Complementarity and the algebraic structure of 4-level quantum systems

TL;DR

This paper reviews the concept of complementarity in quantum systems, extends it to non-commutative subalgebras, and characterizes the Bell basis within 4-level quantum systems using algebraic and entropy-based methods.

Contribution

It introduces a novel algebraic framework for understanding complementarity in 4-level quantum systems and characterizes the Bell basis through this approach.

Findings

Complementarity is extended to non-commutative subalgebras.

A new characterization of the Bell basis is provided.

Decompositions of 4-level systems are described using algebraic structures.

Abstract

The history of complementary observables and mutual unbiased bases is reviewed. A characterization is given in terms of conditional entropy of subalgebras. The concept of complementarity is extended to non-commutative subalgebras. Complementary decompositions of a 4-level quantum system are described and a characterization of the Bell basis is obtained.