相关论文: Tight Contraction Rates for Primitive Channels und…
Quantum f-divergences are a quantum generalization of the classical notion of f-divergences, and are a special case of Petz' quasi-entropies. Many well known distinguishability measures of quantum states are given by, or derived from,…
Expressions for (EPI Shannon type) Divergence-Power Inequalities (DPI) in two cases (time-discrete and band-limited time-continuous) of stationary random processes are given. The new expressions connect the divergence rate of the sum of…
We consider the sequential quantum channel discrimination problem using adaptive and non-adaptive strategies. In this setting the number of uses of the underlying quantum channel is not fixed but a random variable that is either bounded in…
Tight bounds for several symmetric divergence measures are introduced, given in terms of the total variation distance. Each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these bounds…
We show that approximating the trace norm contraction coefficient of a quantum channel within a constant factor is NP-hard. Equivalently, this shows that determining the optimal success probability for encoding a bit in a quantum system…
We study the mixing time of two popular discrete-time Markov chains in continuous space, the Unadjusted Langevin Algorithm and the Proximal Sampler, which are discretizations of the Langevin dynamics. We extend mixing time analyses for…
We investigate the classical communication over quantum channels when assisted by no-signaling (NS) and positive-partial-transpose-preserving (PPT) codes, for which both the optimal success probability of a given transmission rate and the…
We consider the transmission of classical information through a degraded broadcast channel, whose outputs are two quantum systems, with the state of one being a degraded version of the other. Yard et al. proved that the capacity region of…
This paper develops systematic approaches to obtain $f$-divergence inequalities, dealing with pairs of probability measures defined on arbitrary alphabets. Functional domination is one such approach, where special emphasis is placed on…
We investigate the problem of quantifying contraction coefficients of Markov transition kernels in Kantorovich ($L^1$ Wasserstein) distances. For diffusion processes, relatively precise quantitative bounds on contraction rates have recently…
We study the problem of efficient compression of a stochastic source of probability distributions. It can be viewed as a generalization of Shannon's source coding problem. It has relation to the theory of common randomness, as well as to…
In this paper, we propose a new protocol for a data compression task, blind quantum data compression, with finite local approximations. The rate of blind data compression is susceptible to approximations even when the approximations are…
Tight bounds for several symmetric divergence measures are derived in terms of the total variation distance. It is shown that each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these…
One of the basic tenets in information theory, the data processing inequality states that output divergence does not exceed the input divergence for any channel. For channels without input constraints, various estimates on the amount of…
We show that a sequence $\{\Phi_n\}$ of quantum channels strongly converges to a quantum channel $\Phi_0$ if and only if there exist a common environment for all the channels and a corresponding sequence $\{V_n\}$ of Stinespring isometries…
We derive, for a bistochastic strictly contractive quantum channel on a matrix algebra, a relation between the contraction rate and the rate of entropy production. We also sketch some applications of our result to the statistical physics of…
A strong converse bound for the classical identification capacity of a quantum channel is an upper bound on the asymptotic identification rate of classical messages sent through the channel, such that, above this rate, the probability of an…
We study posterior contraction rates for mixing measures in homoscedastic location-scale mixture models with infinitely many components. While posterior convergence at the level of densities is well understood, ensuring convergence of the…
Upon compressing perceptually relevant signals, conventional quantization generally results in unnatural outcomes at low rates. We propose distribution preserving quantization (DPQ) to solve this problem. DPQ is a new quantization concept…
Explicit classical states achieving maximal $f$-divergence are given, allowing for a simple proof of Matsumoto's Theorem, and the systematic extension of any inequality between classical $f$-divergences to quantum $f$-divergences. Our…