Generating pseudo-random discrete probability distributions

TL;DR

This paper discusses methods for generating pseudo-random discrete probability distributions, crucial for stochastic simulations and quantum state sampling, providing detailed implementation guidance and an application to quantum states.

Contribution

It introduces and details the iid, normalization, and trigonometric methods for unbiased probability vector generation, filling a gap in the literature.

Findings

Provides numerical implementation details for the methods.

Demonstrates application to quantum state generation.

Offers a comprehensive exposition of the procedures.

Abstract

The generation of pseudo-random discrete probability distributions is of paramount importance for a wide range of stochastic simulations spanning from Monte Carlo methods to the random sampling of quantum states for investigations in quantum information science. In spite of its significance, a thorough exposition of such a procedure is lacking in the literature. In this article we present relevant details concerning the numerical implementation and applicability of what we call the iid, normalization, and trigonometric methods for generating an unbiased probability vector $\mathbf{p}=(p_{1},\cdots,p_{d})$. An immediate application of these results regarding the generation of pseudo-random pure quantum states is also described.