogorov complexity that was defined by P. Vitanyi has been examined. In the quantum information theory, the information-disturbance relationship, which treats the trade-off relationship between information gain and its caused disturbance, is a fundamental result that is related to Heisenberg's uncertainty principle. The problem was formulated in a cryptographic setting and quantitative relationships between complexities have been derived.