Related papers: A note on the Relationship between Localization an…
We show that there is only one operator having some minimal properties enabling it to be a one photon position operator. These proerties are stated, and the solution is shown to be the photon position operator proposed by Pryce. This…
Integrable quantum field theories in 1+1 dimensions have recently become amenable to a rigorous construction, but many questions about the structure of their local observables remain open. Our goal is to characterize these local observables…
We identify and study a particular class of distinguishability problems for quantum observables (POVMs), in which observables with permuted effects are involved, which we call as the labeling problem. Consequently, we identify the binary…
We describe in a qualitative way a possible picture of the Measurement Process in Quantum Mechanics, which takes into account: 1. the finite and non zero time duration T of the interaction between the observed system and the microscopic…
Recently a study of the first superposed mechanical quantum object ("machine") visible to the naked eye was published. However, as we show, it turns out that if the object would actually be observed, i.e. would interact with an optical…
An implementation of the positive operator valued measure (POVM) is given. By using this POVM one can realize the probabilistic teleportation of an unknown two-particle state.
Random Projection is a foundational research topic that connects a bunch of machine learning algorithms under a similar mathematical basis. It is used to reduce the dimensionality of the dataset by projecting the data points efficiently to…
The continuous transition from a low resolution quantum nondemolition measurement of light field intensity to a precise measurement of photon number is described using a generalized measurement postulate. In the intermediate regime,…
We consider positive operator valued measures whose image is the bounded operators acting on an infinite-dimensional Hilbert space, and we relax, when possible, the usual assumption of positivity of the operator valued measure seen in the…
It had been a long standing problem that there is no consistent definition of photon position operator nor photon number density in the context of quantum theory. In this paper we derive the photon detection operator, which defines location…
We revisit the representation of generalized quantum observables by establishing a geometric picture in terms of their positive operator-valued measures (POVMs). This leads to a clear geometric interpretation of Born's rule by introducing…
We study an operator norm localization property and its applications to the coarse Novikov conjecture in operator K-theory. A metric space X is said to have operator norm localization property if there exists a positive number c such that…
We consider the motion of a quantum particle whose position is measured in random places at random moments in time. We contrast this motion with the motion of a quantum particle in a potential which varies randomly in space and in time,…
In this work we investigate how to quantify the coherence of quantum measurements. First, we establish a resource theoretical framework to address the coherence of measurement and show that any statistical distance can be adopted to define…
Several definitions for the average local value and local variance of a quantum observable are examined and compared with their classical counterparts. An explicit way to construct an infinite number of these quantities is provided. It is…
Quantum Mechanics (QM) predicts the correlation between measurements performed in remote regions of a spatially spread entangled state to be higher than allowed by the intuitive concepts of Locality and Realism (LR). This high correlation…
We describe a recently introduced principle of relative locality which we propose governs a regime of quantum gravitational phenomena accessible to experimental investigation. This regime comprises phenomena in which $\hbar$ and $G_N$ may…
We analyze a conceivable type of local realistic theory, which we call a co-operative phenomena type local realistic theory. In an experimental apparatus to measure second or fourth order interference effects, it images that their exists a…
In Quantum Physics it is not always possible to directly perform the measurement of an obsevable; in some of these cases, however, its value can be {\sl detected}, i.e. it can be inferred by measuring {\sl another} observable characterized…
By a localization property we mean a property that preserved under localizing modules at multiplicative closed sets. The aim of this paper is to find conditions under which we can transfere a certain property of a given module to its…