Local entanglement of multidimensional continuous-variable systems

TL;DR

This paper investigates how local entanglement persists in multidimensional continuous-variable quantum systems after imperfect spatial measurements, providing simple formulas for pure states and applying them to various physical examples.

Contribution

It introduces a method to quantify local entanglement after spatial filtering in multidimensional continuous-variable systems, with explicit formulas for pure states and practical applications.

Findings

Local entanglement can be fully characterized with simple expressions.

The approach applies to semiclassical, harmonic oscillator, and atomic systems.

Results demonstrate how imperfect measurements affect entanglement detection.

Abstract

We study the `local entanglement' remaining after filtering operations corresponding to imperfect measurements performed by one or both parties, such that the parties can only determine whether or not the system is located in some region of space. The local entanglement in pure states of general bipartite multidimensional continuous-variable systems can be completely determined through simple expressions. We apply our approach to semiclassical WKB systems, multi-dimensional harmonic oscillators, and a hydrogen atom as three examples.