Craig Gidney
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1. Trace out everything except the qubit you are interested in. Do this by computing the outer product of the state of the target qubit, for each possible value of the other qubits, and summing up all those outer products. This will produce athe 2x2 density matrix of the target qubit.

2. Get the x, y, z coordinates of the Bloch vector from the 2x2 density matrix $$D$$.

$$D = \begin{bmatrix} a& b^\ast\\b & c \end{bmatrix}$$$$D = \begin{bmatrix} a& b^\ast\\b & 1-a \end{bmatrix}$$

$$x = 2 \cdot \text{RealPart}(b)$$

$$y = 2 \cdot \text{ImaginaryPart}(b)$$

$$z = a - c$$$$z = 2 \cdot a - 1$$

Craig Gidney
• 18k
• 1
• 11
• 56
1. Trace out everything except the qubit you are interested in. This will produce a 2x2 density matrix.

2. Get the x, y, z coordinates of the Bloch vector from the 2x2 density matrix.

$$D = \begin{bmatrix} a& b^\ast\\b & c \end{bmatrix}$$

$$x = 2 \cdot \text{RealPart}(b)$$

$$y = 2 \cdot \text{ImaginaryPart}(b)$$

$$z = a - c$$