Related papers: Entropic trade-off relations for quantum operation…
A large class of strongly correlated quantum systems can be described in certain large-N limits by quadratic in field actions along with self-consistency equations that determine the two-point functions. We use the replica approach and the…
We revisit the relationship between quantum separability and the sign of the relative q-entropies of composite quantum systems. The q-entropies depend on the density matrix eigenvalues p_i through the quantity omega_q = sum_i p_i^q. Renyi's…
We define a natural ensemble of trace preserving, completely positive quantum maps and present algorithms to generate them at random. Spectral properties of the superoperator Phi associated with a given quantum map are investigated and a…
For a given quantum state $\rho$ and two quantum operations $\Phi$ and $\Psi$, the information encoded in the quantum state $\rho$ is quantified by its von Neumann entropy $\S(\rho)$. By the famous Choi-Jamio{\l}kowski isomorphism, the…
The minimum entropy output is computed for rotationally invariant quantum channels acting on spin-1/2 and spin-1 systems. For the case of two parallel such channels and initial entangled (singlet) state the entropy of the output is higher…
In this work we prove that the possibility of superactivation of quantum channel capacities is determined by the mathematical properties of the quantum relative entropy function. Before our work this fundamental and purely mathematical…
Entropy, and its temporal evolution, play a central role in the foundations of quantum theory and in modern quantum technologies. Here we study, in particular, the relations between the --- in general, non-Markovian --- evolution of an open…
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 formulate a universal characterization of the many-particle quantum entanglement in the ground state of a topologically ordered two-dimensional medium with a mass gap. We consider a disk in the plane, with a smooth boundary of length L,…
We offer new methods for characterizing general closed and convex quantum resource theories, including dynamic ones, based on entropic concepts and operational tasks. We propose a resource-theoretic generalization of the quantum conditional…
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…
In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time…
We show that the rate of increase of von Neumann entropy computed from the reduced density matrix of an open quantum system is an excellent indicator of the dynamical behavior of its classical hamiltonian counterpart. In decohering quantum…
We study the scaling behavior of the entanglement entropy of two dimensional conformal quantum critical systems, i.e. systems with scale invariant wave functions. They include two-dimensional generalized quantum dimer models on bipartite…
We characterize different cell states, related to cancer and ageing phenotypes, by a measure of entropy of network ensembles, integrating gene expression values and protein interaction networks. The entropy measure estimates the parameter…
The theory of noncommutative dynamical entropy and quantum symbolic dynamics for quantum dynamical systems is analised from the point of view of quantum information theory. Using a general quantum dynamical system as a communication channel…
Environmental interactions are ubiquitous in any real-world application of a quantum information processing protocol. Such interactions result in depletion of quantum resources. Two important figure of merits in the context of quantum…
Finding the minimal relative entropy of two quantum states under semidefinite constraints is a pivotal problem located at the mathematical core of various applications in quantum information theory. An efficient method for providing…
We study the behavior of bipartite entanglement at fixed von Neumann entropy. We look at the distribution of the entanglement spectrum, that is the eigenvalues of the reduced density matrix of a quantum system in a pure state. We report the…
Fundamental limits on communication rates over quantum channels are given by mathematical expressions involving entropic formulas. Often, it is unclear if these expressions are computable. This thesis describes contributions to the study of…