A Note on Pseudo-Hermitian Systems with Point Interactions and Quantum Separability

We study the quantum entanglement and separability of Hermitian and pseudo-Hermitian systems of identical bosonic or fermionic particles with point interactions. The separability conditions are investigated in detail. PACS: 02.30.Ik, 11.30.Er, 03.65.Fd Key words: Point interactions, PT-symmetry, Separability Pseudo-Hermitian quantum mechanical systems have been extensively investi-gated due to some mathematical and physical considerations [1]. For PT-symmetric systems with singular contact interactions, we have studied the classification, spec-tra and integrability problem in [2]. The results are generalized to the case of identical bosonic and fermionic many-body systems with PT-symmetric contact interactions and spin-coupling interactions [3]. On the other hand, as one of the most striking features of quantum phenom-ena [4], quantum entanglement has been identified as a key non-local resource in quantum information processing such as quantum computation [5], quantum tele-portation, dense coding, quantum cryptographic schemes, entanglement swapping and remote state preparation (RSP). Nevertheless the theory of quantum entan-glement is far from being satisfied. One of main problem in quantum entanglement is to judge a quantum state is separable or entangled, i.e. the separability. In this paper we study separability of Hermitian and pseudo-Hermitian systems of many body systems with contact interactions. We first consider contact interactions without spin coupling. A particle moving in one dimension with point interactions at the origin can be characterized by the non-separated1) boundary conditions imposed on the wave function ϕ at x = 0,