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

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

2008-07-25

arxiv.org/abs/0807.4053v1

New Trends in Quantum Information (Eds. Ammar Sakaji et al), Aracne Editorice (Rome,2010), pp.257-276 (revised and enlarged ve

Mathematics

Dynamical Systems

Scientific paper

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.

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