Aspects of mutually unbiased bases in odd prime power dimensions

Abstract

We rephrase the Wootters-Fields construction [Ann. Phys., {\bf 191}, 363 (1989)] of a full set of mutually unbiased bases in a complex vector space of dimensions $N=p^r$, where $p$ is an odd prime, in terms of the character vectors of the cyclic group $G$ of order $p$. This form may be useful in explicitly writing down mutually unbiased bases for $N=p^r$.

3 pages, latex, no figures

Cited by in corpus (29)

• On mutually unbiased bases
• Discrete phase space based on finite fields
• Evenly distributed unitaries: on the structure of unitary designs
• On the structure of the sets of mutually unbiased bases for N qubits
• Constructions of Mutually Unbiased Bases
• Mutually Unbiased Bases and Finite Projective Planes
• Multicomplementary operators via finite Fourier transform
• Qubits in phase space: Wigner function approach to quantum error correction and the mean king problem
• On Approximately Symmetric Informationally Complete Positive Operator-Valued Measures and Related Systems of Quantum States
• An angular momentum approach to quadratic Fourier transform, Hadamard matrices, Gauss sums, mutually unbiased bases, unitary group and Pauli group
• Measurement driven quantum evolution
• Geometrical approach to mutually unbiased bases
• A SU(2) recipe for mutually unbiased bases
• Efficient Simulation of Random Quantum States and Operators
• Discrete phase-space structure of $n$-qubit mutually unbiased bases
• Mutually unbiased bases and discrete Wigner functions
• Angular Momentum and Mutually Unbiased Bases
• Block circulant matrices with circulant blocks, weil sums and mutually unbiased bases, II. The prime power case
• Spectra of phase point operators in odd prime dimensions and the extended Clifford group
• Coherence makes quantum systems 'magical'
• Optimal reconstruction of states in qutrits system
• A complementarity-based approach to phase in finite-dimensional quantum systems
• Weak mutually unbiased bases
• $BCCB$ complex Hadamard matrices of order 9, and MUBs
• SU(2) nonstandard bases: the case of mutually unbiased bases
• Quantum measurements with prescribed symmetry
• Miscellaneous Applications of Quons
• Cyclic measurements and simplified quantum state tomography
• A New Relation between post and pre-optimal measurement states