A Game Theoretic Approach to Quantum Information

@misc{citeulike:1724283, abstract = {This work is an application of game theory to quantum information. In a quantum state estimate game, we are given observations distributed according to an unknown distribution \$P\_{\theta}\$ (associative with award \$Q\$), which Nature chose at random from the set \$\{P\_{\theta}: \theta \in \Theta \}\$ according to a known prior distribution \$\mu\$ on \$\Theta\$, we produce an estimate \$M\$ for the unknown distribution \$P\_{\theta}\$. In the end of this game, we will suffer a relative entropy cost \$I(P;M)\$, measuring the quality of this estimate, therefore the whole utility is \$P \cdot Q -I(P; M)\$. During an introduction to strategic game, a sufficient condition for minimax theorem is obtained; An estimate game is explored, and further in the view of convex conjugate, we reach one new approach to quantum relative entropy, correspondingly quantum mutual entropy, and quantum channel capacity, which is more general, in the sense, without Radon-Nikodym (RN) derivatives. Also the monotonicity of quantum relative entropy and additivity of quantum channel capacity are investigated.}, author = {Dai, Xianhua and Belavkin, V. P. }, citeulike-article-id = {1724283}, eprint = {0710.0556}, keywords = {quantum}, month = {Oct}, posted-at = {2007-10-03 17:41:16}, priority = {2}, title = {A Game Theoretic Approach to Quantum Information}, url = {http://arxiv.org/abs/0710.0556}, year = {2007} }

TY - ELEC ID - citeulike:1724283 L3 - citeulike-article-id:1724283 TI - A Game Theoretic Approach to Quantum Information N2 - This work is an application of game theory to quantum information. In a quantum state estimate game, we are given observations distributed according to an unknown distribution $P_{\theta}$ (associative with award $Q$), which Nature chose at random from the set $\{P_{\theta}: \theta \in \Theta \}$ according to a known prior distribution $\mu$ on $\Theta$, we produce an estimate $M$ for the unknown distribution $P_{\theta}$. In the end of this game, we will suffer a relative entropy cost $I(P;M)$, measuring the quality of this estimate, therefore the whole utility is $P \cdot Q -I(P; M)$. During an introduction to strategic game, a sufficient condition for minimax theorem is obtained; An estimate game is explored, and further in the view of convex conjugate, we reach one new approach to quantum relative entropy, correspondingly quantum mutual entropy, and quantum channel capacity, which is more general, in the sense, without Radon-Nikodym (RN) derivatives. Also the monotonicity of quantum relative entropy and additivity of quantum channel capacity are investigated. KW - quantum AU - Dai, Xianhua AU - Belavkin, VP PY - 2007/Oct/02/ UR - http://arxiv.org/abs/0710.0556 ER -