Related papers: Asymptotic quantization errors for in-homogeneous …

We extend quantum Stein's lemma in asymmetric quantum hypothesis testing to composite null and alternative hypotheses. As our main result, we show that the asymptotic error exponent for testing convex combinations of quantum states…

In hypothesis testing with quantum states, given a black box containing one of the two possible states, measurement is performed to detect in favor of one of the hypotheses. In postselected hypothesis testing, a third outcome is added,…

The class of $\mu$-compact sets can be considered as a natural extension of the class of compact metrizable subsets of locally convex spaces, to which the particular results well known for compact sets can be generalized. This class…

We construct a general cohomological induction isomorphism from a uniform measure equivalence of locally compact, second countable, unimodular groups which, as a special case, yields that the graded cohomology rings of quasi-isometric,…

We consider self-similar statistical ensembles with the phase space whose volume is invariant under the deformation that squeezes (expands) the coordinate and expands (squeezes) the momentum. Related probability distribution function is…

Non-autonomous self-similar sets are a family of compact sets which are, in some sense, highly homogeneous in space but highly inhomogeneous in scale. The main purpose of this note is to clarify various regularity properties and separation…

The de Finetti representation theorem for continuous variable quantum system is first developed to approximate an N-partite continuous variable quantum state with a convex combination of independent and identical subsystems, which requires…

We consider a group G of isometries acting on a (not necessarily geodesic) delta-hyperbolic space X and possessing a radial limit set of full measure within its limit set. For any continuous quasiconformal measure w supported on the limit…

Let $\Omega\subsetneq\mathbb R^{n+1}$ be open and let $\mu$ be some measure supported on $\partial\Omega$ such that $\mu(B(x,r))\leq C\,r^n$ for all $x\in\mathbb R^{n+1}$, $r>0$. We show that if the harmonic measure in $\Omega$ satisfies…

Let $\mathcal{M}$ be the set of Borel probability measures on $\mathbb{R}$. We denote by $\mu^{\mathrm{ac}}$ the absolutely continuous part of $\mu\in\mathcal{M}$. The purpose of this paper is to investigate the supports and regularity for…

We consider symmetric hypothesis testing in quantum statistics, where the hypotheses are density operators on a finite-dimensional complex Hilbert space, representing states of a finite quantum system. We prove a lower bound on the…

The quantum measurement incompatibility is a distinctive feature of quantum mechanics. We investigate the incompatibility of a set of general measurements and classify the incompatibility by the hierarchy of compatibilities of its subsets.…

In accordance with the Bing-Borsuk conjecture, we show that if X is an n-dimensional homogeneous metric ANR compactum and x\in X, then there is a local basis at x consisting of connected open sets U such that the cohomological properties of…

Given any function $\phi \colon [0,\infty)\to (0,1]$ satisfying $\lim_{\xi\to\infty}\phi(\xi) = 0$, we prove the existence of i) self-similar measures and ii) nonlinear $C^{\infty}$ self-conformal measures which are Rajchman and whose…

Given a $\mathbb Z^r$-action $\alpha$ on a nilmanifold $X$ by automorphisms and an ergodic $\alpha$-invariant probability measure $\mu$, we show that $\mu$ is the uniform measure on $X$, unless modulo finite index modification, one of the…

Let $X$ be a compact complex surface. Consider a finitely supported probability measure $\mu$ on $\text{Aut}(X)$ such that $\Gamma_{\mu} = \langle \text{Supp}(\mu)\rangle<\text{Aut}(X)$ is non-elementary. We do not assume that…

Can one certify the preparation of a coherent, many-body quantum state by measurements with bounded accuracy in the presence of noise and decoherence? Here, we introduce a criterion to assess the fragility of large-scale quantum states…

For singular numbers of integral operators of the form $u(x)\mapsto \int F_1(X)K(X,Y,X-Y)F_2(Y)u(Y)\mu(dY),$ with measure $\mu$ singular with respect to the Lebesgue measure in $\mathbb{R}^\mathbf{N}$, order sharp estimates for the counting…

Let $\xi_0,\xi_1,\ldots$ be independent identically distributed complex- valued random variables such that $\mathbb{E}\log(1+|\xi _0|)<\infty$. We consider random analytic functions of the form…

In this paper, we study the problem of testing whether or not a given probability measure $\mu$ on $\mathbb{R}^{d}$ can be decomposed as a mixture of two probability measures whose second order statistics are significantly different. We…