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The relationships between quantum entangled states and braid matrices have been well studied in recent years. However, most of the results are based on qubits. In this paper, we investigate the applications of 2-qutrit entanglement in the braiding associated with Z 3 parafermion. The 2-qutrit entangled state | Ψ ( θ ) 〉 , generated by the action of the localized unitary solution R ˘ ( θ ) of YBE on 2-qutrit natural basis, achieves its maximal ℓ 1 -norm and maximal von Neumann entropy simultaneously at θ = π / 3 . Meanwhile, at θ = π / 3 , the solutions of YBE reduces braid matrices, which implies the role of ℓ 1 -norm and entropy plays in determining real physical quantities. On the other hand, we give a new realization of 4-anyon topological basis by qutrit entangled states, then the 9 × 9 localized braid representation in 4-qutrit tensor product space ( C 3 ) ⊗ 4 is reduced to Jones representation of braiding in the 4-anyon topological basis. Hence, we conclude that the entangled states are powerful tools in analysing the characteristics of braiding and R ˘ -matrix. [ABSTRACT FROM AUTHOR]

The solutions of Yang-Baxter equation (YBE) associated with quantum information have been reviewed with new progress. The additivity rule for two particles is shown to obey Lorentzian type other than the Gallilean. Acting the braiding operations on the topological basis, it turns out that the -dimensional representations obeying YBE are nothing but the Wigner's -functions. The connection between the extremization of -norm as well as of von Neumann entropy and the reduction of YBE to braid relation is also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we review some results obtained in our works with extension. The new type of braiding matrices called type-II has been extended to the solutions of Yang-Baxter equations (YBE). It is related to quantum entangling states. The four-dimensional realization is connected with Majorana fermions and the two-dimensional realization for the topological basis is the wigner DJ-function with J = 1/2. The YBE leads to the conclusion that the additivity rule of velocities for two anyons obeys Lorentz rather than Galilean. The discussion is extended to three body S-matrix formed by three two-body S-matrices. The three-qubit entanglement based on two-qubit entanglements is discussed. [ABSTRACT FROM AUTHOR]

The connection between Yang-Baxter system and quantum information has been discussed. Based on the topological basis for both Temperley-Lieb (TL) algebra and Birman-Wenzl (BW) algebra the representations of N by N braiding matrices associated with the corresponding N2 by N2 ones are obtained. Some of physical consequences of the braiding matrices connecting with quantum information are shown. [ABSTRACT FROM AUTHOR]

We clarify the on-going confusion on the long-standing gauge invariance problem of the nucleon spin decomposition to the spin and angular momentum of quarks and gluons. We provide two gauge-invariant decompositions of nucleon spin which have different physical meanings, using the gauge independent Abelian decomposition. The first one is based on the assumption that all (binding and valence) gluons contribute to the nucleon spin, but the second one is based on the assumption that only the binding gluons (and the quarks) contribute to it. [ABSTRACT FROM AUTHOR]

We find raising and lowering operators distinguishing the degenerate states for the Hamiltonian H = χ(K + ½)S[sub z] + K · S at χ = ±1 for spin 1 that was given by Happer et al. to interpret the curious degeneracies of the Zeeman effect for condensed vapor of [sup 87]Rb. The operators obey Yangian commutation relations. We show that the curious degeneracies seem to verify the Yangian algebraic structure for quantum tensor space and are consistent with the representation theory of Y(sl(2)). [ABSTRACT FROM AUTHOR]

In this paper it is proved that the nontrivial finite-dimensional irreducible representations of the quantum matrix algebra Mq(2) [or the coordinate ring of the quantum group GLq(2)] exist only when q is a root of unity, and thereby construct such representations for Mq(2). Some finite-dimensional indecomposable representations of Mq(2) are also explicitly presented. Finally, the q-boson realization of Mq(2) is discussed, and it is shown that it works in this case as well as in the quantum algebra case. [ABSTRACT FROM AUTHOR]

A parametrized cyclic representation of the q-deformed Heisenberg–Weyl algebras is constructed. The cyclic representations of any quantum algebras are studied in terms of their q-boson realizations. A general method to construct the q-boson realizations of quantum algebras from their Verma representations is proposed. Two explicit examples sl(2)q and sl(3)q are studied in detail. Some cyclic representations of quantum algebras sl(n)q and UqCn are presented by using their q-boson realizations. [ABSTRACT FROM AUTHOR]

The more general algebraic structures of two-dimensional integrable systems are derived in a model independent manner by using the infinitesimal Riemann–Hilbert transformation. It is found that the resulting algebra decomposes into many families and, for each family, there is a Lie multialgebra structure. Examples of the chiral sigma models, four-dimensional self-dual Yang–Mills field, sine–Gordon, and Liouville equations and the BZ gravity are given with two special Lie products equipped therein. [ABSTRACT FROM AUTHOR]

By directly solving quantum Yang–Baxter equations (QYBE) in terms of the extended expansion scheme, besides the known solutions we find new family of solutions of braid group representations associated with the fundamental representations of An, Bn, Cn, and Dn. [ABSTRACT FROM AUTHOR]

In this paper, a realization of the q-deformed boson operators on the Fock space from a generally algebraic point of view is given. The representations of the quantum group (Cn)q are thereby constructed in terms of this realization. Some infinite- and finite-dimensional representations of the q-analog of the Heisenberg–Weyl algebra are obtained on certain quotient spaces. Finally, the q-deformed differential realization of quantum group given by Alvarez-Gaume, Gomez, and Sierra (Preprint CERN-Th 5369/89) is derived from the boson realization. [ABSTRACT FROM AUTHOR]

A general formulation is given for deriving a Kac–Moody algebra in the spectrum space from the infinitesimal regular Riemann–Hilbert transform. Such a Kac–Moody algebra can be obtained for many nonlinear systems, e.g., the (super) principal chiral model with or without a Wess–Zumino–Witten term, the sine-Gordon, Liouville, and KdV equations; reduced two-dimensional gravity (Belinski–Zakharov gravity), and self-dual supersymmetric Yang–Mills theories. [ABSTRACT FROM AUTHOR]