Related papers: Joint measurability through Naimark's theorem

We give a proof that in settings where Von Neumann deficiency indices are finite the spectral counting functions of two different self-adjoint extensions of the same symmetric operator differ by a uniformly bounded term (see also…

Let $\mathcal{H}$ be a complex Hilbert space and let $\big\{A_{n}\big\}_{n\geq 1}$ be a sequence of bounded linear operators on $\mathcal{H}$. Then a bounded operator $B$ on a Hilbert space $\mathcal{K} \supseteq \mathcal{H}$ is said to be…

In many a traditional physics textbook, a quantum measurement is defined as a projective measurement represented by a Hermitian operator. In quantum information theory, however, the concept of a measurement is dealt with in complete…

We have developed a self consistent technique to predict the behavior of plasmon resonances in multi-component systems as a function of wavelength. This approach, based on the tight lower bounds of the Bergman-Milton formulation, is able to…

We investigate the effect of non-symmetric relatively bounded perturbations on the spectrum of self-adjoint operators. In particular, we establish stability theorems for one or infinitely many spectral gaps along with corresponding…

We introduce several notions of random positive operator valued measures (POVMs), and we prove that some of them are equivalent. We then study statistical properties of the effect operators for the canonical examples, obtaining limiting…

This paper is the third and final component of a three-part effort on observers contracting a Riemannian distance between the state of the system and its estimate. In Part I, we showed that such a contraction property holds if the system…

For the example of the infinitely deep well potential, we point out some paradoxes which are solved by a careful analysis of what is a truly self-adjoint operator. We then describe the self-adjoint extensions and their spectra for the…

A determinant in algebraic $K$-theory is associated to any two almost commuting Fredholm operators. On the other hand, one can calculate a homologically defined invariant known as joint torsion. We answer in the affirmative a conjecture of…

We investigate $\phi^{2n+1}$ deformations of the generalized free theory in the $\epsilon$ expansion, where the canonical kinetic term is generalized to a higher-derivative version. For $n=1$, we use the conformal multiplet recombination…

The Fermilab Muon $g-2$ experiment measures the muon anomalous magnetic moment with high precision. Together with recent improvements on the theory front, the first results of the experiment confirm the long-standing discrepancy between the…

The Dirac oscillator is a relativistic quantum system, characterized by its linearity in both position and momentum. Moreover, considering $(1{+}1)$ and $(2{+}1)$ dimensions, the system can be mapped onto the Jaynes-Cummings and…

When the sizes of photonic nanoparticles are much smaller than the excitation wavelength, their optical response can be efficiently described with a series of polarizability tensors. Here, we propose a universal method to extract the…

We prove $p$-adic uniformization for Shimura curves attached to the group of unitary similitudes of certain binary skew hermitian spaces $V$ with respect to an arbitrary CM field $K$ with maximal totally real subfield $F$. For a place $v|p$…

We show that the unitary group of any SOT-separable $\mathrm{II}_1$ factor $M$, with the strong operator topology, is contractible. Combined with several old results, this implies that the same is true for any SOT-separable von Neumann…

We provide a comparative treatment of some aspects of spectral theory for self-adjoint and non-self-adjoint (but J-self-adjoint) Dirac-type operators connected with the defocusing and focusing nonlinear Schr\"odinger equation, of relevance…

A theorem of Davies states that for symmetric quantum states there exists a symmetric POVM maximizing the mutual information. To apply this theorem the representation of the symmetry group has to be irreducible. We obtain a similar yet…

This article is concerned with measure equivalence and uniform measure equivalence of locally compact, second countable groups. We show that two unimodular, locally compact, second countable groups are measure equivalent if and only if they…

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.

Given a quantum channel it is possible to define the non-commutative operator graph whose properties determine a possibility of error-free transmission of information via this channel. The corresponding graph has a straight definition…