Tomographic entanglement indicators in a coupled oscillator model

Abstract

We study entanglement in a simple model comprising two coupled linear harmonic oscillators of the same natural frequency. The system is separable in the center of mass (COM) and relative coordinates into two oscillators of frequency ${\omega }_c$ and ${\omega }_r$. We compute standard entanglement measures (subsystem linear entropy and subsystem von Neumann entropy) as well as several tomographic entanglement indicators (Bhattacharyya distance, Kullback-Leibler divergence and inverse participation ratio) as functions of the frequency ratio $\eta ={\omega }_c/{\omega }_r$, keeping the COM oscillator in the ground state. We demonstrate that, overall, the entanglement indicators reflect quite faithfully the variations in the standard measures. The entanglement is shown to be minimum at $\eta =1$ and maximum as $\eta \to 0$ or $\infty$.

References in corpus (16)

• Quantum entanglement
• Sudden Death of Entanglement
• Entanglement, avoided crossings and quantum chaos in an Ising model with a tilted magnetic field
• Krylov Complexity in Quantum Field Theory
• Coupled harmonic oscillators and their quantum entanglement
• The Hydrogen Atom as an Entangled Electron-Proton System
• Generalized entanglement as a framework for complex quantum systems: Purity vs delocalization measures
• Divergence of entanglement entropy in quantum systems: Zero-modes
• Zero modes and divergence of entanglement entropy
• Entanglement in Three Coupled Harmonic Oscillators
• Entanglement in Coupled Harmonic Oscillators via Unitary Transformation
• Circuit Complexity in ${\mathcal{Z}}_2$ $\mathcal{EEF}\mathcal{T}$
• Circuit Complexity in an interacting quenched Quantum Field Theory
• Hydrogenic entanglement
• Signatures of avoided energy-level crossings in entanglement indicators obtained from quantum tomograms
• A tomographic approach to the sum uncertainty relation and quantum entanglement in continuous variable systems