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

Macroscopically populated quantum superpositions pose a question to what extent the macroscopic world obeys quantum mechanical laws. Recently, such superpositions for light, generated by an optimal quantum cloner, have been demonstrated. They are of fundamental and technological interest. We present numerical methods useful for modeling of these states. Their properties are governed by a Gaussian hypergeometric function, which cannot be reduced to either elementary or easily tractable functions. We discuss the method of efficient computation of this function for half-integer parameters and a 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. The methods presented here can be adjusted for analysis of similar experimental schemes.