Related papers: Reduced relative quantum entropy
In this article we describe the applications of the relative entropy framework. In particular uniqueness of an entropy solution is proven for a scalar conservation law, using the notion of measure-valued entropy solutions. Further we survey…
We consider the relative entropy between vacuum states of two different theories: a conformal field theory (CFT), and the CFT perturbed by a relevant operator. By restricting both states to the null Cauchy surface in the causal domain of a…
We prove existence and uniqueness of solutions for an entropic version of the semi-geostrophic equations. We also establish convergence to a weak solution of the semi-geostrophic equations as the entropic parameter vanishes. Convergence is…
The measured relative entropy and measured R\'enyi relative entropy are quantifiers of the distinguishability of two quantum states $\rho$ and $\sigma$. They are defined as the maximum classical relative entropy or R\'enyi relative entropy…
The phenomenon of quantum entanglement is explained in a way which is fully consistent with Einstein's Special Theory of Relativity. A subtle flaw is identified in the logic supporting the view that Bell's Inequality precludes all local…
We offer a fresh perspective on the relational interpretation of quantum mechanics as a way of thinking about the world described by quantum theory based on quantifiable notions of information. This allows us to provide a definition of a…
Entropy is a fundamental concept in quantum information theory that allows to quantify entanglement and investigate its properties, for example its monogamy over multipartite systems. Here, we derive variational formulas for relative…
We show that a certain entropy-like function is convex, under an optimal transport problem that is adapted to Ricci flow. We use this to reprove the monotonicity of Perelman's reduced volume.
Let $K$ be a convex body in $\mathbb R^n$. We introduce a new affine invariant, which we call $\Omega_K$, that can be found in three different ways: as a limit of normalized $L_p$-affine surface areas, as the relative entropy of the cone…
In the reductionistic approach, mechanisms are divided into simpler parts interconnected in some standard way (e.g. by a mechanical transmission). We explore the possibility of porting reductionism in quantum operations. Conceptually, first…
A linearized variant of relative entropy is used to quantify in a unified scheme the different kinds of correlations in a bipartite quantum system. As illustration, we consider a two-qubit state with parity and exchange symmetries for which…
The purpose of this paper is to sketch an approach towards a reconciliation of quantum theory with relativity theory. It will actually be argued that these two theories ultimately rely on one another. A general operator-algebraic framework…
We consider systems of conservation laws endowed with a convex entropy. We show the contraction, up to a translation, to extremal entropic shocks, for a pseudo-distance based on the notion of relative entropy. The contraction holds for…
An universal approximation technique for analysis of different characteristics of states of composite infinite-dimensional quantum systems is proposed and used to prove general results concerning the properties of correlation and…
Under the principle that quantum mechanical observables are invariant under relevant symmetry transformations, we explore how the usual, non-invariant quantities may capture measurement statistics. Using a relativisation mapping, viewed as…
We give a local-to-global principle for relative entropy contraction in simplicial complexes. This is similar to the local-to-global principle for variances obtained by Alev and Lau (2020).
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
By a use of the Fredholm determinant theory, the unified quantum entropy notion has been extended to a case of infinite-dimensional systems. Some of the known (in the finite-dimensional case) basic properties of the introduced unified…
Maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This new method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input…
The quantum threshold theorem shows that a noisy quantum computer can accurately and efficiently simulate any ideal quantum computation provided that noise is weakly correlated and its strength is below a critical value known as the quantum…