The Generalized Quantization Scheme for Games and its Application to Quantum Information

Abstract

Theory of quantum games is relatively new to the literature and its applications to various [treas of research are being explored. It is a novel interpretation of strategies and decisions in quantum domain. In the earlier work on quantum games considerable a ttention was given to the resolution of dilemmas present in corresponding classical games. Two separate quantum schemes were presented by Eisert et al. [27) and Marinatto and "Weber [28) to resolve dilemmas in Prisoners' Dilemma and Battle of Sexes games respectively. However for the latter scheme it was argued [39) that dilemma was not resolved. We have modified the quantiza tion scheme of Marinatto and ·Weber to resolve the dilemma. We have developed a generalized quantization scheme for two person non-zero sum games which reduces to the existing schemes under certain conditions. Applications of this generalized quantization scheme to quantum information theory are st udied. Measurement being ubiquitous in quantum mechanics can not be ignored in quantum games. \Vith the help of generalized quantization scheme we have analyzed the efl'ects of measurement on quantum games. Qubits are the important elements for playing quantum games and are generally prone to decoherence due to their interactions with environment. An analysis of quantum games in presence of quantum correlated noise is performed in the context of generalized quantization scheme. Quantum key clistributioI1 is one of the key issues of quantum information theory for the purpose of secure communication. Using mathematical framework of generalized quantization scheme we have proposed a protocol for quantum key d istribution. This protocol is capable of transmitting four symbols for key disnibution using a two dimensional quantum system. Quantum state tomography has a substantial place in quantum information theory. Much like its classical counterpart, its aim is to reconstruct a three dimensional image through a series of different measurements. Making use of the mathematical framework of generalized quantization scheme we have presented a technique for quantum state tomography.