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We study the representation and visualization of finite-dimensional quantumsystems. In a generalized Wigner representation, multi-spin operators can bedecomposed into a symmetry-adapted tensor basis and they are mapped to multiplespherical plots that are each assembled from linear combinations of sphericalharmonics. We apply two different approaches based on explicit projectionoperators and coefficients of fractional parentage in order to obtain thisbasis for up to six spins 1/2 (qubits), for which various examples arepresented. An extension to two coupled spins with arbitrary spin numbers(qudits) is provided, also highlighting a quantum system of a spin 1/2 coupledto a spin 1 (qutrit).

Symmetry-adapted decomposition of tensor operators and the visualization of coupled spin systems