  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.
