2016/01/31 by Pawel Kurzynski, Adrian Kolodziejski, Wieslaw Laskowski +1 · 1 citation
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1103/physreva.93.062126
published as Phys. Rev. A 93, 062126 (2016) · 8 pages, 6 figures, journal version
arxiv created 2016/07/01 · arxiv updated 2016/07/04
We present a surprisingly simple three-dimensional Bloch sphere representation of a qutrit, i.e., a single three-level quantum system. We start with a symmetric state of a two-qubit system and relate it to the spin-1 representation. Using this representation we associate each qutrit state with a three-dimensional vector a and a metric tensor Γ which satisfy a⋅ Γ ⋅ a≤ 1. This resembles the well known condition for qubit Bloch vectors in which case Γ=I. In our case the vector a corresponds to spin-1 polarisation, whereas the tensor Γ is a function of polarisation uncertainties. Alternatively, a is a local Bloch vector of a symmetric two-qubit state and Γ is a function of the corresponding correlation tensor. We also discuss how a purity of states and state-dynamics is depicted in our representation.