Related papers: Upper continuity bounds on the relative $q$-entrop…
While a positive operator valued measure gives the probabilities in a quantum measurement, an instrument gives both the probabilities and the a posteriori states. By interpreting the instrument as a quantum channel and by using the…
The generalized covariant entropy bound is the conjecture that the entropy of the matter present on any non-expanding null hypersurface L will not exceed the difference between the areas, in Planck units, of the initial and final spatial…
We introduce variants of relative entropy of entanglement based on the optimal distinguishability from unentangled states by means of restricted measurements. In this way, we are able to prove that the standard regularized entropy of…
In the first part of this thesis, we present a general technique for establishing local and uniform continuity bounds for Schur concave functions. Our technique uses a particular relationship between majorization and the trace distance…
Based on the q-exponential distribution which has been observed in more and more physical systems, the varentropy method is used to derive the uncertainty measure of such an abnormal distribution function. The uncertainty measure obtained…
In this paper a general definition of quantum conditional entropy for infinite-dimensional systems is given based on recent work of Holevo and Shirokov arXiv:1004.2495 devoted to quantum mutual and coherent informations in the…
In this paper, we introduce two bounds which we call the Upper Differential Entropy and the Lower Differential Entropy for an infinite family of intervals(strips) in quantum field theory. The two bounds are equal provided that the theory is…
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,…
Quantum entanglement in 3 spatial dimensions is studied in systems with physical boundaries when an entangling surface intersects the boundary. We show that there are universal logarithmic boundary terms in the entanglement R\'{e}nyi…
We present upper and lower bounds to the relative entropy of entanglement of multi-party systems in terms of the bi-partite entanglements of formation and distillation and entropies of various subsystems. We point out implications of our…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
We introduce a simplified version of Connes-Narnhofer-Thirring's quantum dynamical entropy for quantum systems. It quantifies the amount of information gained about the initial condition from continuously monitoring an observable. A nonzero…
The relative entropy of entanglement $E_R$ is defined as the distance of a multi-partite quantum state from the set of separable states as measured by the quantum relative entropy. We show that this optimisation is always achieved, i.e. any…
We conjecture a universal upper bound to the entropy of a rotating system. The entropy bound follows from application of the generalized second law of thermodynamics to an idealized gedanken experiment in which an entropy-bearing rotating…
We investigate the behavior of the entanglement entropy of a confining gauge theory near cosmological singularities using gauge/gravity duality. As expected, the coefficients of the UV divergent terms are given by simple geometric…
It is shown that the R\'enyi and Tsallis entropies and the q-expectation values, are continuous and stable if $q>1$ and are not continuous and instable for uniform finite distributions if $q<1$.
The characterization of irreversibility in general quantum processes is an open problem of increasing techno- logical relevance. Yet, the tools currently available to this aim are mostly limited to the assessment of dynamics induced by…
The maximum entropy of a quantized surface is demonstrated to be proportional to the surface area in the classical limit. The result is valid in loop quantum gravity, and in a somewhat more general class of approaches to surface…
Purely multiplicative comparisons of quantum relative entropy are desirable but challenging to prove. We show such comparisons for relative entropies between comparable densities, including the relative entropy of a density with respect to…
We compute the quantum Renyi relative entropies in an infinite spinless fermionic chain with a defect. Doing a numerical analysis we will show that the resulting quantity depends non trivially on the effective central charge of the theory.…