Entanglement Sharing in Real-Vector-Space Quantum Theory

TL;DR

This paper demonstrates that replacing complex vector spaces with real vector spaces in quantum theory eliminates the usual entanglement sharing restrictions, allowing for states where multiple rebits are simultaneously maximally entangled.

Contribution

It shows that the entanglement sharing limitations of standard quantum theory do not hold in real-vector-space quantum theory, revealing fundamental differences between the two frameworks.

Findings

In real-vector-space quantum theory, multiple rebits can be simultaneously maximally entangled.

The usual entanglement sharing restrictions are absent in the real-vector-space formulation.

States with arbitrarily many maximally entangled rebits exist in the real-vector-space theory.

Abstract

The limitation on the sharing of entanglement is a basic feature of quantum theory. For example, if two qubits are completely entangled with each other, neither of them can be at all entangled with any other object. In this paper we show, at least for a certain standard definition of entanglement, that this feature is lost when one replaces the usual complex vector space of quantum states with a real vector space. Moreover, the difference between the two theories is extreme: in the real-vector-space theory, there exist states of arbitrarily many binary objects, "rebits," in which every rebit in the system is maximally entangled with each of the other rebits.