Entanglement and Decoherence in Quantum Walks

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Quantum walks may be described as the natural counterparts of classical random walks, governed by the principles of quantum mechanics. In recent times, because of their potential applications to the development of a new species of super-efficient algorithms, quantum walks have been the focus of extensive research interest. However, largely due to the mathematical challenges involved, some important aspects of the theory have remained relatively unexplored. These challenges have persisted, especially in connection with attempts to treat jointly the effects of the characteristically quantum-mechanical phenomena known as "entanglement" and "decoherence".Through this project, PI aims to elucidate the effects of decoherence on quantum walks over certain networks. His study will address two questions: 1) How is the limiting distribution of the quantum walk related to the level of decoherence to which the quantum walk is exposed? and 2) How does the measure of entanglement between the subsystems (coin and position) depend upon the level of decoherence? In this approach, the measure of entanglement is reflected by the mutual information between the subsystems, which, in turn, is defined in terms of the von Neumann entropy. The outcomes to flow from this proposal will be of interest to a wide audience of active investigators at the forefront of research in the fields of quantum computing and quantum information. Last but not least, through this project, PI aims to introduce his students, both graduate and undergraduate, to the emerging field of Quantum Information Science.