Related papers: Can \v{C}encov meet Petz?
Here we show that the concepts behind such terms as entanglement, qubits, quantum gates, quantum error corrections, unitary time evolution etc., which are usually ascribed to quantum systems, can be adequately realized on a set of coupled…
We extract the information of a quantum motion and decode it into a certain orbit via a single measurable quantity. Such that a quantum chaotic system can be reconstructed as a chaotic attractor. Two configurations for reconstructing this…
A scheme based on a unifying q-deformed algebra and associated with a generalized Lax operator is proposed for generating integrable quantum and statistical models. As important applications we derive known as well as novel quantum models…
We chart out the landscape of $\Winfty$-type algebras using $\Wkpq$---a recently discovered one-parameter deformation of $\W_{\rm KP}$. We relate all hitherto known $\Winfty$-type algebras to $\Wkpq$ and its reductions, contractions, and/or…
We define a categorical framework in which we build a systematic construction that provides generic invariants for C*-algebras. The benefit is significant as we show that any invariant arising this way automatically enjoys nice properties…
We define a Riesz type interpolation property for the Cuntz semigroup of a $C^*$-algebra and prove it is satisfied by the Cuntz semigroup of every $C^*$-algebra with the ideal property. Related to this, we obtain two characterizations of…
We obtain variants of the classical Minkowski Theorem on inhomogeneous approximation where we require moreover that the solutions $p, q$ be coprime integers. We link the subject with density exponents of lattice orbits in the real plane.
Classical and quantum information theory are simply explained. To be more specific it is clarified why Shannon entropy is used as measure of classical information and after a brief review of quantum mechanics it is possible to demonstrate…
We introduce the notion of a topological higher-rank graph, a unified generalization of the higher-rank graph and the topological graph. Using groupoid techniques, we define the Toeplitz and Cuntz-Krieger algebras of topological higher-rank…
We propose a regular way to construct lattice versions of $W$-algebras, both for quantum and classical cases. In the classical case we write the algebra explicitly and derive the lattice analogue of Boussinesq equation from the Hamiltonian…
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…
Using normal coordinates in a Poincar\'e-Birkhoff-Witt basis for the Hopf algebra of renormalization in perturbative quantum field theory, we investigate the relation between the twisted antipode axiom in that formalism, the Birkhoff…
In this paper, we establish coincidence fixed point and common fixed point theorems for two mapping in complete $C^*$-algebra-valued metric spaces which satisfy new contractive conditions. Some applications of our obtained results are…
We define united K-theory for real C*-algebras, generalizing Bousfield's topological united K-theory. United K-theory incorporates three functors -- real K-theory, complex K-theory, and self-conjugate K-theory -- and the natural…
We investigate Cuntz-Pimsner $C^*$-algebras associated with certain correspondences of the unit circle $\mathbb{T}$. We analyze these $C^*$-algebras by analogy with irrational rotation algebras $A_\theta$ and Cuntz algebras $\mathcal{O}_n$.…
Although the suspicion that quantum mechanics is emergent has been lingering for a long time, only now we begin to understand how a bridge between classical and quantum mechanics might be squared with Bell's inequalities and other…
Quantum machine learning algorithms could provide significant speed-ups over their classical counterparts; however, whether they could also achieve good generalization remains unclear. Recently, two quantum perceptron models which give a…
The article builds on several recent advances in the Monge-Kantorovich theory of mass transport which have -- among other things -- led to new and quite natural proofs for a wide range of geometric inequalities such as the ones formulated…
The state-of-the-art physics consists of two irreconcilable branches, i.e., the quantum theory and the general relativity, which work well in their own territories, independently. However, what are quantum and spacetime after all? The key…
We use $K$-theory of the $C^*$-algebras to study the Arakelov geometry, i.e. a compactification of the arithmetic schemes $V\to Spec ~\mathbf{Z}$. In particular, it is proved that the Picard group of $V$ is isomorphic to the $K_0$-group of…