Related papers: Generalized Quantum Baker Maps as perturbations of…
Quantum splines are curves in a Hilbert space or, equivalently, in the corresponding Hilbert projective space, which generalize the notion of Riemannian cubic splines to the quantum domain. In this paper, we present a generalization of this…
For a given set of input-output pairs of quantum states or observables, we ask the question whether there exists a physically implementable transformation that maps each of the inputs to the corresponding output. The physical maps on…
We investigate the set a) of positive, trace preserving maps acting on density matrices of size N, and a sequence of its nested subsets: the sets of maps which are b) decomposable, c) completely positive, d) extended by identity impose…
We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure is generic (with…
We study quantum maps displaying spectral statistics intermediate between Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum computer with a small number of gates, and efficiently yield information about fidelity…
Graph kernels are often used in bioinformatics and network applications to measure the similarity between graphs; therefore, they may be used to construct efficient graph classifiers. Many graph kernels have been developed thus far, but to…
Quantum systems with Hofstadter's butterfly spectrum are of fundamental interest to many research areas. Based upon slight modifications of existing cold-atom experiments, a cold-atom realization of quantum maps with Hofstadter's butterfly…
The notion of a quantum family of maps has been introduced in the framework of C*-algebras. As in the classical case, one may consider a quantum family of maps preserving additional structures (e.g. quantum family of maps preserving a…
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…
This work provides theoretical foundations for kernel methods in the hyperspherical context. Specifically, we characterise the native spaces (reproducing kernel Hilbert spaces) and the Sobolev spaces associated with kernels defined over…
In this article, the two-parameter quantum Heisenberg enveloping algebra, which serves as a model for certain quantum generalized Heisenberg algebras, have been studied at roots of unity. In this context, the quantum Heisenberg enveloping…
Algebro-geometric methods have proven to be very successful in the study of graphical models in statistics. In this paper we introduce the foundations to carry out a similar study of their quantum counterparts. These quantum graphical…
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…
Quantum processors may enhance machine learning by mapping high-dimensional data onto quantum systems for processing. Conventional feature maps, for encoding data onto a quantum circuit are currently impractical, as the number of entangling…
We study the quantum mechanics of a generalized version of the baker's map. We show that the Ruelle resonances (which govern the approach to ergodicity of classical distributions on phase space) also appear in the quantum correlation…
Various generalizations of Cuntz algebras and their relations to symmetry and duality are reviewed. New generalized Cuntz algebras are associated with a subfactor. A characteristic Hilbert space of basic invariants (with respect to the…
The axioms of quantum mechanics provide limited information regarding the structure of the Hilbert space, such as the underlying number system. The latter is generally regarded as complex, but generalizations of complex numbers, so-called…
We introduce the notion of Benjamini-Schramm convergence for quantum graphs. This notion of convergence, intended to play the role of the already existing notion for discrete graphs, means that the restriction of the quantum graph to a…
In this paper, we introduce the notion of reproducing kernel Hilbert spaces for graphs and the Gram matrices associated with them. Our aim is to investigate the Gram matrices of reproducing kernel Hilbert spaces. We provide several bounds…
This paper is devoted to the study of vector valued reproducing kernel Hilbert spaces. We focus on two aspects: vector valued feature maps and universal kernels. In particular we characterize the structure of translation invariant kernels…