
TL;DR
This paper explores the structure and properties of finite quantum instruments and observables, including their combinations, compatibility, and measurement models, within finite-dimensional quantum systems.
Contribution
It introduces a comprehensive framework for finite quantum instruments, extending observable concepts and analyzing their interactions and measurement models.
Findings
Defined finite observables and instruments.
Analyzed combinations and relations of observables and instruments.
Presented various types of instruments and their measurement implications.
Abstract
This article considers quantum systems described by a finite-dimensional complex Hilbert space . We first define the concept of a finite observable on . 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, L\"uders 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsQuantum Mechanics and Applications · Computability, Logic, AI Algorithms · Quantum Computing Algorithms and Architecture
