Related papers: Stationary measure for three-state quantum walk

Measuring a quantum system can randomly perturb its state. The strength and nature of this back-action depends on the quantity which is measured. In a partial measurement performed by an ideal apparatus, quantum physics predicts that the…

The general problems of three-dimensional quantum gravity are recatitulated here, putting the emphasis on the mathematical problems of defining the measure of the path integral over all three-dimensional metrics.This work should be viewed…

The CGMV method allows for the general discussion of localization properties for the states of a one-dimensional quantum walk, both in the case of the integers and in the case of the non negative integers. Using this method we classify,…

One-way quantum computing is experimentally appealing because it requires only local measurements on an entangled resource called a cluster state. Record-size, but non-universal, continuous-variable cluster states were recently demonstrated…

We analyze two families of three-state quantum walks which show the localization effect. We focus on the role of the initial coin state and its coherence in controlling the properties of the quantum walk. In particular, we show that the…

The eigenvalue problem in quantum mechanics is reduced to quantization of the classical action of the physical system. State function of the system, $\psi_0(\phi)$, is written in the form of superposition of two plane waves in the phase…

We aim to address the following question: if we start with a quantum state with a spontaneously broken higher-form symmetry, what is the fate of the system under weak local quantum measurements? We demonstrate that under certain conditions,…

The so-called measurement problem of quantum theory (QT) is still lacking a satisfactory, or at least widely agreed upon, solution. A number of theories, known as interpretations of quantum theory, have been proposed and found differing…

Quantum walks are known to have nontrivial interactions with absorbing boundaries. In particular it has been shown that an absorbing boundary in the one dimensional quantum walk partially reflects information, as observed by absorption…

A new approach to the problem of measurement in quantum mechanics is proposed. In this approach, the process of measurement is described in the Heisenberg picture and divided into two stages. The first stage is to transduce the measured…

In the present paper we consider the problem of description of an arbitrary generalized quantum measurement with outcomes in a measurable space. Analyzing the unitary invariants of a measuring process, we present the most general form of a…

Quantum measurement is a fundamental concept in the field of quantum mechanics. The action of quantum measurement, leading the superposition state of the measured quantum system into a definite output state, not only reconciles…

The phenomenon of quantum steering in bipartite quantum systems can be reduced to the question whether or not the first party can perform measurements such that the conditional states on the second party can be explained by a local hidden…

We present numerical study of a model of quantum walk in periodic potential on the line. We take the simple view that different potentials affect differently the way the coin state of the walker is changed. For simplicity and definiteness,…

To measure an observable of a quantum mechanical system leaves it in one of its eigenstates and the result of the measurement is one of its eigenvalues. This process is shown to be a computational resource. It allows one, in principle, to…

In this paper, we study metrics of quantum states. These metrics are natural generalization of trace metric and Bures metric. We will prove that the metrics are joint convex and contractive under quantum operation. Our results can find…

A necessary and sufficient conditions for certain class of periodic unitary transition operators to have eigenvalues are given. Applying this, it is shown that Grover walks in any dimension has both of $\pm 1$ as eigenvalues and it has no…

We consider the problem of determining the state of a quantum system given one or more readings of the expectation value of an observable. The system is assumed to be a finite dimensional quantum control system for which we can influence…

The quantum walk (QW) is the term given to a family of algorithms governing the evolution of a discrete quantum system and as such has a founding role in the study of quantum computation. We contribute to the investigation of QW phenomena…

For a discrete two-state quantum walk (QW) on the half-line with a general condition at the boundary, we formulate and prove a weak limit theorem describing the terminal behavior of its transition probabilities. In this context,…