Related papers: An anisotropic inhomogeneous ubiquity Theorem
The measurement postulate of quantum theory stands in conflict with the laws of thermodynamics and has evoked debate regarding what actually constitutes a measurement. With the help of modern quantum statistical mechanics, we take the first…
The class of generic structures among those consisting of the measure algebra of a probability space equipped with an automorphism is axiomatizable by positive sentences interpreted using an approximate semantics. The separable generic…
The inhomogeneous metric theory for the set of simultaneously $\psi$-approximable points lying on a planar curve is developed. Our results naturally incorporate the homogeneous Khintchine-Jarnik type theorems recently established in [Ann.…
Gathering data through measurements is at the basis of every experimental science. Ideally, measurements should be repeatable and, when extracting only coarse-grained data, they should allow the experimenter to retrieve the finer details at…
The uncertainty principle brings out intrinsic quantum bounds on the precision of measuring non-commuting observables. Statistical outcomes in the measurement of incompatible observables reveal a trade-off on the sum of corresponding…
In quantum physics the term `contextual' can be used in more than one way. One usage, here called `Bell contextual' since the idea goes back to Bell, is that if $A$, $B$ and $C$ are three quantum observables, with $A$ compatible (i.e.,…
This article begins with a review of quantum measure spaces. Quantum forms and indefinite inner-product spaces are then discussed. The main part of the paper introduces a quantum integral and derives some of its properties. The quantum…
A distributional symmetry is invariance of a distribution under a group of transformations. Exchangeability and stationarity are examples. We explain that a result of ergodic theory provides a law of large numbers: If the group satisfies…
The notion of the ultrametrics can be considered as a zero-dimensional analogue of ordinary metrics, and it is expected to prove ultrametric versions of theorems on metric spaces. In this paper, we provide ultrametric versions of the…
Unavoidable disturbance caused by a quantum measurement implies that the realizable subsequent measurements are getting limited after one performs some measurement. The obvious general limitation that one cannot circumvent by sequential or…
Applications in data science, shape analysis and object classification frequently require comparison of probability distributions defined on different ambient spaces. To accomplish this, one requires a notion of distance on a given class of…
It is shown that Quantum Mechanics is ambiguous when predicting relative frequencies for an entangled system if the measurements of both subsystems are performed in spatially separated events. This ambiguity gives way to unphysical…
A subset of a topological space is said to be \emph{universally measurable} if it is measured by the completion of each countably additive $\sigma$-finite Borel measure on the space, and \emph{universally null} if it has measure zero for…
We show that any unitary transformation performed on the quantum state of a closed quantum system, describes an inner, reversible, generalized quantum measurement. We also show that under some specific conditions it is possible to perform a…
We formalize the ``metric bundle'' viewpoint by defining, for any smooth $n$--manifold $M$, the open fiberwise cones $\mathcal{G}^{p,q}\subset S^2\Tstar M$ of nondegenerate symmetric bilinear forms with fixed signature $(p,q)$, and we…
In a recent paper, Melbourne and Terhesiu [Operator renewal theory and mixing rates for dynamical systems with infinite measure, Invent. Math. 189 (2012), 61-110] obtained results on mixing and mixing rates for a large class of…
We study a symmetric diffusion $X$ on $\mathbb{R}^d$ in divergence form in a stationary and ergodic environment, with measurable unbounded and degenerate coefficients $a^\omega$. The diffusion is formally associated with $L^\omega u =…
Irreversibility in quantum measurements is considered from the point of quantum information theory. For that purpose the information transfer between the measured object S and measuring system O is analyzed. It's found that due to the…
The problem of measuring an unbounded system attribute near a singularity has been discussed. Lenses have been introduced as formal objects to study increasingly precise measurements around the singularity and a specific family of lenses…
The notion of rough set captures indiscernibility of elements in a set. But, in many real life situations, an information system establishes the relation between different universes. This gave the extension of rough set on single universal…