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

References in corpus (2)

• Bell states, mutually unbiased bases and the Mean King's problem
• Tomography of one and two qubit states and factorisation of the Wigner distribution in prime power dimensions

Cited by in corpus (6)

• 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
• Production of Information and Entropy in measurement of entangled states
• Classification of two-particle quantum channels of information transfer