Purity distribution for bipartite random pure states

TL;DR

This paper derives explicit analytic expressions for the probability density distributions of linear entropy and purity in bipartite pure random quantum states, focusing on specific low-dimensional cases.

Contribution

It provides new explicit formulas for the distributions of purity and linear entropy for bipartite states with certain dimensions, advancing understanding of their statistical properties.

Findings

Explicit distributions for p=3, q≥3, and p=q=4 are derived.

Analytic formulas enhance understanding of quantum state purity in bipartite systems.

Results facilitate analysis of entanglement properties in random quantum states.

Abstract

Analytic expressions for the probability density distribution of the linear entropy and the purity are derived for bipartite pure random quantum states. The explicit distributions for a state belonging to a product of Hilbert spaces of dimensions p and q are given for p=3 and any q>=3, as well as for p=q=4.