Shannon Entropic Entanglement Criterion in the Simple Harmonic Oscillator
arXiv:2002.05858
Abstract
We apply the Walborn [Walborn S P, Taketani B G, Salles A, Toscano F and de Matos Filho R L 2009 Entropic Entanglement Criteria for Continuous Variables Phys. Rev. Lett. 103 160505] Shannon Entropic Entanglement Criterion (SEEC), to simple harmonic oscillators, a system typically discussed in undergraduate quantum mechanics courses. In particular, we investigate the entanglement of a system of coupled harmonic oscillators. A simple form of entanglement criterion in terms of their interaction is found. It is shown that a pair of interacting ground state coupled oscillators are more likely to be entangled for weaker coupling strengths while coupled oscillators in excited states entangle at higher coupling strengths. Interacting oscillators are more likely to be entangled as their interaction increases.
arXiv comment15 pages
References in corpus (12)
- Peres-Horodecki separability criterion for continuous variable systems
- Inseparability criterion for continuous variable systems
- Entropic Uncertainty Relations and their Applications
- Entangling macroscopic oscillators exploiting radiation pressure
- Detecting genuine multipartite continuous-variable entanglement
- Entropic Entanglement Criteria for Continuous Variables
- Coupled harmonic oscillators and their quantum entanglement
- A Family of Continuous Variable Entanglement Criteria using General Entropy Functions
- Coupled oscillators, entangled oscillators, and Lorentz-covariant harmonic oscillators
- Exact Shannon entropies for the multidimensional harmonic states
- Entanglement entropies of coupled harmonic oscillators
- Entropies for Coupled Harmonic Oscillators and Temperature