Inhibition of spread of typical bipartite and genuine multiparty entanglement in response to disorder

TL;DR

This paper investigates how disorder in quantum state parameters affects the distribution of entanglement, revealing that disorder tends to increase non-uniformity in entanglement distribution across various quantum states.

Contribution

It demonstrates that disorder generally enhances the non-uniformity of entanglement distribution in typical multiparty quantum states, across different disorder types and strengths.

Findings

Disorder increases non-uniformity of entanglement distribution.

The effect is consistent across Gaussian and non-Gaussian disorders.

Results hold for both pure and noisy states.

Abstract

The distribution of entanglement of typical multiparty quantum states is not uniform over the range of the measure utilized for quantifying the entanglement. We intend to find the response to disorder in the state parameters on this non-uniformity for typical states. We find that the typical entanglement, averaged over the disorder, is taken farther away from uniformity, as quantified by decreased standard deviation, in comparison to the clean case. The feature is seemingly generic, as we see it for Gaussian and non-Gaussian disorder distributions, for varying strengths of the disorder, and for disorder insertions in one and several state parameters. The non-Gaussian distributions considered are uniform and Cauchy-Lorentz. Two- and three-qubit pure state Haar-uniform generations are considered for the typical state productions. We also consider noisy versions of the initial states produced in the Haar-uniform generations. A genuine multiparty entanglement monotone is considered for the three-qubit case, while concurrence is used to measure two-qubit entanglement.