Bases for qudits from a nonstandard approach to SU(2)

TL;DR

This paper introduces a method to construct mutually unbiased bases for qudits using angular momentum theory and su(2) algebra, enabling efficient generation of bases in prime power dimensions relevant for quantum information.

Contribution

A new formula for deriving complete sets of mutually unbiased bases in prime and prime power dimensions using su(2) algebraic methods.

Findings

Derived a one-step formula for p+1 mutually unbiased bases in C^p.

Extended the method to generate bases in dimensions p^e.

Discussed the connection between mutually unbiased bases and SU(d).

Abstract

Bases of finite-dimensional Hilbert spaces (in dimension d) of relevance for quantum information and quantum computation are constructed from angular momentum theory and su(2) Lie algebraic methods. We report on a formula for deriving in one step the (1+p)p qupits (i.e., qudits with d = p a prime integer) of a complete set of 1+p mutually unbiased bases in C^p. Repeated application of the formula can be used for generating mutually unbiased bases in C^d with d = p^e (e > or = 2) a power of a prime integer. A connection between mutually unbiased bases and the unitary group SU(d) is briefly discussed in the case d = p^e.