Subspace detection in measurement-induced quantum walks

Abstract

This thesis extends the formalism of first detection in quantum walks from the detection of a single state to the detection of a subspace within the quantum system. Using the insight of bright/dark state formalism, which effectively calculates the state detection probability, further development is done to encompass subspace detection. We state the necessary conditions for stationary dark states in the subspace detection problem. We analytically calculate dark states and the subspace detection probability for position subspaces on a ring system and give expressions for the subspace detection probability for subspaces of various dimensions.