Entanglement properties of random invariant quantum states

TL;DR

This paper studies the entanglement characteristics of random quantum states invariant under SU(d), showing they are typically highly entangled and robust to disturbances as system dimensions grow large.

Contribution

It provides analytical results on the entanglement of random SU(d)-invariant states, demonstrating their near-maximal entanglement and robustness in high-dimensional systems.

Findings

Random SU(d)-invariant states are nearly maximally entangled with high probability.

Entanglement concentration occurs as the system dimension increases.

The entanglement properties are robust against finite perturbations.

Abstract

Entanglement properties of random multipartite quantum states which are invariant under global SU($d$) action are investigated. The random states live in the tensor power of an irreducible representation of SU($d$). We calculate and analyze the expectation and fluctuation of the second-order R\'enyi entanglement measure of the random invariant and near-invariant states in high dimension, and reveal the phenomenon of concentration of measure the random states exhibit. We show that with high probability a random SU($d$)-invariant state is close to being maximally entangled with respect to any bipartite cut as the dimension of individual system goes to infinity. We also show that this generic entanglement property of random SU(2)-invariant state is robust to arbitrarily finite disturbation.