Entanglement of the Non-Gaussian Two-Mode Quantum Vortex State

We study the entanglement properties of a non-Gaussian two-mode vortex state that was theoretically proposed by Agarwal [New J Phys 13:073008 (2011)] by using the technique of photon subtraction from a two-mode squeezed state and detection of one photon by a single-photon detector. There are different conditions to quantify the entanglement of non-classical states. We compare the entanglement conditions for this state in terms of the Hillery–Zubairy (HZ) criterion, Hillery–Dung–Zhong (HDZ) criterion, Shchukin–Vogel (SV) criterion, and Duan–Giedke–Cirac–Zoller (DGCZ) criterion. We confirm that this non-Gaussian state shows strong entanglement under these different conditions, thus suggesting that this state may have potential applications in quantum information processing.