Abstract
Using the tomographic probability representation of qudit states and the inverse spin-portrait method, we suggest a bijective map of the qudit density operator onto a single probability distribution. Within the framework of the approach proposed, any quantum spin-j state is associated with the (2j+1)(4j+1)-dimensional probability vector whose components are labeled 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 the (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 the optimum reconstruction of qudit states, where the optimality implies a minimum relative error of the density matrix due to the errors in measured probabilities.
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Filippov, S.N., Man’ko, V.I. Inverse spin-s portrait and representation of qudit states by single probability vectors. J Russ Laser Res 31, 32–54 (2010). https://doi.org/10.1007/s10946-010-9122-x
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DOI: https://doi.org/10.1007/s10946-010-9122-x