January saw a new article devoted to bijective mapping of qudit states onto single probability vectors. It is available at LANL Preprint http://arxiv.org/abs/1001.4813

Abstract

Using the tomographic probability representation of qudit states and the inverse spin-portraitmethod, a bijective map of the qudit density operator onto a single probability distribution is suggested. Within the framework of proposed approach, any quantum spin-j state is associated with (2j + 1)(4j + 1)-dimensional probability vector whose components are labelled by spin projections and points on the sphere S2. Such a vector has a clear physical meaning and can be relatively easily measured. Quantum states form a convex subset of the 2j(4j + 3)-simplex, with the boundary being illustrated for qubits (j = 1=2) and qutrits (j = 1). A relation to (2j +1)2 and (2j +1)(2j +2)-dimensional probability vectors is established in terms of spin-s portraits. We also address an auxiliary problem of optimal reconstruction of qudit states, where the optimality implies minimal relative error of the density matrix due to errors in measured probabilities.