Related papers: On Ruelle transfer operators and completely positi…
In this work we explain the necessity for consistently labeled rotation maps for efficiently computing coined discrete time quantum walks on regular graphs.
We show a general relation between fixed point stability of suitably perturbed transfer operators and convergence to equilibrium (a notion which is strictly related to decay of correlations). We apply this relation to deterministic…
Quantum channels, a subset of quantum maps, describe the unitary and non-unitary evolution of quantum systems. We study a generalization of the concept of Pauli maps to the case of multipartite high dimensional quantum systems through the…
Information-theoretic measures such as relative entropy and correlation are extremely useful when modeling or analyzing the interaction of probabilistic systems. We survey the quantum generalization of 5 such measures and point out some of…
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…
Quantum mechanics and information theory are among the most important scientific discoveries of the last century. Although these two areas initially developed separately it has emerged that they are in fact intimately related. In this…
We establish the general framework of quantum fluctuation theorems by finding the symmetry between the forward and backward transitions of any given quantum channel. The Petz recovery map is adopted as the reverse quantum channel, and the…
Electron transport in realistic physical and chemical systems often involves the non-trivial exchange of energy with a large environment, requiring the definition and treatment of open quantum systems. Because the time evolution of an open…
Transfer operators and Ruelle zeta functions for super-continuous functions on one-sided topological Markov shifts are considered. For every super-continuous function, we construct a Banach space on which the associated transfer operator is…
We consider the analysis of probability distributions through their associated covariance operators from reproducing kernel Hilbert spaces. We show that the von Neumann entropy and relative entropy of these operators are intimately related…
In a certain sense we generalize the recently introduced and extensively studied notion called quantum R\'enyi divergence (in another name, sandwiched R\'enyi relative entropy) and describe the structures of corresponding symmetries. More…
The transfer operator corresponding to a uniformly expanding map enjoys good spectral properties. Here it is verified that coupling yields explicit estimates that depend continuously on the expansion and distortion constants of the map. For…
It is shown that a fixed point of a completely positive map on a semi-finite von Neumann algebra must commute with the operators determining the map (the Lueders phenomenon) if the element is finite or has finite square.
One of the most challenging open problems in quantum information theory is to clarify and quantify how entanglement behaves when part of an entangled state is sent through a quantum channel. Of central importance in the description of a…
The theme of the paper is the question of existence and basic structure of transfer operators for endomorphisms of a unital C*-algebra. We establish a complete description of non-degenerate transfer operators, characterize complete transfer…
Given a unitary operator in a finite dimensional complex Hilbert space, its unitary reduction to a subspace is defined. The application to quantum graphs is discussed. It is shown how the reduction allows to generate the scattering matrices…
Quantum operations provide a general description of the state changes allowed by quantum mechanics. Simple necessary and sufficient conditions for an ideal quantum operation to be reversible by a unitary operation are derived in this paper.…
Transfer entropy (TE) is an information theoretic measure that reveals the directional flow of information between processes, providing valuable insights for a wide range of real-world applications. This work proposes Transfer Entropy…
We develop a new duality between endomorphisms of measure spaces, on the one hand, and a certain family of positive operators, called transfer operators, acting in spaces of measurable functions on, on the other. A framework of standard…
We apply random matrix and free probability techniques to the study of linear maps of interest in quantum information theory. Random quantum channels have already been widely investigated with spectacular success. Here, we are interested in…