Entanglement of Formation of an Arbitrary State of Two Rebits

TL;DR

This paper explores the entanglement of two-rebit quantum states, providing a new explicit formula for their entanglement of formation, which enhances understanding of real versus complex quantum entanglement.

Contribution

It introduces a novel formula for the entanglement of formation of two-rebit states, contrasting with previous complex quantum entanglement formulas.

Findings

Derived an explicit formula for two-rebit entanglement of formation

Compared real and complex quantum entanglement properties

Provided insights into the nature of quantum entanglement

Abstract

We consider entanglement for quantum states defined in vector spaces over the real numbers. Such real entanglement is different from entanglement in standard quantum mechanics over the complex numbers. The differences provide insight into the nature of entanglement in standard quantum theory. Wootters [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 concurrence of the joint density operator. We give a contrasting formula for the 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.