| # | Basis | Result | Expectation |
|---|
A qubit's state is described by a point on the Bloch sphere: (x, y, z) where x²+y²+z²=1. By measuring in the X, Y, and Z bases repeatedly, we estimate <X>, <Y>, <Z> (the expectation values). A measurement result of |0> maps to +1, and |1> maps to -1. The density matrix is reconstructed as ρ = (I + xσx + yσy + zσz)/2.