Related papers: The time distribution of quantum events
For a discrete time quantum walk (QW) on the $N$-cycle, allowing for decoherence on the coin, we derive a number of new results, including an explicit formula for the position probability distribution. For a QW of this type, we show that…
A realization of the concept of "crossing state" invoked, but not implemented, by Wigner, allows to advance in two important aspects of the time of arrival in quantum mechanics: (i) For free motion, we find that the limitations described by…
Quantum computers are susceptible to noises from the outside world. We investigate the effect of perturbation on the hitting time of a quantum walk and the stationary distribution prepared by a quantum walk based algorithm. The perturbation…
In any given experimental scenario, the rules of quantum theory provide statistical distributions that the observed outcomes are expected to follow. The set formed by all these distributions contains the imprint of quantum theory, capturing…
Out of equilibrium quantum systems, on top of quantum fluctuations, display complex temporal patterns. Such time fluctuations are generically exponentially small in the system volume and can be therefore safely ignored in most of the cases.…
It is often stated that quantum mechanics only makes statistical predictions and that a quantum state is described by the various probability distributions associated with it. Can we describe a quantum state completely in terms of…
The time of the first occurrence of a threshold crossing event in a stochastic process, known as the first passage time, is of interest in many areas of sciences and engineering. Conventionally, there is an implicit assumption that the…
The problem of time is a deep paradox in our physical description of the world. According to Aristotle's relational theory, time is a measure of change and does not exist on its own. In contrast, quantum mechanics, just like Newtonian…
The projected normal distribution, also known as the angular Gaussian distribution, is obtained by dividing a multivariate normal random variable $\mathbf{x}$ by its norm $\sqrt{\mathbf{x}^T \mathbf{x}}$. The resulting random variable…
The paper addresses the problem of calculating the noise-induced switching rates in systems with delay-distributed kernels and Gaussian noise. A general variational formulation for the switching rate is derived for any distribution kernel,…
We show that a quantum state may be represented as the sum of a joint probability and a complex quantum modification term. The joint probability and the modification term can both be observed in successive projective measurements. The…
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…
Extreme events can come either from point processes, when the size or energy of the events is above a certain threshold, or from time series, when the intensity of a signal surpasses a threshold value. We are particularly concerned by the…
A self-adjoint operator with dimensions of time is explicitly constructed, and it is shown that its complete and orthonormal set of eigenstates can be used to define consistently a probability distribution of the time of arrival at a…
It is common to model random errors in a classical measurement by the normal (Gaussian) distribution, because of the central limit theorem. In the quantum theory, the analogous hypothesis is that the matrix elements of the error in an…
In quantum mechanical experiments one distinguishes between the state of an experimental system and an observable measured in it. Heuristically, the distinction between states and observables is also suggested in scattering theory or when…
Quantum walks are powerful tools not only to construct the quantum speedup algorithms but also to describe specific models in physical processes. Furthermore, the discrete time quantum walk has been experimentally realized in various…
We analyse a proposition which considers quantum theory as a mere tool for calculating probabilities for sequences of outcomes of observations made by an Observer, who him/herself remains outside the scope of the theory. Predictions are…
Textbook quantum mechanics treats time as a classical parameter, and not as a quantum observable with an associated Hermitian operator. For this reason, to make sense of usual time-energy uncertainty relations such as $\Delta {t}\Delta…
We conjecture that the relative rate of time evolution depends on the amount of quantum correlations in a system. This is motivated by the experimental work [1] which showed that quantum tunneling is not instantaneous. The non-zero…