PreprintCC BY 4.0arXiv
Simultaneous extensions of states on quantum logics
Abstract
Suppose that L is a quantum logic (= an orthomodular poset) and A, B are Boolean subalgebras of L. Suppose further that s1(resp. s2) is a state on A (resp. on B). We ask when both s1 and s2 allow for a simultaneous extension over L. Under a natural necessity condition on A, B, s1, s2 we find a sufficient condition for the existence of the extension. This condition is the requirement of an abundance of two-valued states on L. We then show by the Greechie pasting technique that this condition is far from necessary even for state-space-rich logics.
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BibTeX
@misc{buresova2026simultaneous,
title = {{Simultaneous extensions of states on quantum logics}},
author = {Dominika Burešová and Pavel Pták and Jan Ševic},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10770},
eprint = {2609.10770},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10770},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Simultaneous extensions of states on quantum logics
AU - Dominika Burešová
AU - Pavel Pták
AU - Jan Ševic
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10770
UR - https://arxiv.org/abs/2609.10770
AB - Suppose that L is a quantum logic (= an orthomodular poset) and A, B are Boolean subalgebras of L. Suppose further that s1(resp. s2) is a state on A (resp. on B). We ask when both s1 and s2 allow for a simultaneous extension over L. Under a natural necessity condition on A, B, s1, s2 we find a sufficient condition for the existence of the extension. This condition is the requirement of an abundance of two-valued states on L. We then show by the Greechie pasting technique that this condition is far from necessary even for state-space-rich logics.
ER -