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

A gradient system on the quantum information space that realizes the Karmarkar flow for linear programming