Related papers: Maximizing dimension for Bernoulli measures and th…
Self-testing is a powerful certification of quantum systems relying on measured, classical statistics. This paper considers self-testing in bipartite Bell scenarios with small number of inputs and outputs, but with quantum states and…
We prove that Bernoulli convolutions are absolutely continuous provided the parameter lambda is an algebraic number sufficiently close to 1 depending on the Mahler measure of lambda.
We consider a complete metric space $(X,d)$ and a countable number of contractive mappings on $X$, $\mathcal{F}=\{F_i:i\in\mathbb N\}$. We show the existence of a {\em smallest} invariant set (with respect to inclusion) for $\mathcal{F}$.…
Heap monoids equipped with Bernoulli measures are a model of probabilistic asynchronous systems. We introduce in this framework the notion of asynchronous stopping time, which is analogous to the notion of stopping time for classical…
Are Gaussian measurements enough to distinguish between Gaussian states? Here, we tackle this question by focusing on the max-relative entropy as an operational distinguishability metric. Given two general multimode Gaussian states, we…
When working with quantum states, analysis of the final quantum state generated through probabilistic measurements is essential. This analysis is typically conducted by constructing the density matrix from either partial or full tomography…
In this paper, we study regular sets in metric measure spaces with bounded Ricci curvature. We prove that the existence of a point in the regular set of the highest dimension implies the positivity of the measure of such regular set. Also…
This note contains the complete mathematical proof of the main Theorem of the paper "How continuous measurements in finite dimension are actually discrete" (quant-ph/0702068), thus showing that in finite dimension any measurement with…
Consistency with relativistic causality narrows down dramatically the class of measurable observables. We argue that by weakening the preparation role of ideal measurements, many of these observables become measurable. Particularly, we show…
Let $f \colon X \rightarrow Y$ be a resolvable-measurable mapping of a metrizable space $X$ to a regular space $Y$. Then $f$ is piecewise continuous. Additionally, for a metrizable completely Baire space $X$, it is proved that $f$ is…
Maximal correlation is a measure of correlation for bipartite distributions. This measure has two intriguing features: (1) it is monotone under local stochastic maps; (2) it gives the same number when computed on i.i.d. copies of a pair of…
We show somewhat unexpectedly that whenever a general Bernstein-type maximal inequality holds for partial sums of a sequence of random variables, a maximal form of the inequality is also valid.
We discuss possibility of upper-bounding dimension of quantum states device-independently. Provided that the states are pure, it is possible to generate certain four states whose dimension is bounded by two.
We construct equilibrium states, including measures of maximal entropy, for a large (open) class of non-uniformly expanding maps on compact manifolds. Moreover, we study uniqueness of these equilibrium states, as well as some of their…
In this paper, we study physical measures for partially hyperbolic diffeomorphisms with multi one-dimensional centers under the condition that all Gibbs $u$-states are hyperbolic. We prove the finiteness of ergodic physical measures. Then…
We show exact dimensionality of harmonic measures associated with random walks on groups acting on a hyperbolic space under finite first moment condition, and establish the dimension formula by the entropy over the drift. We also treat the…
Cubic phase states provide the essential non-Gaussian resource for continuous-variable quantum computing. We show that they also offer significant potential for quantum metrology, surpassing the phase-sensing sensitivity of all Gaussian…
We describe the local structure of Riemannian manifolds with harmonic curvature which admit a maximum number, in a well-defined sense, of local warped-product decompositions, and at the same time their Ricci tensor has, at some point, only…
We show that if an infinite measure preserving system is well approximated on most of the phase space by a system satisfying the local limit theorem, then the original system enjoys mixing with respect to global observables, that is, the…
Two observables are called complementary if preparing a physical object in an eigenstate of one of them yields a completely random result in a measurement of the other. We investigate small sets of complementary observables that cannot be…