Jauch-Piron states on quantum logics

被引：0

作者：

Hroch, Michal ^{[1
]}

Ptak, Pavel ^{[1
]}

机构：

[1] Czech Tech Univ, Fac Elect Engn, Dept Math, Tech 2, Prague 16627, Czech Republic

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2020年 / 19卷 / 01期

关键词：

Boolean algebra; orthomodular lattice; quantum logic; Jauch-Piron states; extensions of states;

D O I：

10.1142/S0219498820500176

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show in this note that if B is a Boolean subalgebra of the lattice quantum logic L, then each state on B can be extended over L as a Jauch-Piron state provided L is Jauch-Piron unital with respect to B (i.e. for each nonzero b is an element of B, there is a Jauch-Piron state s on L such that s(b) = 1). We then discuss this result for the case of L being the Hilbert space logic L(H) and L being a set-representable logic.

引用

页数：5

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