相关论文: Quantum anchor : $\uqs$ case

Let $k(S^2_q)$ be the "coordinate ring" of a quantum sphere. We introduce the cotangent module on the quantum sphere as a one-sided $k(S^2_q)$-module and show that there is no Yang-Baxter type operator converting it into a…

A new approach is suggested to quantum differential calculus on certain quantum varieties. It consists in replacing quantum de Rham complexes with differentials satisfying Leibniz rule by those which are in a sense close to Koszul complexes…

Lie groups and quantum algebras are connected through their common universal enveloping algebra. The adjoint action of Lie group on its algebra is naturally extended to related q-algebra and q-coalgebra. In such a way, quantum structure can…

Correlation functions of quantum systems -- central objects in quantum field theories -- are defined in high-dimensional space-time domains. Their numerical treatment thus suffers from the curse of dimensionality, which hinders the…

We introduce the notion of a braided Lie algebra consisting of a finite-dimensional vector space $\CL$ equipped with a bracket $[\ ,\ ]:\CL\tens\CL\to \CL$ and a Yang-Baxter operator $\Psi:\CL\tens\CL\to \CL\tens\CL$ obeying some axioms. We…

Entanglement in high-dimensional quantum systems, where one or more degrees of freedom of light are involved, offers increased information capacities and enables new quantum protocols. Here, we demonstrate a functional source of…

Motivated by topology, we develop a general theory of traces and shadows for an endobicategory, which is a~pair: bicategory $\mathbf{C}$ and endobifunctor $\Sigma\colon \mathbf C \to\mathbf C$. For a graded linear bicategory and a fixed…

Quantum integrable systems and their classical counterparts are considered. We show that the symplectic structure and invariant tori of the classical system can be deformed by a quantization parameter $\hbar$ to produce a new (classical)…

Using a super-realization of the Wigner-Heisenberg algebra a new realization of the q-deformed Wigner oscillator is implemented.

Entanglement is a non local property of quantum states which has no classical counterpart and plays a decisive role in quantum information theory. Several protocols, like the teleportation, are based on quantum entangled states. Moreover,…

A q-deformed version of classical analysis is given to quantum spaces of physical importance, i.e. Manin plane, q-deformed Euclidean space in three or four dimensions, and q-deformed Minkowski space. The subject is presented in a rather…

We introduce an analog of the Maxwell operator on a q-Minkowski space algebra (treated as a particular case of the so-called Reflection Equation Algebra) and on certain of its quotients. We treat the space of "quantum differential forms" as…

It is shown that the principle of locality and noncommutative geometry can be connnected by a sheaf theoretical method. In this framework quantum spaces are introduced and examples in mathematical physics are given. With the language of…

We construct an explicit categorification of the action of tangles on tensor powers of the fundamental representation of quantum sl(2).

Entanglement is defined for each vector subspace of the tensor product of two finite-dimensional Hilbert spaces, by applying the notion of operator entanglement to the projection operator onto that subspace. The operator Schmidt…

Attention is focused on q-deformed quantum algebras with physical importance, i.e. $U_{q}(su_{2})$, $U_{q}(so_{4})$ and q-deformed Lorentz algebra. The main concern of this article is to assemble important ideas about these symmetry…

Considering anyonic oscillators in a two-dimensional lattice, we realize the quantum semi-group $sl_{(q,s)}(2)$ by means of a generalized Schwinger construction. We find that the parameter $q$ of the algebra is connected to the statistical…

Quantum annealing is analogous to simulated annealing with a tunneling mechanism substituting for thermal activation. Its performance has been tested in numerical simulation with mixed conclusions. There is a class of optimization problems…

In this note we present preliminary study on the relation between the quantum entanglement of boundary states and the quantum geometry in the bulk in the framework of spin networks. We conjecture that the emergence of space with non-zero…

This paper discusses relationships between topological entanglement and quantum entanglement. Specifically, we propose that for this comparison it is fundamental to view topological entanglements such as braids as "entanglement operators"…