Entanglement Sharing in Real-Vector-Space Quantum 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-vectorspace 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.

The Feynman problem and fermionic entanglement: Fermionic theory versus qubit theory

“…(53), having maximal entanglement of formation and concurrence. Therefore, in the fqt as well as in rqt 26 each pair of subsystems can share any amount of entanglement of formation.…”

“…24 allows for many other theories. Among them we will discuss briefly the case of rqt-which also lacks local tomography 23 and monogamy of entanglement 26 -and the theory with number superselectionwhich only admits superposition of states having the same particle occupation number.…”

Virial theorem and generalized momentum in quaternionic quantum mechanics

“…However, Stueckelberg's theory is involved; it demands an anti-unitary operator J that replaces the complex imaginary unit i in Schrödinger equation, and this anti-unitary operator J is specific for each anticommuting pair of operators [3]. In spite of these problems, RQM is still an object of research, and plays a role within quantum information [7][8][9][10] and mathematical physics [11], thus indicating that alternatives to complex quantum mechanics (CQM) may be useful for understanding new physics. The next possibility is to use quaternions to build a quantum theory.…”

Quantum Theory, Namely the Pure and Reversible Theory of Information

“…All these alternative theories could be rightfully called "quantum", for they share with the standard Quantum Theory its distinctive feature. One natural weakening of the principles would be to relax Local Tomography, thus allowing Quantum Theory on real Hilbert spaces, an interesting toy theory which exhibits quite peculiar information-theoretic features [56]. More challenging and more exciting at the same time would be to venture in the realm of non-causal theories that satisfy the Purity and Reversibility principle, a much broader family of theories that are interesting in view of a formulation of quantum theory in the absence of a definite causal structure.…”