Related papers: Optimal Extensions of Resource Measures and their …
Given an irreducible subshift of finite type X, a subshift Y, a factor map \pi : X \to Y, and an ergodic invariant measure \nu on Y, there can exist more than one ergodic measure on X which projects to \nu and has maximal entropy among all…
The resource theory of coherence addresses the extent to which quantum properties are present in a given quantum system. While coherence has been extensively studied for individual quantum states, measures of coherence for ensembles of…
Among the most fundamental questions in the manipulation of quantum resources such as entanglement is the possibility of reversibly transforming all resource states. The key consequence of this would be the identification of a unique…
Two families of dependence measures between random variables are introduced. They are based on the R\'enyi divergence of order $\alpha$ and the relative $\alpha$-entropy, respectively, and both dependence measures reduce to Shannon's mutual…
The relative entropy of a correlated state and an uncorrelated reference state is a reasonable measure for the degree of correlations. A key question is however which uncorrelated state to compare to. The relative entropy becomes minimal…
Inspired by works on information transmission through quantum channels, we propose the use of a couple of mutual entropies to quantify the efficiency of continual measurement schemes in extracting information on the measured quantum system.…
Complementary relationships exist regarding interference properties of particles such as pattern visibility, predictability and distinguishability. Additionally, relationships are known between information gain $G$ and measurement…
Entanglement is defined between subsystems of a quantum system, and at fixed time two regions of space can be viewed as two subsystems of a relativistic quantum field. The entropy of entanglement between such subsystems is ill-defined…
We present the modified relative entropy of entanglement for multi-party systems by a given relative density matrix which is spanned by a linear combination of the direct products of so-called basis of relative density matrices and reduced…
The principle of maximum entropy provides a useful method for inferring statistical mechanics models from observations in correlated systems, and is widely used in a variety of fields where accurate data are available. While the assumptions…
One of the key tasks in physics is to perform measurements in order to determine the state of a system. Often, measurements are aimed at determining the values of physical parameters, but one can also ask simpler questions, such as "is the…
We develop a unified approach to defining a point at infinity for an arbitrary space and formalizing convergence to this point. Central to our work is a method to quantify and classify the rates at which functions approach their limits at…
We derive a trade-off relation between the accuracy of implementing a desired unitary evolution using a restricted set of free unitaries and the size of the assisting system, in terms of the resource generating/losing capacity of the target…
Are Gaussian measurements enough to distinguish between Gaussian states? Here, we tackle this question by focusing on the max-relative entropy as an operational distinguishability metric. Given two general multimode Gaussian states, we…
We review the basic idea behind resource theories, where we quantify quantum resources by specifying a restricted class of operations. This divides the state space into various sets, including states which are free (because they can be…
The aim of this study is to generalise recent results of the two last authors on en-tropy methods for measure solutions of the renewal equation to other classes of structured population problems. Specifically, we develop a generalised…
Using the algebraic approach to entanglement entropy, we study several dual pairs of lattice theories and show how the entropy is completely preserved across each duality. Our main result is that a maximal algebra of observables in a region…
How can we quantify the entanglement in a quantum state, if only the expectation value of a single observable is given? This question is of great interest for the analysis of entanglement in experiments, since in many multiparticle…
Various theories that aim at unifying gravity with quantum mechanics suggest modifications of the Heisenberg algebra for position and momentum. From the perspective of quantum mechanics, such modifications lead to new uncertainty relations…
Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum theory, they have practical applications such as for…