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arXiv · 1001.4813

Inverse spin-s portrait and representation of qudit states by single probability vectors

S. N. Filippov·V. I. Man'ko
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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. 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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S. N. Filippov, V. I. Man'ko. 2010-03-03. Inverse spin-s portrait and representation of qudit states by single probability vectors. https://doi.org/10.1007/s10946-010-9122-x

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