Maximum likelihood estimation of qubit density matrix from Pauli measurements
True State |ψ⟩
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Pauli Expectations
MLE Reconstructed ρ
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Fidelity
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Quantum state tomography reconstructs an unknown qubit state by measuring copies in X, Y, Z Pauli bases.
MLE finds the physical density matrix (positive semidefinite, Tr=1) that maximizes the likelihood of observed outcomes.
True state shown as orange dot on Bloch sphere; reconstructed as blue dot.
Fidelity F=1 means perfect reconstruction; noise and finite samples reduce it.