Mutually unbiased bases and discrete Wigner functions

Abstract

Mutually unbiased bases and discrete Wigner functions are closely, but not uniquely related. Such a connection becomes more interesting when the Hilbert space has a dimension that is a power of a prime $N=d^n$, which describes a composite system of $n$ qudits. Hence, entanglement naturally enters the picture. Although our results are general, we concentrate on the simplest nontrivial example of dimension $N=8=2^3$. It is shown that the number of fundamentally different Wigner functions is severely limited if one simultaneously imposes translational covariance and that the generating operators consist of rotations around two orthogonal axes, acting on the individual qubits only.

9 pages, 6 tables, 6 figures. Accepted for publication in J. Opt. Soc. Am. B, special issue on Optical Quantum Information Science

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Cited by in corpus (12)

• On mutually unbiased bases
• Wigner tomography of two qubit states and quantum cryptography
• Geometrical approach to mutually unbiased bases
• Optimal quantum state reconstruction for cold trapped ions
• Discrete phase-space structure of $n$-qubit mutually unbiased bases
• Generation of all sets of mutually unbiased bases for three-qubit systems
• Minimal sets of dequantizers and quantizers for finite-dimensional quantum systems
• Discrete phase-space mappings, tomographic condition and permutation invariance
• Unitary and Non-Unitary Matrices as a Source of Different Bases of Operators Acting on Hilbert Spaces
• Production of Information and Entropy in measurement of entangled states
• Classification of two-particle quantum channels of information transfer
• Mutually disjoint, maximally commuting set of physical observables for optimum state determination