# Operational quasiprobabilities for continuous variables

## TL;DR

This paper extends the concept of operational quasiprobabilities to continuous-variable systems in quantum optics, enabling direct comparison with classical statistics and revealing non-classical features through negativity.

## Contribution

It introduces a commensurate operational quasiprobability framework for continuous variables, facilitating interpretation and comparison with classical theories.

## Key findings

- Operational quasiprobability can be negative, indicating non-classicality.
- The approach allows comparison with the Glauber-Sudarshan P function.
- An experimental scheme for sequential quadrature measurements is proposed.

## Abstract

We generalize the operational quasiprobability involving sequential measurements proposed by Ryu {\em et al.} [Phys. Rev. A {\bf 88}, 052123] to a continuous-variable system. The quasiprobabilities in quantum optics are incommensurate, i.e., they represent a given physical observation in different mathematical forms from their classical counterparts, making it difficult to operationally interpret their negative values. Our operational quasiprobability is {\em commensurate}, enabling one to compare quantum and classical statistics on the same footing. We show that the operational quasiprobability can be negative against the hypothesis of macrorealism for various states of light. Quadrature variables of light are our examples of continuous variables. We also compare our approach to the Glauber-Sudarshan $\mathcal{P}$ function. In addition, we suggest an experimental scheme to sequentially measure the quadrature variables of light.