The Generalized Quantization Schemes for Games and its Application to Quantum Information
arXiv:1012.1933
Abstract
Theory of quantum games is relatively new to the literature and its applications to various areas 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 attention was given to the resolution of dilemmas present in corresponding classical games. Two separate quantum schemes were presented by Eisert et al. and Marinatto and Weber to resolve dilemmas in Prisoners' Dilemma and Battle of Sexes games respectively. However for the latter scheme it was argued that dilemma was not resolved. We have modified the quantization 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 studied. Measurement being ubiquitous in quantum mechanics can not be ignored in quantum games. With the help of generalized quantization scheme we have analyzed the effects 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 distribution 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 distribution and a technique for quantum state tomography.
144 pages, 15 figures, PhD. Thesis, Submitted to Department of Electronics Quaid-i-Azam University Islamabad, Pakistn in 2007
References in corpus (28)
- Quantum Mechanics helps in searching for a needle in a haystack
- Quantum Games and Quantum Strategies
- Quantum strategies
- Quantum Teleportation with a Complete Bell State Measurement
- Optimal Cloning of Pure States
- Quantum process tomography of a controlled-NOT gate
- Measuring Entangled Qutrits and Their Use for Quantum Bit Commitment
- Experimental realization of quantum games on a quantum computer
- Entanglement enhanced information transmission over a quantum channel with correlated noise
- New paradoxical games based on Brownian ratchets
- Classical Rules in Quantum Games
- Exploring Hilbert Space: accurate characterisation of quantum information
- Playing a quantum game with a corrupted source
- A universal programmable quantum state discriminator that is optimal for unambiguously distinguishing between unknown states
- Advantage of a quantum player over a classical one in 2x2 quantum games
- Quantum mechanics gives stability to a Nash equilibrium
- Efficiency and formalism of quantum games
- Backwards-induction outcome in a quantum game
- The Capacity of Quantum Channel with General Signal States
- Quantum random walks with history dependence
- State Tomography: Hidden Differences
- Comment on: "A quantum approach to static games of complete information''
- Proposal for optically realizing quantum game
- Game-theoretic discussion of quantum state estimation and cloning
- Parrondo Games and Quantum Algorithms
- Nash Equilibrium in the Quantum Battle of Sexes Game
- Altruistic Contents of Quantum Prisoner's Dilemma
- Classification of Quantum Symmetric Non-zero Sum 2x2 Games in the Eisert Scheme