Related papers: Asymptotic Redundancies for Universal Quantum Codi…

This paper shows that the probability that the error exponent of a given code randomly generated from a pairwise independent ensemble being smaller than a lower bound on the typical random-coding exponent tends to zero as the codeword…

We address the statistics of continuous weak linear measurement on a few-state quantum system that is subject to a conditioned quantum evolution. For a conditioned evolution, both the initial and final states of the system are fixed: the…

We study the distribution of the length of longest increasing subsequences in random permutations of $n$ integers as $n$ grows large and establish an asymptotic expansion in powers of $n^{-1/3}$. Whilst the limit law was already shown by…

We develop finite-population asymptotic theory for covariate adjustment in randomization-based causal inference for 2K factorial designs. In particular, we confirm that both the unadjusted and covariate-adjusted estimators of the factorial…

We prove a variety of new and refined uniform continuity bounds for entropies of both classical random variables on an infinite state space and of quantum states of infinite-dimensional systems. We obtain the first tight continuity estimate…

In this work we develop an open quantum system view of the parametric approximation, which allows us to obtain systematic perturbative corrections to it. We consider the Jaynes-Cummings model with dissipation, assuming that the field is in…

We consider the uniform asymptotic expansion for the Gauss hypergeometric function \[F(a+\epsilon\lambda,m;c+\lambda;x),\qquad \lambda\to+\infty\] for $x<1$ and positive integer $m$ when the parameter $\epsilon>1$ and the constants $a$ and…

We introduce and study certain asymptotic invariants associated with fusion algebras (equipped with a dimension function), which arise naturally in the representation theory of compact quantum groups. Our invariants generalise the analogous…

For noncomposite systems in classical and quantum domains, we obtain new inequalities such as the subadditivity and strong subadditivity conditions for Shannon entropies and information determined by the probability distributions and for…

We consider redundant binary joint digital expansions of integer vectors. The redundancy is used to minimize the Hamming weight, i.e., the number of nonzero digit vectors. This leads to efficient linear combination algorithms in abelian…

We derive an asymptotic lower bound on the Bayes risk when N identical quantum systems whose state depends on a vector of unknown parameters are jointly measured in an arbitrary way and the parameters of interest estimated on the basis of…

We consider a 1-parameter family of self-adjoint extensions of the Hamiltonian for a particle confined to a finite interval with perfectly reflecting boundary conditions. In some cases, one obtains negative energy states which seems to…

Weakly almost i.i.d. quantum sources are sequences of multipartite states whose fixed-size marginals converge, on average, to tensor powers of a reference state, while allowing arbitrary global correlations and entanglement. We establish…

Edgeworth-type expansions for convolutions of probability densities and powers of the characteristic functions with non-uniform error terms are established for i.i.d. random variables with finite (fractional) moments of order $s \geq 2$,…

We study the asymptotic behavior of the output states of sequences of quantum channels. Under a natural assumption, we show that the output set converges to a compact convex set, clarifying and substantially generalizing results in [BCN13].…

In this article, we provide a comprehensive analysis of the asymptotic behavior of Bell numbers, enhancing and unifying various results previously dispersed in the literature. We establish several explicit lower and upper bounds. The main…

The intuition that the precision of observables is constrained by thermodynamic costs has recently been formalized through thermodynamic and kinetic uncertainty relations. While such trade-offs have been extensively studied in Markovian…

We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptotic exponential rate at which the specified error…

This paper studies expurgated random-coding bounds and exponents for channel coding with a given (possibly suboptimal) decoding rule. Variations of Gallager's analysis are presented, yielding several asymptotic and non-asymptotic bounds on…

This paper studies majorization of high tensor powers of finitely supported probability distributions. Viewing probability distributions as a resource with majorization as a means of transformation corresponds to the resource theory of pure…