  In the paper of Uwano [Czech. J. of Phys., vol.56, pp.1311-1316 (2006)], a
gradient system is found on the space of density matrices endowed with the
quantum SLD Fisher metric (to be referred to as the quantum information space)
that realizes a generalization of a gradient system on the space of multinomial
distributions studied by Nakamura [Japan J. Indust. Appl. Math., vol.10,
pp.179-189 (1993)]. On motived by those papers, the present paper aims to
construct a gradient system on the quantum information space that realizes the
Karmarkar flow, the continuous limit of the Karmarkar projective scaling
algorithm for linear programming.
