相关论文: Uniqueness and Optimality of Dynamical Extensions …
We describe the class (semigroup) of quantum channels mapping states with finite entropy into states with finite entropy. We show, in particular, that this class is naturally decomposed into three convex subclasses, two of them are closed…
We generalize our results in paper I in this series to quantum channels between general v. Neumann algebras, proving the approximate recoverability of states which undergo a small change in relative entropy through the channel. To this end,…
We propose an extension of the sandwiched R\'enyi relative $\alpha$-entropy to normal positive functionals on arbitrary von Neumann algebras, for the values $\alpha>1$. For this, we use Kosaki's definition of noncommutative $L_p$-spaces…
Tight bounds on the minimum mean square error for the additive Gaussian noise channel are derived, when the input distribution is constrained to be epsilon-close to a Gaussian reference distribution in terms of the Kullback--Leibler…
We study the problem of estimating a distribution over a finite alphabet from an i.i.d. sample, with accuracy measured in relative entropy (Kullback-Leibler divergence). While optimal bounds on the expected risk are known, high-probability…
We establish existence, uniqueness and optimal regularity results for very weak solutions to certain nonlinear elliptic boundary value problems. We introduce structural asymptotic assumptions of Uhlenbeck type on the nonlinearity, which are…
The maximal correlation coefficient measures the linear correlation in a bipartite distribution and contraction coefficients measure how much information is lost under a noisy channel. Remarkably, Raginsky established a close relation…
We announce the extension of optimal regularity and Uhlenbeck compactness to the general setting of connections on vector bundles with non-compact gauge groups over non-Riemannian manifolds, including the Lorentzian metric connections of…
Quantum channel capacities give the fundamental performance limits for information flow over a communication channel. However, the prevalence of superadditivity is a major obstacle to understanding capacities, both quantitatively and…
In this paper, some new upper bounds for Kullback-Leibler divergence(KL-divergence) based on $L^1, L^2$ and $L^\infty$ norms of density functions are discussed. Our findings unveil that the convergence in KL-divergence sense sandwiches…
A random unitary channel is one that is given by a convex combination of unitary channels. It is shown that the conjectures on the additivity of the minimum output entropy and the multiplicativity of the maximum output $p$-norm can be…
Unextendibility of quantum states and channels is inextricably linked to the no-cloning theorem of quantum mechanics, it has played an important role in understanding and quantifying entanglement, and more recently it has found applications…
We introduce a new transformation called \emph{relative differential-escort}, which extends the usual differential-escort transformation by relating the change of variable to a reference probability density. As an application of it, we…
We give a detailed analysis of the Gibbs-type entropy notion and its dynamical behavior in case of time-dependent continuous probability distributions of varied origins: related to classical and quantum systems. The purpose-dependent usage…
The optimized quantum $f$-divergences form a family of distinguishability measures that includes the quantum relative entropy and the sandwiched R\'enyi relative quasi-entropy as special cases. In this paper, we establish physically…
The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomisation of network connections is a commonly used tool. However,…
We investigate decoherence induced by a quantum channel in terms of minimal output entropy and of map entropy. The latter is the von Neumann entropy of the Jamiolkowski state of the channel. Both quantities admit q-Renyi versions. We prove…
Information-theoretic measures such as the entropy, cross-entropy and the Kullback-Leibler divergence between two mixture models is a core primitive in many signal processing tasks. Since the Kullback-Leibler divergence of mixtures provably…
We construct a class of quantum channels in arbitrary dimensions for which entanglement improves the performance of the channel. The channels have correlated noise and when the level of correlation passes a critical value we see a sharp…
The channel output entropy of a transmitted sequence is the entropy of the possible channel outputs and similarly the channel input entropy of a received sequence is the entropy of all possible transmitted sequences. The goal of this work…