Nine Lorentz covariant bitensors for two Dirac spinors to indicate all entangled states

Abstract

The spinorial degrees of freedom of two spacelike separated Dirac particles are considered and a collection of nine locally Lorentz covariant bitensors is constructed. Four of these bitensors have been previously described in [Phys. Rev. A 105, 032402 (2022), arXiv:2103.07784]. The collection of bitensors has the property that all nine bitensors are simultaneously zero if and only if the state of the two particles is a product state. Thus this collection of bitensors indicates any type of spinor entanglement between two spacelike separated Dirac particles.