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arXiv · 2609.10770

Simultaneous extensions of states on quantum logics

Dominika Burešová·Pavel Pták·Jan Ševic
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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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Dominika Burešová, Pavel Pták, Jan Ševic. 2026-09-09. Simultaneous extensions of states on quantum logics. https://arxiv.org/abs/2609.10770

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