Real-Vector-Space Quantum Theory with a Universal Quantum Bit
Antoniya Aleksandrova, Victoria Borish, and William K. Wootters

TL;DR
This paper investigates a real-vector-space quantum model featuring a universal binary object called the ubit, which can reproduce standard quantum theory under certain conditions and introduces a family of modified theories with spontaneous decoherence.
Contribution
It presents a model of quantum theory based on real vectors with a universal ubit, deriving standard quantum mechanics without restrictions and exploring effective theories with decoherence effects.
Findings
Effective theories satisfy Stueckelberg's rule automatically
Small ubit-environment interaction leads to decoherence
Model recovers standard quantum theory in a specific limit
Abstract
We explore a model of the world based on real-vector-space quantum theory. In our model the familiar complex phase appearing in quantum states is replaced by a single binary object that we call the ubit, which is not localized and which can interact with any object in the world. Ordinary complex-vector-space quantum theory can be recovered from this model if we simply impose a certain restriction on the sets of allowed measurements and transformations (Stueckelberg's rule), but in this paper we try to obtain the standard theory, or a close approximation to it, without invoking such a restriction. We look particularly at the effective theory that applies to a subsystem when the ubit is interacting with a much larger environment. In a certain limit it turns out that the ubit-environment interaction has the effect of enforcing Stueckelberg's rule automatically, and we obtain a…
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