Related papers: Explicit formula for the Holevo bound for two-para…
We study numerical integration of functions depending on an infinite number of variables. We provide lower error bounds for general deterministic linear algorithms and provide matching upper error bounds with the help of suitable multilevel…
The paper is devoted to two-weight estimates for the fractional maximal operators $\mathcal{M}^\alpha$ on general probability spaces equipped with a tree-like structure. For given $1<p\leq q<\infty$, we study the sharp universal upper bound…
In this article, we design and analyze a Hybrid High-Order (HHO) finite element approximation for a class of strongly nonlinear boundary value problems. We consider an HHO discretization for a suitable linearized problem and show its…
Entanglement is widely regarded as an essential resource for a number of tasks and can in some cases be quantified by figures of merit related to those tasks. In quantum metrology, this is showcased by the connections between the quantum…
In this article, we design fast algorithms for the computation of approximant bases in shifted Popov normal form. We first recall the algorithm known as PM-Basis, which will be our second fundamental engine after polynomial matrix…
The top Lyapunov exponent $\lambda_+(A, p)$ of a random product of matrices in $\mathrm{GL}(d, \mathbb{R})$, $d \geq 2$, with simple top spectrum, depends real-analytically on the probability weights $p$ and the matrix coefficients $A$. We…
Hypothesis testing is a fundamental issue in statistical inference and has been a crucial element in the development of information sciences. The Chernoff bound gives the minimal Bayesian error probability when discriminating two hypotheses…
HHL algorithm \cite{harrow} to solve linear system is a powerful and efficient quantum technique to deal with many matrix operations (such as matrix multiplication, powers and inversion). It inspires many applications in quantum machine…
Motivated by recent work on three-point QCD sum rules in heavy quark physics, we use the simple quantum mechanical models to study the basic issue of duality in three-point sum rules. We show that while in all of these models the duality in…
We compute perturbative matching coefficients to the Heavy Quark Effective Theory representation for the QCD effective local $\Delta B=2$ Hamiltonian that determines the mass difference in $B^0-\bar{B}^0$ system of states. We report on the…
In this paper, we give necessary and sufficient conditions for weighted $L^2$ estimates with matrix-valued measures of well localized operators. Namely, we seek estimates of the form: \[ \| T(\mathbf{W} f)\|_{L^2(\mathbf{V})} \le…
In any realistic quantum metrology scenarios, the ultimate precision in the estimation of parameters is limited not only by the so-called Heisenberg scaling, but also the environmental noise encountered by the underlying system. In the…
We prove a sparse bound in the context of Schauder theory for divergence form elliptic partial differential equations. In addition, we show how an iteration argument inspired by sparse domination bounds can be used to deduce gradient…
We address the issue of precisely estimating small parameters encoded in a general linear transformation of the modes of a bosonic quantum field. Such Bogoliubov transformations frequently appear in the context of quantum optics. We provide…
We introduce new formulations of the quantum Cram\'{e}r-Rao bound (QCRB) and the Holevo Cram\'{e}r-Rao bound (HCRB) in multi-parameter quantum metrology via purification, where we show their values for any mixed state are connected to that…
We provide a systematic treatment of boundaries based on subgroups $K\subseteq G$ with the Kitaev quantum double $D(G)$ model in the bulk. The boundary sites are representations of a $*$-subalgebra $\Xi\subseteq D(G)$ and we explicate its…
Every sufficiently rich set of measurements on a fixed quantum system defines a statistical norm on the states of that system via the optimal bias that can be achieved in distinguishing the states using measurements from that set (assuming…
The information-geometric statistical analysis on the stability of model reductions, reported previously [Imbri\v{s}ak and Nomura, Phys. Rev. C 107, 034304 (2023)] with a focus on the manifold boundary approximation method in the…
We prove an extended convexity for quantum Fisher information of a mixed state with a given convex decomposition. This convexity introduces a bound which has two parts: i. classical part associated to the Fisher information of the…
A natural extension of the non-Hermitian qubit is to place it in a single-mode cavity. This setup corresponds to the quantum Rabi model (QRM) with a purely imaginary bias on the qubit, exhibiting parity-time ($\mathcal{P}\mathcal{T}$)…