Numerical model for macroscopic quantum superpositions based on phase-covariant quantum cloning

TL;DR

This paper introduces numerical methods for modeling macroscopic quantum superpositions generated by optimal quantum cloning, focusing on efficient computation of complex functions and dynamic cutoff estimation to improve simulation accuracy.

Contribution

It presents novel numerical algorithms for modeling quantum superpositions involving Gaussian hypergeometric functions, enhancing computational efficiency and precision.

Findings

Algorithm exceeds double precision accuracy

Method is parallelizable and adaptable to various experimental parameters

Provides efficient computation of complex hypergeometric functions

Abstract

Macroscopically populated quantum superpositions pose a question to what extent macroscopic world obeys quantum mechanical laws. Recently such superpositions for light, generated by optimal quantum cloner, were demonstrated. They are of fundamental and technological interest. We present numerical methods useful for modeling of these states. Their properties are governed by Gaussian hypergeometric function, which cannot be reduced to neither elementary nor easily tractable functions. We discuss the method of efficient computation of this function for half integer parameters and moderate value of its argument. We show how to dynamically estimate a cutoff for infinite sums involving this function performed over its parameters. Our algorithm exceeds double precision and is parallelizable. Depending on the experimental parameters it chooses one of the several ways of summation to achieve the best efficiency. Methods presented here can be adjusted for analysis of similar experimental schemes.