2020/05/27 by Stan Gudder, Gudder, Stan
Computer Science · Physics and Astronomy · #Computability, Logic, AI Algorithms #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2005.13642
openalex publication_date 2020/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article considers quantum systems described by a finite-dimensional complex Hilbert space H. We first define the concept of a finite observable on H. We then discuss ways of combining observables in terms of convex combinations, post-processing and sequential products. We also define complementary and coexistent observables. We then introduce finite instruments and their related compatible observables. The previous combinations and relations for observables are extended to instruments and their properties are compared. We present four types of instruments; namely, identity, trivial, Lüders and Kraus instruments. These types are used to illustrate different ways that instruments can act. We next consider joint probabilities for observables and instruments. The article concludes with a discussion of measurement models and the instruments they measure.