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Recently, a quantum version of Painleve equations from the point of view oftheir symmetries was proposed by H. Nagoya. These quantum Painleve equationscan be written as Hamiltonian systems with a (noncommutative) polynomialHamiltonian. We give a characterization of the quantum Painleve equations bycertain holomorphic properties. Namely, we introduce canonical transformationssuch that the Painleve Hamiltonian system is again transformed into apolynomial Hamiltonian system, and we show that the Hamiltonian can be uniquelycharacterized through this holomorphic property.

Takano's Theory of Quantum Painleve Equations