Pedagogical introduction to the entropy of entanglement for Gaussian states

TL;DR

This paper provides a clear, step-by-step explanation of how to calculate the entanglement entropy for Gaussian states in continuous-variable quantum systems, emphasizing practical computation methods.

Contribution

It offers a pedagogical derivation of the entropy of entanglement for Gaussian states using symplectic eigenvalues, clarifying an important measure in quantum information.

Findings

Derivation of entanglement entropy in terms of symplectic eigenvalues

Simplified formulas for practical calculations of Gaussian state entanglement

Educational insights into bipartite entanglement measures

Abstract

The most useful measure of a bipartite entanglement is the von Neumann entropy of either of the reduced density matrices. For a particular class of continuous-variable states, the Gaussian states, the entropy of entanglement can be expressed rather elegantly in terms of the symplectic eigenvalues, elements that characterize a Gaussian state and depend on the correlations of the canonical variables. We give a pedagogical step-by-step derivation of this result and provide some insights that can be useful in practical calculations.