Average Entropy of a Subsystem

TL;DR

This paper proves D. Page's conjecture that the average entropy of a subsystem in a random pure quantum state can be exactly calculated, confirming a key theoretical prediction in quantum information theory.

Contribution

The paper provides a rigorous proof of Page's conjecture on the average entropy of a subsystem in a random pure state.

Findings

Confirmed the formula for average subsystem entropy in random pure states.

Validated the conjecture with a mathematical proof.

Strengthened theoretical understanding of quantum entanglement in large systems.

Abstract

It was recently conjectured by D. Page that if a quantum system of Hilbert space dimension $nm$ is in a random pure state then the average entropy of a subsystem of dimension $m$ where $m \leq n$ is $ S_{mn} = \sum^{mn}_{k=n+1}(1/k) - (m-1)/2n$. In this letter this conjecture is proved.