Entanglement induced by noncommutativity: anisotropic harmonic oscillator in noncommutative space

Quantum entanglement, induced by spatial noncommutativity, is investigated for an anisotropic harmonic oscillator. Exact solutions the system are obtained after model re-expressed in terms of canonical variables, performing a particular Bopp’s shift to noncommutating degrees freedom. Employing Simon’s separability criterion, we find that states entangled provided unique function (mass and frequency) parameters obeys inequality. Entanglement Formation this also computed its relation degree anisotropy discussed. It worth mentioning that, even noncommutative space, entanglement generated only if oscillator anisotropic. Interestingly, saturates higher values deformation parameter \(\theta \), quantifies noncommutativity.