Second Quantized Kolmogorov Complexity

TL;DR

This paper introduces a second quantized version of Kolmogorov complexity, measuring the average length of superpositions, and explores its properties and relation to von Neumann entropy.

Contribution

It defines a novel second quantized Kolmogorov complexity and establishes its basic properties and connections to quantum entropy measures.

Findings

Second quantized Kolmogorov complexity is well-defined and exhibits properties similar to classical complexity.

The prefix complexity obeys inequalities analogous to those of von Neumann entropy.

Establishes a link between quantum description complexity and quantum entropy measures.

Abstract

The Kolmogorov complexity of a string is the length of its shortest description. We define a second quantised Kolmogorov complexity where the length of a description is defined to be the average length of its superposition. We discuss this complexity's basic properties. We define the corresponding prefix complexity and show that the inequalities obeyed by this prefix complexity are also obeyed by von Neumann entropy.