We analyze the iterative procedure introduced by Ježek et al. [Phys. Rev. A 65, 060301 (2002)] for computing optimal measurements in minimum-error quantum state discrimination. By representing an $n$-outcome positive operator-valued measurements as a block column vector, we identify each update as the partial isometry arising from a polar decomposition, which provides a transparent proof that the corresponding guessing probability increases monotonically along the iteration. Exploiting this monotonicity, we prove the convergence of the algorithm for arbitrary ensembles of pure states under a mild initialization condition on the supports of the states. Finally, we introduce an embedding into a larger $dn$-dimensional space that links minimum-error discrimination to a fidelity optimization over block-diagonal states, and shows that an optimal strategy can be realized by a projective measurement in the embedded space.

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• Quantum information theory
• Quantum measurements