Group theoretical construction of mutually unbiased bases in Hilbert spaces of prime dimensions

Abstract

Mutually unbiased bases in Hilbert spaces of finite dimensions are closely related to the quantal notion of complementarity. An alternative proof of existence of a maximal collection of N+1 mutually unbiased bases in Hilbert spaces of prime dimension N is given by exploiting the finite Heisenberg group (also called the Pauli group) and the action of SL(2,Z_N) on finite phase space Z_N x Z_N implemented by unitary operators in the Hilbert space. Crucial for the proof is that, for prime N, Z_N is also a finite field.

13 pages; accepted in J. Phys. A: Math. Theor

References in corpus (1)

• Security bound of two-bases quantum key-distribution protocols using qudits

Cited by in corpus (8)

• An angular momentum approach to quadratic Fourier transform, Hadamard matrices, Gauss sums, mutually unbiased bases, unitary group and Pauli group
• Variations on a theme of Heisenberg, Pauli and Weyl
• Feynman's path integral and mutually unbiased bases
• Weak mutually unbiased bases
• Symmetries of the finite Heisenberg group for composite systems
• Symmetries of finite Heisenberg groups for multipartite systems
• An analytic function approach to weak mutually unbiased bases
• A classification of finite quantum kinematics