PreprintCC BY-NC-ND 4.0arXiv
A New Definition of Quantum Superposition
Abstract
The usual description of the superposition of two (pure quantum) states is ambiguous, since the binary operation of addition in a Hilbert space does not pass down to the quotient projective space. In the setting of complex projective space this paper gives a new geometrical definition of the superposition of two pure states, viewed as two distinct points in the projective space, as the unique (complex) line on which those two points lie. Using the Erlangen program the geometry appropriate for quantum theory of the projective space is precisely defined. Also this rigorous approach is compared with others.
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BibTeX
@misc{sontz2026definition,
title = {{A New Definition of Quantum Superposition}},
author = {Stephen Bruce Sontz},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.15607},
eprint = {2606.15607},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.15607},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A New Definition of Quantum Superposition
AU - Stephen Bruce Sontz
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2606.15607
UR - https://arxiv.org/abs/2606.15607
AB - The usual description of the superposition of two (pure quantum) states is ambiguous, since the binary operation of addition in a Hilbert space does not pass down to the quotient projective space. In the setting of complex projective space this paper gives a new geometrical definition of the superposition of two pure states, viewed as two distinct points in the projective space, as the unique (complex) line on which those two points lie. Using the Erlangen program the geometry appropriate for quantum theory of the projective space is precisely defined. Also this rigorous approach is compared with others.
ER -