Related papers: Relative Entropy Convergence for Depolarizing Chan…
We introduce a meta logarithmic-Sobolev (log-Sobolev) inequality for the Lindbladian of all single-mode phase-covariant Gaussian channels of bosonic quantum systems, and prove that this inequality is saturated by thermal states. We show…
In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi-Jamio{\l}kowski state. The second one is based on the relative entropy…
In this paper we establish some explicit and sharp estimates of the spectral gap and the log-Sobolev constant for mean field particles system, uniform in the number of particles, when the confinement potential have many local minimums. Our…
This paper introduces a method for calculating the quantum relative entropy of channels, an essential quantity in quantum channel discrimination and resource theories of quantum channels. By building on recent developments in the…
We derive a lower bound for the Wehrl entropy in the setting of SU(1,1). For asymptotically high values of the quantum number k, this bound coincides with the analogue of the Lieb-Wehrl conjecture for SU(1,1) coherent states. The bound on…
Uniform continuity bounds on entropies are generally expressed in terms of a single distance measure between a pair of probability distributions or quantum states, typically, the total variation distance or trace distance. However, if an…
We consider the central limit theorem for stable laws in the case of the standardized sum of independent and identically distributed random variables with regular probability density function. By showing decay of different entropy…
We establish optimal convergence rates for the continuous piecewise affine finite element approximation of the Sobolev constant in arbitrary dimensions N\geq 2 and for Lebesgue exponents 1<p<N. Our analysis relies on a refined study of the…
We consider a family of Gagliardo-Nirenberg-Sobolev interpolation inequalities which interpolate between Sobolev's inequality and the logarithmic Sobolev inequality, with optimal constants. The difference of the two terms in the…
We study the relations between (tight) logarithmic Sobolev inequalities, entropy decay and spectral gap inequalities for Markov evolutions on von Neumann algebras. We prove that log-Sobolev inequalities (in the non-commutative form defined…
In this paper we obtain the best constants in some higher order Sobolev inequalities in the critical exponent. These inequalities can be separated into two types: those that embed into $L^\infty(\mathbb{R}^N)$ and those that embed into…
We reformulate the R\'enyi entanglement of purification as a constrained minimum output R\'enyi entropy problem. Equivalently, for $p>1$, this formulation can be expressed in terms of a constrained maximal output Schatten $p$-norm. More…
We prove that every GNS-symmetric quantum Markov semigroup on a finite dimensional matrix algebra satisfies a modified log-Sobolev inequality. In the discrete time setting, we prove that every finite dimensional GNS-symmetric quantum…
In this paper we study the Sobolev embedding theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. The proof is based on a suitable refinement…
We introduce the notion of an interpolating path on the set of probability measures on finite graphs. Using this notion, we first prove a displacement convexity property of entropy along such a path and derive Prekopa-Leindler type…
Tight lower and upper bounds on the ratio of relative entropies of two probability distributions with respect to a common third one are established, where the three distributions are collinear in the standard $(n-1)$-simplex. These bounds…
We consider generalizations of depolarizing channels to maps in which the identity channel is replaced by a convex combinations of unitary conjugations. We show that one can construct unital channels of this type for which the input which…
In this paper, we derive a new generalisation of the strong subadditivity of the entropy to the setting of general conditional expectations onto arbitrary finite-dimensional von Neumann algebras. The latter inequality, which we call…
In this article, we prove linear stability, scattering and inviscid damping with optimal decay rates for the linearized 2D Euler equations around a large class of strictly monotone shear flows, $(U(y),0)$, in a periodic channel under…
We show that the stability theorem of the depolarizing channel holds for the output quantum $p$-R\'enyi entropy for $p \ge 2$ or $p=1$, which is an extension of the well known case $p=2$. As an application, we present a protocol in which…