Toolbox for non-classical state calculations

TL;DR

This paper introduces a generating function-based toolbox to efficiently compute Wigner functions and photon statistics of non-classical states, addressing computational challenges in quantum state analysis.

Contribution

It presents a novel method using generating functions for calculating Wigner functions of photon-subtracted states with arbitrary photon numbers, bridging theory and experimental implementation.

Findings

Efficient computation of Wigner functions for photon-subtracted states.

Analysis of photon statistics using generating functions.

Insights into parameter dependencies of non-classical states.

Abstract

Computational challenges associated with the use of Wigner functions to identify non-classical properties of states are addressed with the aid of generating functions. It allows the computation of the Wigner functions of photon-subtracted states for an arbitrary number of subtracted photons. Both the formal definition of photon-subtracted states in terms of ladder operators and the experimental implementation with heralded photon detections are analyzed. These techniques are demonstrated by considering photon subtraction from squeezed thermal states as well as squeezed Fock states. Generating functions are also used for the photon statistics of these states. These techniques reveal various aspects of the parameter dependences of these states.