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We introduce a novel geometric approach to characterize entanglement relations in large quantum systems. Our approach is inspired by Schumacher's singlet state triangle inequality, which used an entropic-based distance to capture the…
Entangled systems in experiments may be lost or offline in distributed quantum information processing. This inspires a general problem to characterize quantum operations which result in breaking of entanglement or not. Our goal in this work…
Interpolation inequalities play an essential role in Analysis with fundamental consequences in Mathematical Physics, Nonlinear Partial Differential Equations (PDEs), Markov Processes, etc., and have a wide range of applications in various…
In this article, we generalize a proof technique by Alicki, Fannes and Winter and introduce a method to prove continuity bounds for entropic quantities derived from different quantum relative entropies. For the Umegaki relative entropy, we…
We examine the conjecture that entropy production in subsystems of a given system can be used as a dynamical criterion for quantum chaos in the latter. Numerical results are presented for finite dimensional spin systems as also for the…
Long sequences of successive direct (projective) measurements or observations of a few "uninteresting" physical quantities of a quantum system may reveal indirect, but precise and unambiguous information on the values of some very…
In a quantum system, there may be many density matrices associated with a state on an algebra of observables. For each density matrix, one can compute its entropy. These are in general different. Therefore one reaches the remarkable…
We consider large time asymptotics for damped nonlinear Schr\"{o}dinger equations. It is known that the nonlinear solution asymptotically behaves like a linear solution when time $t$ tends to infinity in the energy space. We prove that its…
This work develops analytic methods to quantitatively demarcate quantum reality from its subset of classical phenomenon, as well as from the superset of general probabilistic theories. Regarding quantum nonlocality, we discuss how to…
Given $A,B\in M_n(\mathbb R)$, we consider the Cauchy problem for partially dissipative hyperbolic systems having the form \begin{equation*} \partial_{t}u+A\partial_{x}u+Bu=0, \end{equation*} with the aim of providing a detailed description…
The relation between the violation of the Bell-CHSH inequalities and entanglement properties of quantum states is not clear so one may consider the mixedness of the system to understand the entanglement properties better than the Bell-CHSH…
We consider the Cauchy problem for the isentropic compressible Euler equations in a three-dimensional periodic domain under general pressure laws. For any smooth initial density away from the vacuum, we construct infinitely many entropy…
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…
We find the nodes that minimise divided differences and use them to find the sharp constant in a sublevel set estimate. We also find the sharp constant in the first instance of the van der Corput Lemma using a complex mean value theorem for…
We show that Frenkel's integral representation of the quantum relative entropy provides a natural framework to derive continuity bounds for quantum information measures. Our main general result is a dimension-independent semi-continuity…
The existence of a global causal order between events places constraints on the correlations that parties may share. Such "causal correlations" have been the focus of recent attention, driven by the realization that some extensions of…
In 2003, Del Pino and Dolbeault [14] and Gentil [19] investigated, independently, best constants and extremals associated to Euclidean Lp-entropy inequalities for p > 1. In this work, we present some contributions in the Riemannian context.…
We introduce a hierarchy of linear systems for showing that a given subspace of pure quantum states is entangled (i.e., contains no product states). This hierarchy outperforms known methods already at the first level, and it is complete in…
We examine the inference of quantum density operators from incomplete information by means of the maximization of general non-additive entropic forms. Extended thermodynamic relations are given. When applied to a bipartite spin 1/2 system,…
This paper studies the behavior of the entropy numbers of classes of functions with bounded integral norms from a given finite dimensional linear subspace. Upper bounds of these entropy numbers in the uniform norm are obtained and applied…