Wootters, W. (2009). Quantum Mechanics as a Real-Vector-Space Theory with a Universal Auxiliary Rebit. Perimeter Institute. https://pirsa.org/08080100

MLA

Wootters, William. Quantum Mechanics as a Real-Vector-Space Theory with a Universal Auxiliary Rebit. Perimeter Institute, Aug. 11, 2009, https://pirsa.org/08080100

BibTex

@misc{ pirsa_PIRSA:08080100,
doi = {10.48660/08080100},
url = {https://pirsa.org/08080100},
author = {Wootters, William},
keywords = {Quantum Foundations},
language = {en},
title = {Quantum Mechanics as a Real-Vector-Space Theory with a Universal Auxiliary Rebit},
publisher = {Perimeter Institute},
year = {2009},
month = {aug},
note = {PIRSA:08080100 see, \url{https://pirsa.org}}
}

In a 1960 paper, E. C. G. Stueckelberg showed how one can obtain the familiar complex-vector-space structure of quantum mechanics by starting with a real-vector-space theory and imposing a superselection rule. In this talk I interpret Stueckelberg’s construction in terms of a single auxiliary real-vector-space binary object—a universal rebit, or “ubit." The superselection rule appears as a limitation on our ability to measure the ubit or to use it in state transformations. This interpretation raises the following questions: (i) What is the ubit? (ii) Could the superselection rule emerge naturally as a result of decoherence? (iii) If so, could one hope to see experimentally any effects of imperfect decoherence?
Background reading:
E. C. G. Stueckelberg, "Quantum Theory in Real Hilbert Space," Helv. Phys. Acta 33, 727 (1960).
P. Goyal, "From Information Geometry to Quantum Theory," arXiv:0805.2770.
C. M. Caves, C. A. Fuchs, and P. Rungta, "Entanglement of Formation of an Arbitrary State of Two Rebits," arXiv:quant-ph/0009063.