SU(N)-symmetric quasi-probability distribution functions

TL;DR

This paper introduces a new set of SU(N)-symmetric quasi-probability distribution functions for finite-dimensional quantum states, enhancing tools for quantum state analysis.

Contribution

It develops SU(N)-symmetric coherent state-based functions representing Wigner, Q, and P functions for N-dimensional quantum systems, with analysis of their properties.

Findings

Defines SU(N)-symmetric quasi-probability functions

Demonstrates their fundamental properties

Shows their usefulness in quantum state analysis

Abstract

We present a set of N-dimensional functions, based on generalized SU(N)-symmetric coherent states, that represent finite-dimensional Wigner functions, Q-functions, and P-functions. We then show the fundamental properties of these functions and discuss their usefulness for analyzing N-dimensional pure and mixed quantum states.