Real-Vector-Space Quantum Theory with a Universal Quantum Bit

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 one-parameter family of effective theories--modifications of standard quantum theory--that all satisfy this rule. The one parameter is the ratio s/omega, where s quantifies the strength of the ubit's interaction with the rest of the world and omega is the ubit's rotation rate. We find that when this parameter is small but not zero, the effective theory is similar to standard quantum theory but is characterized by spontaneous decoherence of isolated systems.