  Recently, a quantum version of Painleve equations from the point of view of
their symmetries was proposed by H. Nagoya. These quantum Painleve equations
can be written as Hamiltonian systems with a (noncommutative) polynomial
Hamiltonian. We give a characterization of the quantum Painleve equations by
certain holomorphic properties. Namely, we introduce canonical transformations
such that the Painleve Hamiltonian system is again transformed into a
polynomial Hamiltonian system, and we show that the Hamiltonian can be uniquely
characterized through this holomorphic property.
