We derive the information theory form of the quantum statistical opera
tor that reproduces all available (generalized) expectation values and
extremalizes the entropy functional proposed by Tsallis. We also demo
nstrate that a generalized Euler equation relates Tsallis' entropy to
the relevant expectation values and to the pertinent Lagrange multipli
ers. These expectation values are seen to obey the Ehrenfest theorem.
Additionally, an appropriate generalization of Jaynes' equation allows
one to obtain the Lagrange multipliers from the (input) expectation v
alues.