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Multivariable Quantum Signal Processing (M-QSP) [1] is expected to provide anefficient means to handle polynomial transformations of multiple variablessimultaneously. However, we noticed several inconsistencies in the main Theorem2.3 and its proof in Ref. [1]. Moreover, a counterexample for Conjecture 2.1 inRef. [1], which is used as an assumption in the proof of Theorem 2.3, ispresented at Quantum Information Processing 2023 [2], meaning the requirementof the conjecture should be included as a condition in Theorem 2.3. Here wenote our observations and propose the revised necessary conditions of M-QSP. Wealso show that these necessary conditions cannot be sufficient conditions, andthus some additional condition on top of these revisions is essentiallyrequired for complete M-QSP Theorem.

Comment on "Multivariable quantum signal processing (M-QSP): prophecies of the two-headed oracle"