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

TL;DR

This paper introduces nine Lorentz covariant bitensors for two Dirac spinors that can detect all types of spinor entanglement between spacelike separated particles, extending previous work with four such bitensors.

Contribution

The paper constructs a complete set of nine Lorentz covariant bitensors that uniquely identify entangled states of two Dirac particles, improving the tools for analyzing relativistic quantum entanglement.

Findings

Nine covariant bitensors fully characterize entanglement.

All nine bitensors are zero only for product states.

Extension of previous four-bitensor framework.

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.