Related papers: Asymptotic Redundancies for Universal Quantum Codi…
We study asymptotic state transformations in continuous variable quantum resource theories. In particular, we prove that monotones displaying lower semicontinuity and strong superadditivity can be used to bound asymptotic transformation…
The recent article "Entropic Updating of Probability and Density Matrices" [1] derives and demonstrates the inferential origins of both the standard and quantum relative entropies in unison. Operationally, the standard and quantum relative…
We report a universal improvement to the standard Robertson--Schr\"odinger uncertainty relation. Our result shows that the Robertson--Schr\"odinger lower bound can be supplemented by a new noncommutativity-induced term. This term represents…
In this paper we provide a method to obtain tight lower bounds on the minimum redundancy achievable by a Huffman code when the probability distribution underlying an alphabet is only partially known. In particular, we address the case where…
We prove the existence of a 1/N expansion in unitary multimatrix models which are Gibbs perturbations of the Haar measure, and express the expansion coefficients recursively in terms of the unique solution of a noncommutative initial value…
Universal source coding at short blocklengths is considered for an exponential family of distributions. The \emph{Type Size} code has previously been shown to be optimal up to the third-order rate for universal compression of all memoryless…
We construct asymptotic expansions of Laplace type for the time-dependent quantum averages for Bose systems with many degrees of freedom, initially populated in coherent states. These solutions are localized in phase space, and they are…
We study non-asymptotic fundamental limits for transmitting classical information over memoryless quantum channels, i.e. we investigate the amount of classical information that can be transmitted when a quantum channel is used a finite…
Bayesian estimation of a mixed quantum state can be approximated via maximum likelihood (MaxLike) estimation when the likelihood function is sharp around its maximum. Such approximations rely on asymptotic expansions of multi-dimensional…
The Heisenberg position-momentum uncertainty relation is a cornerstone of quantum mechanics. However, its standard formulation is not fully consistent with special relativity. While partial understanding has been achieved in the…
We establish bounds on quantum correlations in many-body systems. They reveal what sort of information about a quantum system can be simultaneously recorded in different parts of its environment. Specifically, independent agents who monitor…
Traditionally, quantum amplification limit refers to the property of inevitable noise addition on canonical variables when the field amplitude of an unknown state is linearly transformed through a quantum channel. Recent theoretical studies…
According to quantum theory, measurements generate random outcomes, in stark contrast with classical mechanics. This raises the question of whether there could exist an extension of the theory which removes this indeterminism, as suspected…
We revisit the maximum-entropy inference of the state of a finite-level quantum system under linear constraints. The constraints are specified by the expected values of a set of fixed observables. We point out the existence of…
A theorem about asymptotic estimation of multiple integral of a special type is proved for the case when the integrand peaks at the integration domain bound, but not at a point of extremum. Using this theorem the asymptotic expansion of the…
Hyperasymptotics is an analytical method that incorporates exponentially small contributions into asymptotic approximations, thereby expanding their domain of validity, improving accuracy, and providing deeper insight into the underlying…
We establish higher-order nonasymptotic expansions for a difference between probability distributions of sums of i.i.d. random vectors in a Euclidean space. The derived bounds are uniform over two classes of sets: the set of all Euclidean…
In this paper, we give explicit error bounds for the asymptotic expansion of the shifted distinct partition function $q(n +s)$ for any nonnegative integer $s$. Then based on this refined asymptotic formula, we give the exact thresholds of…
We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set…
This paper discusses the asymptotic behaviour of the number of descents in a random signed permutation and its inverse, which was posed as an open problem by Chatterjee and Diaconis in a recent publication. For that purpose, we generalize…