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Homework Help: Qutrit States

  1. Sep 26, 2009 #1
    1. The problem statement, all variables and given/known data
    Design a procedure (consisting of unitary operators and a measurement) that best distinguishes the following states
    [tex] \frac1{\sqrt3} \left( | 0 \rangle + | 1 \rangle + |2 \rangle \right) [/tex]
    [tex] \frac1{\sqrt3} \left( | 0 \rangle - | 1 \rangle - |2 \rangle \right) [/tex]
    [tex] \frac1{\sqrt3} \left( -| 0 \rangle + | 1 \rangle - |2 \rangle \right) [/tex]
    [tex] \frac1{\sqrt3} \left( -| 0 \rangle - | 1 \rangle + |2 \rangle \right) [/tex]

    3. The attempt at a solution
    The inner product of all four states is the same, and comes out to [itex] -\frac13 [/itex]. Geometrically, if we were to consider the linear space spanned by the basis states [itex] |a \rangle [/itex] for [itex] a = 1 ,2 , 3[/itex] then these states would form the vertices of a tetrahedron. I can then find a mapping that puts two of these states onto the same basis state, but I'm unsure if this is optimal. Any ideas?
  2. jcsd
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