Collective decoding is not separate measurement

The one-use phase-pair calculation contains no receiver POVM. The repeated-use external record permits a collective POVM. The inspected Lean scope explicitly excludes a theorem that separate measurements always attain the optimum LeanScope276.

At the frozen interior parameters the two displayed output states have opposite nonzero coherences and nonzero population bias. They need not be simultaneously diagonalizable. Their entropy difference does not by itself identify a one-copy measurement with equal mutual information.

No separate-measurement optimum, quantum-capacity formula, or secret-key-capacity formula is proved here.