Largest Schmidt eigenvalue of entangled random pure states and conductance distribution in chaotic cavities

TL;DR

This paper develops a method to compute the distribution of the largest Schmidt eigenvalue in entangled bipartite quantum states, linking it to conductance distributions in chaotic quantum cavities, and validates results with simulations.

Contribution

It introduces a novel approach connecting quantum entanglement eigenvalues with conductance distributions in chaotic systems, enabling analytical calculations for both symmetry classes.

Findings

Analytical distribution matches numerical simulations.

Distribution is continuous but not analytic everywhere.

Method applies to systems with and without time reversal symmetry.

Abstract

A strategy to evaluate the distribution of the largest Schmidt eigenvalue for entangled random pure states of bipartite systems is proposed. We point out that the multiple integral defining the sought quantity for a bipartition of sizes N, M is formally identical (upon simple algebraic manipulations) to the one providing the probability density of Landauer conductance in open chaotic cavities supporting N and M electronic channels in the two leads. Known results about the latter can then be straightforwardly employed in the former problem for both systems with broken ({\beta} = 2) and preserved ({\beta} = 1) time reversal symmetry. The analytical results, yielding a continuous but not everywhere analytic distribution, are in excellent agreement with numerical simulations.