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We provide a compendium of inequalities between several quantum state distinguishability measures. For each measure these inequalities consist of the sharpest possible upper and lower bounds in terms of another measure. Some of these…
We derive tight quadratic inequalities for all kinds of hybrid separable-inseparable $n$-particle density operators on an arbitrary dimensional space. This methodology enables us to truly derive a tight quadratic inequality as tests for…
The tight, in a sense, lower estimates of diamond-norm distance from a given quantum channel to the sets of degradable, antidegradable and entanglement-breaking channels are obtained via the tight continuity bounds for quantum mutual…
We give a pedagogical introduction to quantum discord. We the discuss the problem of separation of total correlations in a given quantum state into entanglement, dissonance, and classical correlations using the concept of relative entropy…
A renormalized version of the von Neumann quantum entropy (which is finite and continuous in general, infinite dimensional case) and which obeys several of the natural physical demands (as expected for a "good" measure of entanglement in…
A well-known boundary observability inequality for the elasticity system establishes that the energy of the system can be estimated from the solution on a sufficiently large part of the boundary for a sufficiently large time. This…
We propose in this work a practical approach to address the longstanding and challenging problem of quantum separability, leveraging the correlation matrices of generic observables. General separability conditions are obtained by dint of…
Clausius inequality has deep implications for reversibility and the arrow of time. Quantum theory is able to extend this result for closed systems by inspecting the trajectory of the density matrix on its manifold. Here we show that this…
For any Bell locality scenario (or Kochen-Specker noncontextuality scenario), the joint Shannon entropies of local (or noncontextual) models define a convex cone for which the non-trivial facets are tight entropic Bell (or contextuality)…
We present an analytical solution for classical correlation, defined in terms of linear entropy, in an arbitrary $d\otimes 2$ system when the second subsystem is measured. We show that the optimal measurements used in the maximization of…
We sharpen the moment comparison inequalities with sharp constants for sums of random vectors uniform on Euclidean spheres, providing a deficit term (optimal in high dimensions).
We show that universal quantum computation can be achieved in the standard pure-state circuit model while, at any time, the entanglement entropy of all bipartitions is small---even tending to zero with growing system size. The result is…
Summary. A simple derivation of finite Schmidt decomposition of pure states describing finite dimensional systems interacting with the infinite dimensional ones is presented. In particular, maximally entangled pure states in such systems…
Separability is an important problem in theory of quantum entanglement. By using the Bloch representation of quantum states in terms of the Heisenberg-Weyl observable basis, we present a new separability criterion for bipartite quantum…
Entanglement entropy appears as a central property of quantum systems in broad areas of physics. However, its precise value is often sensitive to unknown microphysics, rendering it incalculable. By considering parametric dependence on…
The uncertainty relation based on the Shannon entropies of the probability densities in position and momentum spaces is improved for quantum systems in arbitrary $D$-dimensional spherically symmetric potentials. To find it, we have used the…
Entanglement entropies have revealed, in the last years, to be a powerful tool to extract information about the physics of condensed-matter systems. In the first part of this thesis, we show how to extract essential details about the…
A criterion and necessary conditions for convergence (local continuity) of the quantum relative entropy are obtained. Some applications of these results are considered. In particular, the preservation of local continuity of the quantum…
A short and elementary proof of the joint convexity of relative entropy is presented, using nothing beyond linear algebra. The key ingredients are an easily verified integral representation and the strategy used to prove the Cauchy-Schwarz…
For any discrete time dynamical system with a rational evolution, we define an entropy, which is a global index of complexity for the evolution map. We analyze its basic properties and its relations to the singularities and the…