Related papers: Quantum walks: the first detected passage time pro…
We investigate the statistics of the first detected passage time of a quantum walk. The postulates of quantum theory, in particular the collapse of the wave function upon measurement, reveal an intimate connection between the wave function…
The problem of the detection statistics of a quantum walker has received increasing interest, connected as it is to the problem of quantum search. We investigate the effect of employing a moving detector, using a projective measurement…
We investigate a tight binding quantum walk on a graph. Repeated stroboscopic measurements of the position of the particle yield a measured "trajectory", and a combination of classical and quantum mechanical properties for the walk are…
The first detection of a quantum particle on a graph has been shown to depend sensitively on the sampling time {\tau} . Here we use the recently introduced quantum renewal equation to investigate the statistics of first detection on an…
We consider the quantum first detection problem for a particle evolving on a graph under repeated projective measurements with fixed rate $1/\tau$. A general formula for the mean first detected transition time is obtained for a quantum walk…
The quantum first-detection problem concerns the statistics of the time at which a system, subject to repeated measurements, is observed in a prescribed target state for the first time. Unlike its classical counterpart, the measurement back…
We investigate a quantum walk on a ring represented by a directed triangle graph with complex edge weights and monitored at a constant rate until the quantum walker is detected. To this end, the first hitting time statistics is recorded…
Classical first-passage times under restart are used in a wide variety of models, yet the quantum version of the problem still misses key concepts. We study the quantum hitting time with restart using a monitored quantum walk. The restart…
We investigate in depth the relation between the first detection time of an isolated quantum system that is repeatedly perturbed by strong local measurements with a large fixed frequency $1/\tau$, determining whether it is in some given…
We consider a quantum walk where a detector repeatedly probes the system with fixed rate $1/\tau$ until the walker is detected. This is a quantum version of the first-passage problem. We focus on the total probability, $P_{\mathrm{det}}$,…
In recent work, the so-called quasi-Zeno dynamics of a system has been investigated in the context of the quantum first passage problem. This dynamics considers the time evolution of a system subjected to a sequence of selective projective…
We consider a quantum system that is initially localized at $x_{in}$ and that is repeatedly projectively probed with a fixed period $\tau$ at position $x_d$. We ask for the probability that the system is detected in $x_d$ for the very first…
We study the mean first passage time of a one-dimensional random walker with step sizes decaying exponentially in discrete time. That is step sizes go like $\lambda^{n}$ with $\lambda\leq1$ . We also present, for pedagogical purposes, a…
We investigate the splitting probability of a monitored continuous-time quantum walk with two targets and show that, in stark contrast to a classical random walk, it exhibits a nonanalytic, phase-transition-like behavior controlled by the…
How long does it take a quantum particle to return to its origin? As shown previously under repeated projective measurements aimed to detect the return, the closed cycle yields a geometrical phase which shows that the average first detected…
The problem of the time of arrival of a quantum system in a specified state is considered in the framework of the repeated measurement protocol and in particular the limit of continuous measurements is discussed. It is shown that for a…
We study the first detected recurrence time problem of continuous-time quantum walks on graphs. While previous works have employed projective measurements to determine the first return time, we implement a protocol based on weak…
We define the hitting (or absorbing) time for the case of continuous quantum walks by measuring the walk at random times, according to a Poisson process with measurement rate $\lambda$. From this definition we derive an explicit formula for…
We investigate the first passage statistics of active continuous time random walks with Poissonian waiting time distribution on a one dimensional infinite lattice and a two dimensional infinite square lattice. We study the small and large…
We provide a general framework to compute the probability distribution $F_r(t)$ of the first detection time of a 'state of interest' in a generic quantum system subjected to random projective measurements. In our 'quantum resetting'…