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I Qubit mixed state density matrix coordinates on a Bloch ball

  1. Feb 23, 2017 #1
    What are the coordinates on the 3D Bloch ball of a qubit's mixed state of the form:
    ##\rho=p_{00}|0\rangle \langle 0|+p_{01}|0\rangle \langle 1|+p_{10}|1\rangle \langle 0|+p_{11}|1\rangle \langle 1|##

    451px-Bloch_sphere.svg.png
     
    Last edited: Feb 23, 2017
  2. jcsd
  3. Feb 24, 2017 #2
    Do we have to diagonalize the density matrix everytime and then use the forumla for the coordinates
    ##(\sum p_i x_i, \sum p_i y_i,\sum p_i z_i)## ?
    https://en.wikipedia.org/wiki/Bloch_sphere

    Not very practical.
     
  4. Feb 24, 2017 #3

    Strilanc

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    Science Advisor

    From stackoverflow: "Convert from qubit density matrix to Bloch vector"

    Code (Text):
    def toBloch(matrix):
       [[a, b], [c, d]] = matrix
       x = complex(c + b).real
       y = complex(c - b).imag
       z = complex(d - a).real
       return x, y, z
    In other words, yes you have to use the formula. But I'm not sure why you think it's impractical... it's just three additions/subtractions.
     
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