Entanglement and Wigner function negativity of multimode non-Gaussian states

TL;DR

This paper develops an analytical framework to study entanglement and Wigner function negativity in multimode non-Gaussian states created via photon addition and subtraction, highlighting their quantum advantages.

Contribution

It introduces a novel analytical expression for the Wigner function after photon operations on multimode states, linking non-Gaussianity to entanglement and negativity conditions.

Findings

Derived an explicit Wigner function formula for multimode non-Gaussian states.

Identified conditions for Wigner function negativity in these states.

Analyzed the impact of photon addition/subtraction on Gaussian states.

Abstract

Non-Gaussian operations are essential to exploit the quantum advantages in optical continuous variable quantum information protocols. We focus on mode-selective photon addition and subtraction as experimentally promising processes to create multimode non-Gaussian states. Our approach is based on correlation functions, as is common in quantum statistical mechanics and condensed matter physics, mixed with quantum optics tools. We formulate an analytical expression of the Wigner function after subtraction or addition of a single photon, for arbitrarily many modes. It is used to demonstrate entanglement properties specific to non-Gaussian states, and also leads to a practical and elegant condition for Wigner function negativity. Finally, we analyse the potential of photon addition and subtraction for an experimentally generated multimode Gaussian state.