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Compatibility and partial compatibility in quantum logics

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Compatibility and partial compatibility in quantum logics ANNALES DE L’I. H. P., SECTION A SYLVIA PULMANNOVÁ Compatibility and partial compatibility in quantum logics Annales de l’I. H. P., section A, tome 34, no 4 (1981), p. 391-403. <http://www.numdam.org/item?id=AIHPA_1981__34_4_391_0> © Gauthier-Villars, 1981, tous droits réservés. L’accès aux archives de la revue « Annales de l’I. H. P., section A », implique l’accord avec les conditions générales d’utilisation (http://www. numdam.org/legal.php). Toute utilisation commerciale ou impression systé- matique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ 391 Compatibility and partial compatibility in quantum logics Sylvia PULMANNOVÁ Institute for Measurement and Measurement Technique, Slovak Academy of Sciences, 88527 Brastislava, Czechoslovakia Inst. Henri Poincaré, ’ Vol. XXXIV, n° 4, 1981, Section A : Physique theorique. ABSTRACT. 2014 Compatibility relation, commensurability of observables and existence of joint distributions in quantum logics are considered. A weakened form of compatibility, so-called partial compatibility of pro- positions is introduced and its connections with a relativized commensura- bility of observables and with the existence of joint probability distributions of Gudder’s type are studied. 1. INTRODUCTION In the quantum logic approach to quantum theory, the structure of the set of all yes-no measurements (called also propositions, questions, events), which is called the logic of a physical system, is of a primary importance. The logic of a classical system is found to be the Boolean lattice of all Borel subsets of the phase space of the system, while the logic of a standard quantum mechanical system is the complete ortholattice of all closed sub-spaces of a (complex, separable) Hi

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