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Diagonalization in the spirit of Cantor's diagonal arguments is a widely usedtool in theoretical computer sciences to obtain structural results aboutcomputational problems and complexity classes by indirect proofs. The UniformDiagonalization Theorem allows the construction of problems outside complexityclasses while still being reducible to a specific decision problem. This paperprovides a generalization of the Uniform Diagonalization Theorem by extendingit to promise problems and the complexity classes they form, e.g. randomizedand quantum complexity classes. The theorem requires from the underlyingcomputing model not only the decidability of its acceptance and rejectionbehaviour but also of its promise-contradicting indifferent behaviour - aproperty that we will introduce as "total decidability" of promise problems.  Implications of the Uniform Diagonalization Theorem are mainly of two kinds:1. Existence of intermediate problems (e.g. between BQP and QMA) - also knownas Ladner's Theorem - and 2. Undecidability if a problem of a complexity classis contained in a subclass (e.g. membership of a QMA-problem in BQP). Like theoriginal Uniform Diagonalization Theorem the extension applies besides BQP andQMA to a large variety of complexity class pairs, including combinations fromdeterministic, randomized and quantum classes.

Uniform Diagonalization Theorem for Complexity Classes of Promise Problems including Randomized and Quantum Classes