Operational Quantification of Continuous Variable Correlations

TL;DR

This paper introduces a practical method to quantify quantum and classical correlations in continuous variable systems by measuring correlated bits via quadrature signs, applicable to Gaussian and non-Gaussian states, facilitating experimental entanglement assessment.

Contribution

It proposes an operational measure of correlations based on sign measurements of quadratures, which simplifies entanglement quantification without full state tomography.

Findings

Bit correlations majorize entanglement for Gaussian states.

For non-Gaussian states, bit correlations are monotonic with negativity.

Method enables direct homodyne detection-based entanglement measurement.

Abstract

We quantify correlations (quantum and/or classical) between two continuous variable modes in terms of how many correlated bits can be extracted by measuring the sign of two local quadratures. On Gaussian states, such `bit quadrature correlations' majorize entanglement, reducing to an entanglement monotone for pure states. For non-Gaussian states, such as photonic Bell states, ideal and real de-Gaussified photon-subtracted states, and mixtures of pure Gaussian states, the bit correlations are shown to be a {\em monotonic} function of the negativity. This yields a feasible, operational way to quantitatively measure non-Gaussian entanglement in current experiments by means of direct homodyne detection, without a full tomographical reconstruction of the Wigner function.