Geometrical approach to mutually unbiased bases

Abstract

We propose a unifying phase-space approach to the construction of mutually unbiased bases for a two-qubit system. It is based on an explicit classification of 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 also consider the feasible transformations between different kinds of curves and show that they correspond to local rotations around the Bloch-sphere principal axes. We suggest how to generalize the method to systems in dimensions that are powers of a prime.

10 pages. Some typos in the journal version have been corrected

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Cited by in corpus (19)

• On mutually unbiased bases
• Discrete phase-space structure of $n$-qubit mutually unbiased bases
• Discrete coherent and squeezed states of many-qudit systems
• Pauli graphs when the Hilbert space dimension contains a square: why the Dedekind psi function ?
• Mutually unbiased bases and generalized Bell states
• Informational completeness of continuous-variable measurements
• Optimal quantum tomography of permutationally invariant qubits
• Projective Ring Line of a Specific Qudit
• Optimal reconstruction of states in qutrits system
• Generation of all sets of mutually unbiased bases for three-qubit systems
• Bipartite entangled stabilizer mutually unbiased bases as maximum cliques of Cayley graphs
• States that are far from being stabilizer states
• Graph states in phase space
• Minimal sets of dequantizers and quantizers for finite-dimensional quantum systems
• Coarse graining the phase space of $N$ qubits
• The correspondence between mutually unbiased bases and mutually orthogonal extraordinary supersquares
• Least-bias state estimation with incomplete unbiased measurements
• Generalized reduction formula for Discrete Wigner functions of multiqubit systems
• Measuring Unrecorded Measurement