Orthogonal Polynomials on the Unit Circle, Mutually Unbiased Bases, and Balanced States
Abstract
Abstract Two interesting phenomena for the construction of quantum states are that of mutually unbiased bases and that of balanced states. We explore a constructive approach to each phenomenon that involves orthogonal polynomials on the unit circle. In the case of mutually unbiased bases, we show that this approach does not produce such bases. In the case of balanced states, we provide examples of pairs of orthonormal bases and states that are balanced with respect to them. We also consider extensions of these ideas to the infinite dimensional setting.
Fields of Study & Subjects
Mathematical functions and polynomials
Quantum Information and Cryptography
Quantum Mechanics and Applications
Publication details
- Journal / source
- Analysis and Mathematical Physics
- Volume
- 16
- Issue
- 2
- Publication date
- 12 March 2026
- Language
- EN