Calculation of the unitary part of the Bures measure for N-level quantum systems

TL;DR

This paper derives a formula for the unitary component of the Bures measure in N-level quantum systems using canonical coset parameterization, facilitating random state sampling.

Contribution

It introduces a new formula for the unitary part of the Bures measure based on coset parameterization, aligning with random unitary matrix generation.

Findings

Formula expressed as a product of even Euclidean balls

Consistent with random state sampling methods

Provides a practical approach for quantum state analysis

Abstract

We use the canonical coset parameterization and provide a formula with the unitary part of the Bures measure for non-degenerate systems in terms of the product of even Euclidean balls. This formula is shown to be consistent with the sampling of random states through the generation of random unitary matrices.