Tensor product of quantum logics

1985/01/01 by Sylvia Pulmannová · 48 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Algebra and Logic #Algebra over a field #Hilbert space #Logic, Reasoning, and Knowledge #Mathematical analysis #Mathematics #Open quantum system #Physics #Pure mathematics #Quantum #Quantum Mechanics and Applications #Quantum computer #Quantum logic #Quantum mechanics #Quantum operation #SIC-POVM #Tensor contraction #Tensor product #Tensor product of Hilbert spaces #Tensor product of algebras #Theoretical physics #Uniqueness

paper · doi:10.1063/1.526784

published in Journal of Mathematical Physics 26(1), 1-5 (American Institute of Physics)

openalex publication_date 1985/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21

Abstract

A quantum logic is the couple (L,M) where L is an orthomodular σ-lattice and M is a strong set of states on L. The Jauch–Piron property in the σ-form is also supposed for any state of M. A ‘‘tensor product’’ of quantum logics is defined. This definition is compared with the definition of a free orthodistributive product of orthomodular σ-lattices. The existence and uniqueness of the tensor product in special cases of Hilbert space quantum logics and one quantum and one classical logic are studied.

Cited by

• Physical Properties as Modal Operators in the Topos Approach to Quantum Mechanics
• A quantum logical and geometrical approach to the study of improper mixtures

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