# Generalized Entanglement Measure for Continuous Variable Systems

## TL;DR

This paper extends a well-known entanglement measure from discrete qubits to continuous variable systems, providing a unified framework that applies to various states and simplifies entanglement analysis.

## Contribution

It introduces a generalized entanglement measure for continuous variable systems based on Lagrange's identity and wedge product, applicable to multiple degrees of freedom.

## Key findings

- The measure matches known results for Gaussian and non-Gaussian states.
- It provides necessary and sufficient conditions for separability.
- Simplifies analysis of quantum entanglement in continuous variables.

## Abstract

Concurrence introduced by Hill and Wootters [Phys. Rev. Lett. 78, 5022 (1997)], provides an important measure of entanglement for a general pair of qubits that is strictly positive entangled states and vanishes for all separable states. We present an extension of entanglement measure to general continuous variable states of multiple degrees of freedom by generalizing the Lagrange's identity and wedge product framework proposed by Bhaskara et al. [Quantum Inf. Process. 16, 118 (2017)] for pure discrete variable systems in arbitrary dimensions. A family of faithful entanglement measures is constructed that admit necessary and sufficient conditions for separability across arbitrary bipartitions presented by Vedral et al. [Phys. Rev. Lett. 16 2275 (1997)]. The computed entanglement measure in the present approach for general Gaussian states, pair coherent states and non Gaussian continuous variable Bell states, matches with known results. We also quantify entanglement of phase randomized squeezed states and superposition of squeezed states. Our results also simplify several results in quantum entanglement theory.