Quantum Random Walk

We present an in-depth analysis of the "quantum first detection problem," in other words, quantum renewal equation (QRE) [1] and how it relates to the basic postulates of quantum existence in this thesis. It shows how the Schrödinger equation and projective measurement postulate a guide to the solution of the problem and present equations that describe the system’s behavior. The text highlights the surprising features of the problem for closed systems and the sensitivity of the problem to the sampling rate. It also notes that the probability of being eventually detected can be less than unity for finite-sized systems.