Quantum Walks with Bipartite Entangled Coins

Abstract

The Quantum Walk is the quantum version of classical random walk. In a conventional "Discrete-time Quantum Walk (DTQW)", coin and shift unitary operators guide the evolution of the walker after some steps. While the direction of motion is determined by the coin operator, the shift operator displaces the walker’s position by one or more unit steps to the right or left. In this thesis, we have highlighted the important measures to inquire the degree of entanglement in discrete and bipartite system. Entanglement of particles is a predominant aspect of quantum mechanical systems and is the most contradictory with classical intuitions. The use of entanglement as a resource is ex plored in the computational tool of quantum walks wherein, entanglement in the coin states enhances the probability distribution of the walker to far off positions. This is exploited to devise quantum algorithms that are much fast paced as compared to their classical counterparts. Applications include secure quantum key distribution in cryp tography, super-dense coding, teleportation, etc and the most striking implementation in quantum computers which make use of entangled bits as data registers for faster processing of information.