  The aim of this paper is to bring together the notions of quantum game and
game isomorphism. The work is intended as an attempt to introduce a new
criterion for quantum game schemes. The generally accepted requirement forces a
quantum scheme to generate the classical game in a particular case. Now, given
a quantum game scheme and two isomorphic classical games, we additionally
require the resulting quantum games to be isomorphic as well. We are concerned
with the Eisert-Wilkens-Lewenstein quantum game scheme and the strong
isomorphism between games in strategic form.
