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The phenomenon of quantum entanglement is thoroughly investigated, focussing especially on geometrical aspects and on bipartite systems. After introducing the formalism and discussing general aspects, some of the most important separability…
Through the quantum trajectory approach, we calculate the geometric phase acquired by a bipartite system subjected to decoherence. The subsystems that compose the bipartite system interact with each other, and then are entangled in the…
We use geometric ideas coming from certain classic algebraic constructions to associate, to every classical field theory, a symmetric monoidal double functor from the double category of cobordisms with corners to a certain symmetric…
When the Euclidean algorithm produces a symmetric sequence of quotients, we give explicit formulas for the remainders that allow the analysis of two families of quadratic forms in the remainders.
The q-binomial formula in the limit q->1 is shown to be equivalent to the Rogers five term dilogarithm identity.
A class of quantum analogues of compact symmetric spaces of classical type is introduced by means of constant solutions to the reflection equations. Their zonal spherical functions are discussed in connection with $q$-orthogonal…
Quantum Entanglement is one of the key manifestations of quantum mechanics that separate the quantum realm from the classical one. Characterization of entanglement as a physical resource for quantum technology became of uppermost…
We reexamine quantum correlation from the fundamental perspective of its consanguineous quantum property, the coherence. We emphasize the importance of specifying the tensor product structure of the total state space before discussing…
We define and study the space of $q$-opers associated with Bethe equations for integrable models of XXZ type with quantum toroidal algebra symmetry. Our construction is suggested by the study of the enumerative geometry of cyclic quiver…
In this paper, we construct the multicomponent modified KP hierarchy and its additional symmetries. The additional symmetries constitute an interesting multi-folds quantum torus type Lie algebra. By a reduction, we also construct the…
Entanglement is one of important resources for quantum communication tasks. Most of results are focused on qubit entanglement. Our goal in this work is to characterize the multipartite high-dimensional entanglement. We firstly derive an…
Quantum coherence and quantum correlations are of fundamental and practical significance for the development of quantum mechanics.They are also cornerstones of quantum computation and quantum communication theory. Searching physically…
In this talk, we give a brief overview of several aspects of the theory of the chiral Potts model, including higher-genus solutions of the star-triangle and tetrahedron equations, cyclic representations of affine quantum groups, basic…
Several kinds of q-orthogonal polynomials with |q|=1 are constructed as the main parts of the eigenfunctions of new solvable discrete quantum mechanical systems. Their orthogonality weight functions consist of quantum dilogarithm functions,…
We describe a cohomological framework for measurement based quantum computation, in which symmetry plays a central role. Therein, the essential information about the computational output is contained in topological invariants, namely…
We consider some generalization of the theory of quantum states and demonstrate that the consideration of quantum states as sheaves can provide, in principle, more deep understanding of some well-known phenomena. The key ingredients of the…
Obtaining the symmetries of a model is a critical step towards developing an understanding and ultimately analytically or numerically solving the model. However, finding symmetries is generally extremely complicated, often being the result…
In this paper, we consider three types of polynomial equations in quantum computer: linear divisibility equation, which belongs to a special type of binary-quadratic Diophantine equation; quadratic congruence equation with restriction in…
The article provides an overview of some advances in the mathematical understanding of the nature of the kinetic equations of quantum systems of many particles. The fundamental equations of modern mathematical physics are studied, in…
We geometrically prove that in a d-dimensional cube with edges of length n, the number of particular d-dimensional tetrahedrons are given by Eulerian numbers. These tetrahedrons tassellate the cube, In this way the sum of the cubes are the…