相关论文: Smooth min-entropy lower bounds for approximation …

We develop new techniques for proving lower bounds on the least singular value of random matrices with limited randomness. The matrices we consider have entries that are given by polynomials of a few underlying base random variables. This…

A new approach to inference in state space models is proposed, based on approximate Bayesian computation (ABC). ABC avoids evaluation of the likelihood function by matching observed summary statistics with statistics computed from data…

The precise one-shot characterisation of operational tasks in classical and quantum information theory relies on different forms of smooth entropic quantities. A particularly important connection is between the hypothesis testing relative…

We prove a tight uniform continuity bound for Arimoto's version of the conditional $\alpha$-R\'enyi entropy, for the range $\alpha \in [0, 1)$. This definition of the conditional R\'enyi entropy is the most natural one among the multiple…

This paper is concerned with the development of rigorous approximations to various expectations associated with Markov chains and processes having non-stationary transition probabilities. Such non-stationary models arise naturally in…

We show that a simple telescoping sum trick, together with the triangle inequality and a tensorisation property of expected-contractive coefficients of random channels, allow us to achieve general simultaneous decoupling for multiple users…

Extending corresponding results for matrix product states [Verstraete and Cirac, PRB 73, 094423 (2006); Schuch et al. PRL 100, 030504 (2008)], it is shown how the approximation error of tree tensor network states (TTNS) can be bounded using…

We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…

We study the approximability of two related problems on graphs with $n$ nodes and $m$ edges: $n$-Pairs Shortest Paths ($n$-PSP), where the goal is to find a shortest path between $O(n)$ prespecified pairs, and All Node Shortest Cycles…

This paper reveals a conceptually new connection from information theory to approximation theory via quantum algorithms for entropy estimation. Specifically, we provide an information-theoretic lower bound $\Omega(\sqrt{n})$ on the…

Subentropy is an entropy-like quantity that arises in quantum information theory; for example, it provides a tight lower bound on the accessible information for pure state ensembles, dual to the von Neumann entropy upper bound in Holevo's…

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 uncertainty principle determines the distinction between the classical and quantum worlds. This principle states that it is not possible to measure two incompatible observables with the desired accuracy simultaneously. In quantum…

Losses are one of the main bottlenecks for the distribution of entanglement in quantum networks, which can be overcome by the implementation of quantum repeaters. The most basic form of a quantum repeater chain is the swap ASAP repeater…

We investigate sampling procedures that certify that an arbitrary quantum state on $n$ subsystems is close to an ideal mixed state $\varphi^{\otimes n}$ for a given reference state $\varphi$, up to errors on a few positions. This task makes…

Let $G$ be a sofic group, and let $\Sigma = (\sigma_n)_{n\geq 1}$ be a sofic approximation to it. For a probability-preserving $G$-system, a variant of the sofic entropy relative to $\Sigma$ has recently been defined in terms of sequences…

We study the entropy of pure shift-invariant states on a quantum spin chain. Unlike the classical case, the local restrictions to intervals of length $N$ are typically mixed and have therefore a non-zero entropy $S_N$ which is, moreover,…

We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a…

There has been a recent surge of powerful tools to show rapid mixing of Markov chains, via functional inequalities such as Poincar\'e inequalities. In many situations, Markov chains fail to mix rapidly from a worst-case initialization, yet…

We revisit the well-studied problem of estimating the Shannon entropy of a probability distribution, now given access to a probability-revealing conditional sampling oracle. In this model, the oracle takes as input the representation of a…