Entanglement of formation of an arbitrary state of two rebits

We consider entanglement for quantum states defined in vector spaces over t he real numbers. Such real entanglement is different from entanglement in s tandard quantum mechanics over the complex numbers. The differences provide insight into the nature of entanglement in standard quantum theory. Wootte rs [Phys. Rev. Lett. 80, 2245 (1998)] has given an explicit formula for the entanglement of formation of two qubits in terms of what he calls the conc urrence of the joint density operator. We give a contrasting formula for th e entanglement of formation of an arbitrary state of two "rebits," a rebit being a system whose Hilbert space is a 2-dimensional real vector space.