Discrete phase-space structure of $n$-qubit mutually unbiased bases

Abstract

We work out the phase-space structure for a system of $n$ qubits. We replace the field of real numbers that label the axes of the continuous phase space by the finite field $\Gal{2^n}$ and investigate the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties. We provide a simple classification of such curves and study in detail the four- and eight-dimensional cases, analyzing also the effect of local transformations. In this way, we provide a comprehensive phase-space approach to the construction of mutually unbiased bases for $n$ qubits.

Title changed. Improved version. Accepted for publication in Annals of Physics

References in corpus (1)

• Geometrical approach to mutually unbiased bases

Cited by in corpus (3)

• Discrete coherent and squeezed states of many-qudit systems
• Mutually unbiased bases and generalized Bell states
• Block circulant matrices with circulant blocks, weil sums and mutually unbiased bases, II. The prime power case