Related papers: Marginal-constrained entropy accumulation theorem

Variational techniques have been recently developed to find tighter bounds on the von Neumann entropy in a completely device-independent (DI) setting. This, in turn, has led to significantly improved key rates of DI protocols, in both the…

Using the graphical calculus and integration techniques introduced by the authors, we study the statistical properties of outputs of products of random quantum channels for entangled inputs. In particular, we revisit and generalize models…

Entropic quantifiers of states lie at the cornerstone of the quantum information theory. While a quantum state can be abstracted as a device that only has outputs, the most general quantum device is a quantum channel that also has inputs.…

This paper introduces a method for calculating the quantum relative entropy of channels, an essential quantity in quantum channel discrimination and resource theories of quantum channels. By building on recent developments in the…

We prove that all R\'enyi entanglement entropies of spin-chains described by generic (gapped), translational invariant matrix product states (MPS) are extensive for disconnected sub-systems: All R\'enyi entanglement entropy densities of the…

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…

The chain rule for the Shannon and von Neumann entropy, which relates the total entropy of a system to the entropies of its parts, is of central importance to information theory. Here we consider the chain rule for the more general smooth…

Uniform continuity bounds on entropies are generally expressed in terms of a single distance measure between a pair of probability distributions or quantum states, typically, the total variation distance or trace distance. However, if an…

Existing polarization theories have mostly been concerned with Shannon's information measures, such as Shannon entropy and mutual information, and some related measures such as the Bhattacharyya parameter. In this work, we extend…

Relative entropy is the standard measure of distinguishability in classical and quantum information theory. In the classical case, its loss under channels admits an exact chain rule, while in the quantum case only asymptotic, regularized…

We ask the question whether entropy accumulates, in the sense that the operationally relevant total uncertainty about an $n$-partite system $A = (A_1, \ldots A_n)$ corresponds to the sum of the entropies of its parts $A_i$. The Asymptotic…

We investigate quantum R\'enyi entropic quantities, specifically those derived from 'sandwiched' divergence. This divergence is one of several proposed R\'enyi generalisations of the quantum relative entropy. We may define R\'enyi…

We prove that under mild positivity assumptions the entropy rate of a hidden Markov chain varies analytically as a function of the underlying Markov chain parameters. A general principle to determine the domain of analyticity is stated. An…

The entropic uncertainty relations are a very active field of scientific inquiry. Their applications include quantum cryptography and studies of quantum phenomena such as correlations and non-locality. In this work we find…

We derive a new entropic quantum uncertainty relation involving min-entropy. The relation is tight and can be applied in various quantum-cryptographic settings. Protocols for quantum 1-out-of-2 Oblivious Transfer and quantum Bit Commitment…

The von Neumann entropy plays a vital role in quantum information theory. The von Neumann entropy determines, e.g., the capacities of quantum channels. Also, entropies of composite quantum systems are important for future quantum networks,…

The thermodynamic resourcefulness of quantum channels primarily depends on their underlying causal structure and their ability to generate quantum correlations. We quantify this interplay within the resource theory of athermality for…

We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…

We initiate the study of computational entropy in the quantum setting. We investigate to what extent the classical notions of computational entropy generalize to the quantum setting, and whether quantum analogues of classical theorems hold.…

We summarize some results of geometric measure theory concerning rectifiable sets and measures. Combined with the entropic chain rule for disintegrations (Vigneaux, 2021), they account for some properties of the entropy of rectifiable…