GHZ States, Almost-Complex Structure and Yang--Baxter Equation (I)

Direct Experimental Simulation of the Yang-Baxter Equation

Introduced in the field of many-body statistical mechanics, Yang-Baxter equation has become an important tool in a variety fields of physics. In this work, we report the first direct experimental simulation of the Yang-Baxter equation using linear quantum optics. The equality between the two sides of the Yang-Baxter equation in two dimension has been demonstrated directly, and the spectral parameter transformation in the Yang-Baxter equation is explicitly confirmed.

Berry phase and quantum criticality in Yang--Baxter systems

Spin interaction Hamiltonians are obtained from the unitary Yang--Baxter $\breve{R}$-matrix. Based on which, we study Berry phase and quantum criticality in the Yang--Baxter systems.

Action in Hamiltonian Models Constructed by Yang-Baxter Equation: Entanglement and Measures of Correlation

By using the quantum Yang-Baxterization approach, we investigate the dynamics of quantum entanglement under the actions of different Hamiltonians on the different two-qubit input states and analyze the effects of the Yang-Baxter operations on it. During any quantum process that takes place in a noisy environment, quantum correlations display behavior that does not increase. We point out that for two-qubit systems subject to actions of different Yang-Baxter operations the loss of correlations can be mitigated by the appropriate choice of the initial states and the Yang-Baxterization process. We…

Temperley-Lieb Algebra, Yang-Baxterization and Universal Gate

A method of constructing $n^{2}\times n^{2}$ matrix solutions(with $n^{3}$ matrix elements) of Temperley-Lieb algebra relation is presented in this paper. The single loop of these solutions are $d=\sqrt{n}$. Especially, a $9\times9-$matrix solution with single loop d=$\sqrt{3}$ is discussed in detail. An unitary Yang-Baxter $\breve{R}(θ,q_{1},q_{2})$ matrix is obtained via the Yang-Baxterization process. The entanglement property and geometric property (\emph{i.e.} Berry Phase) of this Yang-Baxter system are explored.

Unitary Solutions to the Yang-Baxter Equation in Dimension Four

In this paper, we determine all unitary solutions to the Yang-Baxter equation in dimension four. Quantum computation motivates this study. This set of solutions will assist in clarifying the relationship between quantum entanglement and topological entanglement. We present a variety of facts about the Yang-Baxter equation for the reader unfamiliar with the equation.

Quantum Yang-Baxter equation, arbitrary gradings and exchange Hecke braidings

Generalization of the quantum Yang-Baxter equation solutions to an arbitrary grading is studied. The noncommutative differential calculi corresponding to such solutions is considered. The connection with the ordinary and supersymmetric solutions of the quantum Yang-Baxter equation is given.

Optical Simulation of Yang-Baxter Equation

In this paper, several proposals of optically simulating Yang-Baxter equations have been presented. Motivated by the recent development of anyon theory, we apply Temperley-Lieb algebra as a bridge to recast four-dimentional Yang-Baxter equation into its two-dimensional counterpart. In accordance with both representations, we find the corresponding linear-optical simulations, based on the highly efficient optical elements. Both the freedom degrees of photon polarization and location are utilized as the qubit basis, in which the unitary Yang-Baxter matrices are decomposed into combination of act…

The representations of Temperley-Lieb algebras and entanglement in a Yang-Baxter system

A method of constructing Temperley-Lieb algebras(TLA) representations has been introduced in [Xue \emph{et.al} arXiv:0903.3711]. Using this method, we can obtain another series of $n^{2}\times n^{2}$ matrices $U$ which satisfy the TLA with the single loop $d=\sqrt{n}$. Specifically, we present a $9\times9$ matrix $U$ with $d=\sqrt{3}$. Via Yang-Baxterization approach, we obtain a unitary $ \breve{R}(θ,φ_{1},φ_{2})$-matrix, a solution of the Yang-Baxter Equation. This $9\times9$ Yang-Baxter matrix is universal for quantum computing.

All Pure Two-Qudit Entangled States Can be Generated via a Universal Yang--Baxter Matrix Assisted by Local Unitary Transformations

We show that all pure entangled states of two $d$-dimensional quantum systems (i.e., two qudits) can be generated from an initial separable state via a universal Yang--Baxter matrix if one is assisted by local unitary transformations.

Entanglement and Berry Phase in a $9\times 9$ Yang-Baxter system

A M-matrix which satisfies the Hecke algebraic relations is presented. Via the Yang-Baxterization approach, we obtain a unitary solution $\breve{R}(θ,φ_{1},φ_{2})$ of Yang-Baxter Equation. It is shown that any pure two-qutrit entangled states can be generated via the universal $\breve{R}$-matrix assisted by local unitary transformations. A Hamiltonian is constructed from the $\breve{R}$-matrix, and Berry phase of the Yang-Baxter system is investigated. Specifically, for $ φ_{1}=φ_{2}$, the Hamiltonian can be represented based on three sets of SU(2) operators, and three oscillator Hamiltonians …

带杨-巴克斯特门的砖墙电路中算子纠缠的增长

On the growth of operator entanglement in brickwork circuits with Yang--Baxter gates

该研究针对带杨-巴克斯特门的一维砖墙电路，建立了算子施密特秩的多种增长上界，构造了反例证明部分情形下的指数增长，相关结果为算子纠缠增长问题提供了重要进展。

Yang-Baxter operators need quantum entanglement to distinguish knots

Any solution to the Yang-Baxter equation yields a family of representations of braid groups. Under certain conditions, identified by Turaev, the appropriately normalized trace of these representations yields a link invariant. Any Yang-Baxter solution can be interpreted as a two-qudit quantum gate. Here we show that if this gate is non-entangling, then the resulting invariant of knots is trivial. We thus obtain a general connection between topological entanglement and quantum entanglement, as suggested by Kauffman et al.

Yang-Baxter integrable Lindblad equations

We consider Lindblad equations for one dimensional fermionic models and quantum spin chains. By employing a (graded) super-operator formalism we identify a number of Lindblad equations than can be mapped onto non-Hermitian interacting Yang-Baxter integrable models. Employing Bethe Ansatz techniques we show that the late-time dynamics of some of these models is diffusive.