Related papers: Entropy accumulation with improved second-order te…
We study the use of von Neumann entropy constraints for obtaining lower bounds on the ground energy of quantum many-body systems. Known methods for obtaining certificates on the ground energy typically use consistency of local observables…
Operationally accessible entanglement in bipartite systems of indistinguishable particles could be reduced due to restrictions on the allowed local operations as a result of particle number conservation. In order to quantify this effect,…
The time decay of fully discrete finite-volume approximations of porous-medium and fast-diffusion equations with Neumann or periodic boundary conditions is proved in the entropy sense. The algebraic or exponential decay rates are computed…
The classical problem of maximizing the Shannon entropy of a sum of independent random variables supported on a finite alphabet is considered and settled in the ternary case. Namely, the following theorem is established: if…
We derive an exact (classical and quantum) expression for the entropy production of a finite system placed in contact with one or several finite reservoirs each of which is initially described by a canonical equilibrium distribution.…
We propose a series of quantum algorithms for computing a wide range of quantum entropies and distances, including the von Neumann entropy, quantum R\'{e}nyi entropy, trace distance, and fidelity. The proposed algorithms significantly…
Quantum information-theoretic approach has been identified as a way to understand the foundations of quantum mechanics as early as 1950 due to Shannon. However there hasn't been enough advancement or rigorous development of the subject. In…
In this article, we present quantum algorithms for estimating von Neumann entropy and Renyi entropy, which are crucial physical and information-theoretical properties of a given quantum state $\rho$. Although there have been existing works…
Given an arbitrary quantum state ($\sigma$), we obtain an explicit construction of a state $\rho^*_\varepsilon(\sigma)$ (resp. $\rho_{*,\varepsilon}(\sigma)$) which has the maximum (resp. minimum) entropy among all states which lie in a…
Entropic uncertainty relations are quantitative characterizations of Heisenberg's uncertainty principle, which make use of an entropy measure to quantify uncertainty. In quantum cryptography, they are often used as convenient tools in…
In this work, we propose a soft covering problem for fully quantum channels using relative entropy as a criterion for operator closeness. We establish covering lemmas by deriving one-shot bounds on the achievable rates in terms of smooth…
A novel definition of the conditional smooth Renyi entropy, which is different from that of Renner and Wolf, is introduced. It is shown that our definition of the conditional smooth Renyi entropy is appropriate to give lower and upper…
Statistical correlations that can be generated across the nodes in a quantum network depend crucially on its topology. However, this topological information might not be known a priori, or it may need to be verified. In this paper, we…
Entanglement entropy for a spatial partition of a quantum system is studied in theories which admit a dual description in terms of the anti-de Sitter (AdS) gravity one dimension higher. A general proof of the holographic formula which…
Lower bounds for the R\'enyi entropies of sums of independent random variables taking values in cyclic groups of prime order under permutations are established. The main ingredients of our approach are extended rearrangement inequalities in…
The uncertainty principle sets a bound on our ability to predict the measurement outcomes of two incompatible observables which are measured on a quantum particle simultaneously. In quantum information theory, the uncertainty principle can…
Our capacity to process information depends on the computational power at our disposal. Information theory captures our ability to distinguish states or communicate messages when it is unconstrained with unrivaled beauty and elegance. For…
Given a probability distribution P, what is the minimum amount of bits needed to store a value x sampled according to P, such that x can later be recovered (except with some small probability)? Or, what is the maximum amount of uniform…
Weakly almost i.i.d. quantum sources are sequences of multipartite states whose fixed-size marginals converge, on average, to tensor powers of a reference state, while allowing arbitrary global correlations and entanglement. We establish…
We test Boltzmann's H-theorem for several models of particle random walk. We study the influence of interaction between the particle and reservoir/detectors on entropy and find entropy increasing in time for some models and behaving…