Related papers: Uncertainty relation between detection probability…
We investigate a generic discrete quantum system prepared in state $|\psi_\text{in}\rangle$, under repeated detection attempts aimed to find the particle in state $|d\rangle$, for example a quantum walker on a finite graph searching for a…
The assumption that an ensemble of classical particles is subject to nonclassical momentum fluctuations, with the fluctuation uncertainty fully determined by the position uncertainty, has been shown to lead from the classical equations of…
Uncertainty relations are among the unique fingerprints of quantum physics, being direct expression of non-commutativity and complementarity. Entropic uncertainty relations arise in quantum information theory as the most natural expression…
We quantitatively differentiate between the spreads of discrete-time quantum and classical random walks on a cyclic graph. Due to the closed nature of any cyclic graph, there is additional "collision"- like interference in the quantum…
Temporal fluctuations in the Hadamard walk on circles are studied. A temporal standard deviation of probability that a quantum random walker is positive at a given site is introduced to manifest striking differences between quantum and…
The task of finding an entry in an unsorted list of $N$ elements famously takes $O(N)$ queries to an oracle for a classical computer and $O(\sqrt{N})$ queries for a quantum computer using Grover's algorithm. Reformulated as a spatial search…
We numerically analyse quantum survival probability fluctuations in an open, classically chaotic system. In a quasi-classical regime, and in the presence of classical mixed phase space, such fluctuations are believed to exhibit a fractal…
We study the motion of two non-interacting quantum particles performing a random walk on a line and analyze the probability that the two particles are detected at a particular position after a certain number of steps (meeting problem). The…
When confined to a topological environment consisting of a cycle coupled with a half-line, quantum walks exhibit long-term statistical tendencies which differ dramatically from the tendencies of classical random walks in the same…
In a measurement-induced continuous-time quantum walk, we address the problem of detecting a particle in a subspace, instead of a fixed position. In this configuration, we develop an approach of bright and dark states based on the unit and…
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, $P_{\mathrm{det}}$,…
All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…
It is shown that nearly-flat 3+1D spacetime emerging from a dual quantum field theory in 2+1D displays quantum fluctuations from classical Euclidean geometry on macroscopic scales. A covariant holographic mapping is assumed, where plane…
We undertake a detailed analysis of ergodicity for homogeneous discrete-time quantum walks on the integer lattice. The most significant result of our paper holds in dimension one, and gives a complete equivalence between the absolutely…
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…
Our knowledge of quantum mechanics can satisfactorily describe simple, microscopic systems, but is yet to explain the macroscopic everyday phenomena we observe. Here we aim to shed some light on the quantum-to-classical transition as seen…
We introduce a framework to identify Fluctuation Relations for vector-valued observables in physical systems evolving through a stochastic dynamics. These relations arise from the particular structure of a suitable entropic functional and…
Quantum walks are standard tools for searching graphs for marked vertices, and they often yield quadratic speedups over a classical random walk's hitting time. In some exceptional cases, however, the system only evolves by sign flips,…
Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes, the structure of the graph causes the walker to get trapped, such that the probability of finding the marked…
We study the discrete-time quantum walk-based search for a marked vertex on a graph. By considering various structures in which not all vertices are equivalent, we investigate the relationship between the successful search probability and…