Related papers: Unambiguous discrimination among oracle operators
The required set of operations for universal continuous-variable quantum computation can be divided into two primary categories: Gaussian and non-Gaussian operations. Furthermore, any Gaussian operation can be decomposed as a sequence of…
In contrast with differential operators on modules over commutative and graded commutative rings, there is no satisfactory notion of a differential operator in noncommutative geometry.
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded perturbation is considered. The objective is to estimate the norm of the difference of two spectral projections associated with isolated parts…
We demonstrate new abstract characterizations for unital and non-unital operator spaces. We characterize unital operator spaces in terms of the cone of accretive operators (operators whose real part is positive). Defining the gauge of an…
In this paper we establish optimal regularity estimates and smoothness of free boundaries for nonlocal obstacle problems governed by a very general class of integro-differential operators with possibly singular kernels. More precisely, in…
We present several operator versions of the Dunkl--Williams inequality with respect to the $p$-angular distance for operators. More precisely, we show that if $A, B \in \mathbb{B}(\mathscr{H})$ such that $|A|$ and $|B|$ are invertible,…
Quantum information processing using linear optics is challenging due to the limited set of deterministic operations achievable without using complicated resource-intensive methods. While techniques such as the use of ancillary photons can…
A complete classification of linear differential operators possessing finite-dimensional invariant subspace with a basis of monomials is presented.
We prove an entanglement principle for fractional Laplace operators on $\mathbb R^n$ for $n\geq 2$ as follows; if different fractional powers of the Laplace operator acting on several distinct functions on $\mathbb R^n$, which vanish on…
A classical theorem of von Neumann asserts that every unbounded self-adjoint operator $A$ in a separable Hilbert space $H$ is unitarily equivalent to an operator $B$ in $H$ such that $D(A)\cap D(B)=\{0\}$. Equivalently this can be…
We present an in-depth study of the problem of multiple-shot discrimination of von Neumann measurements in finite-dimensional Hilbert spaces. Specifically, we consider two scenarios: minimum error and unambiguous discrimination. In the case…
The aim of the paper is firstly to study domains of definitions in terms of boundary conditions of minimal and maximal operators, as well as selfadjoint extensions of a minimal operator associated with the fourth-order differential operator…
The uncertainty principle lemma for the Laplacian on Euclidean spaces shows the borderline-behavior of a potential for the following question : whether the Schr\"odinger operator has a finite or infinite number of the discrete pectrum. In…
We explicitly establish a unitary correspondence between spherical irreducible tensor operators and cartesian tensor operators of any rank. That unitary relation is implemented by means of a basis of integer-spin wave functions that…
We study a regular closure operator in the category of quandles. We show that the regular closure operator and the pullback closure operator corresponding to the reflector from the category of quandles to its full subcategory of trivial…
We identify a strong structural obstruction to Uniform Separation in constructive arithmetic. The mechanism is independent of semantic content; it emerges whenever two distinct evaluator predicates are sustained in parallel and inference…
We prove oracle inequalities for a penalized log-likelihood criterion that hold even if the data are not independent and not stationary, based on a martingale approach. The assumptions are checked for various contexts: density estimation…
An operator connection is a binary operation assigned to each pair of positive operators satisfying monotonicity, continuity from above and the transformer inequality. In this paper, we introduce and characterize the concepts of…
In the theory of singular integral operators significant effort is often required to rigorously define such an operator. This is due to the fact that the kernels of such operators are not locally integrable on the diagonal, so the integral…
We study eigenvalues of polyharmonic operators on compact Riemannian manifolds with boundary (possibly empty). In particular, we prove a universal inequality for the eigenvalues of the polyharmonic operators on compact domains in a…