Related papers: General entropy-like uncertainty relations in fini…
We introduce a new generalization of relative entropy to non-negative vectors with sums $\gt 1$. We show in a purely combinatorial setting, with no probabilistic considerations, that in the presence of linear constraints defining a convex…
We give an overview of joint unsharp measurements of non-commuting observables using positive operator valued measures (POVMs). We exemplify the role played by joint measurability of POVMs in entropic uncertainty relation for Alice's pair…
Entanglement criteria for an $n$-partite quantum system with continuous variables are formulated in terms of R\'{e}nyi entropies. R\'{e}nyi entropies are widely used as a good information measure due to many nice properties. Derived…
It is known that the variance and entropy of quantum observables decompose into intrinsically quantum and classical contributions. Here a general method of constructing quantum-classical decompositions of resources such as uncertainty is…
Fundamental properties for the Tsallis relative entropy in both classical and quantum systems are studied. As one of our main results, we give the parametric extension of the trace inequality between the quantum relative entropy and the…
We characterize the asymptotic performance of a class of positive operator valued measurements (POVMs) where the only task is to make measurements on independent and identically distributed quantum states on finite-dimensional systems. The…
Let $A$ be a self-adjoint operator acting over a space $X$ endowed with a partition. We give lower bounds on the energy of a mixed state $\rho$ from its distribution in the partition and the spectral density of $A$. These bounds improve…
Entropic uncertainty relations are underpinning to compute the quantitative security bound in quantum cryptographic applications, such as quantum random number generation (QRNG) and quantum key distribution (QKD). All security proofs derive…
We generalize, improve and unify theorems of Rumin, and Maassen--Uffink about classical entropies associated to quantum density matrices. These theorems refer to the classical entropies of the diagonals of a density matrix in two different…
We build a solvability theory of elliptic boundary-value problems in normed Sobolev spaces of generalized smoothness for any integrability exponent $p>1$. The smoothness is given by a number parameter and a supplementary function parameter…
Dependence among marginally constrained observations can break a finite-sample barrier. To formalize this phenomenon, we introduce the \emph{minimum list entropy coupling} $H(P\|Q_1,\dots,Q_m)$, the minimum conditional entropy…
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…
We develop a new framework for establishing approximate factorization of entropy on arbitrary probability spaces, using a geometric notion known as non-negative sectional curvature. The resulting estimates are equivalent to entropy…
Consider a sphere of radius root(n) in n dimensions, and consider X, a random variable uniformly distributed on its surface. Poincare's Observation states that for large n, the distribution of the first k coordinates of X is close in total…
We consider the uncertainty between two pairs of local projective measurements performed on a multipartite system. We show that the optimal bound in any linear uncertainty relation, formulated in terms of the Shannon entropy, is additive.…
Images obtained from coherent illumination processes are contaminated with speckle noise, with polarimetric synthetic aperture radar (PolSAR) imagery as a prominent example. With an adequacy widely attested in the literature, the scaled…
Integral representations of quantum relative entropy, and of the directional second and higher order derivatives of von Neumann entropy, are established, and used to give simple proofs of fundamental, known data processing inequalities: the…
The phenomenon of entropy concentration provides strong support for the maximum entropy method, MaxEnt, for inferring a probability vector from information in the form of constraints. Here we extend this phenomenon, in a discrete setting,…
For certain families of finite quantum graphs, we study the question of how eigenfunctions are distributed over the graph. To characterize properties of the distribution, generalized entropies of the R\'{e}nyi and Tsallis types are…
To characterize strongly interacting statistical systems within a thermodynamical framework - complex systems in particular - it might be necessary to introduce generalized entropies, $S_g$. A series of such entropies have been proposed in…