Related papers: Quantum conditional entropies from convex trace fu…
In this paper we show existence of traces of functions of bounded variation on the boundary of a certain class of domains in metric measure spaces equipped with a doubling measure supporting a $1$-Poincar\'e inequality, and obtain $L^1$…
High-order phenomena play crucial roles in many systems of interest, but their analysis is often highly nontrivial. There is a rich literature providing a number of alternative information-theoretic quantities capturing high-order…
Employing the notion of operator log-convexity, we study joint concavity$/$ convexity of multivariable operator functions: $(A,B)\mapsto F(A,B)=h\left[ \Phi(f(A))\ \sigma\ \Psi(g(B))\right]$, where $\Phi$ and $\Psi$ are positive linear maps…
Uncertainty relations and quantum entanglement are pivotal concepts in quantum theory. Beyond their fundamental significance in shaping our understanding of the quantum world, they also underpin crucial applications in quantum information…
We revisit the derivation of a formula for the $q$-generalised multinomial coefficient rooted in the $q$-deformed algebra, a foundational framework in the study of nonextensive statistics. Previous approximate expressions in the literature…
The entanglement entropy of a subsystem $A$ of a quantum system is expressed, in the replica method, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix $\tr\rho_A^n$. We study the…
We present a general class of entanglement criteria for continuous variable systems. Our criteria are based on the Husimi $Q$-distribution and allow for optimization over the set of all concave functions rendering them extremely general and…
Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not have a quantum entropy assigned to them. We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair…
Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…
Our knowledge of quantum mechanics can satisfactorily describe simple, microscopic systems, but is yet to explain the macroscopic everyday phenomena we observe. Here we aim to shed some light on the quantum-to-classical transition as seen…
Quantum channels can represent dynamic resources, which are indispensable elements in many physical scenarios. To describe certain facets of nonclassicality of the channels, it is necessary to quantify their properties. In the framework of…
The asymptotic restriction problem for tensors can be reduced to finding all parameters that are normalized, monotone under restrictions, additive under direct sums and multiplicative under tensor products, the simplest of which are the…
We revisit entropy methods to prove new sharp trace logarithmic Sobolev and sharp Gagliardo-Nirenberg-Sobolev inequalities on the half space, with a focus on the entropy inequality itself and not the actual flow, allowing for somewhat…
Incremental information, as measured by the quantum entropy, is increasing when two ensembles are united. This result was proved by Lieb and Ruskai, and it is the foundation for the proof of strong subadditivity of quantum entropy. We…
The concept of wave-particle duality holds significant importance in the field of quantum mechanics, as it elucidates the dual nature encompassing both wave-like and particle-like properties exhibited by microscopic particles. In this…
We introduce a remarkable new family of norms on the space of $n \times n$ complex matrices. These norms arise from the combinatorial properties of symmetric functions, and their construction and validation involve probability theory,…
We consider the family of piecewise linear maps $F(x,y)=\left(|x| - y + a, x - |y| + b\right),$ where $(a,b)\in \R^2$. In previous work, we identified a novel phenomenon: certain maps of this class possess one-dimensional invariant sets,…
The paper presents variational formulae for entropy-like functionals, including Segal and R\'enyi entropies, for normal states on semifinite von Neumann algebras. The considered functionals are of the form $\tau(f(h))$ where $\tau$ is a…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
In developing quantum science and technologies, it is essential to demonstrate the so-called quantum advantages, which are performances that can be achieved only with the assistance of quantum resources. Most of the time, different quantum…