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

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 ≥ 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.