Generating W states with braiding operators

Braiding operators can be used to create entangled states out of product states, thus establishing a correspondence between topological and quantum entanglement. This is well-known for maximally entangled Bell and GHZ states and their equivalent states under Stochastic Local Operations and Classical Communication, but so far a similar result for W states was missing. Here we use generators of extraspecial 2-groups to obtain the W state in a four-qubit space and partition algebras to generate the W state in a three-qubit space. We also present a unitary generalized Yang-Baxter operator that embeds the W$_n$ state in a $(2n-1)$-qubit space.Comment: 13 pages, Published versio

Solutions to generalized Yang-Baxter equations via ribbon fusion categories

Inspired by quantum information theory, we look for representations of the braid groups $B_n$ on $V^{\otimes (n+m-2)}$ for some fixed vector space $V$ such that each braid generator $\sigma_i, i=1,...,n-1,$ acts on $m$ consecutive tensor factors from $i$ through $i+m-1$. The braid relation for $m=2$ is essentially the Yang-Baxter equation, and the cases for $m>2$ are called generalized Yang-Baxter equations. We observe that certain objects in ribbon fusion categories naturally give rise to such representations for the case $m=3$. Examples are given from the Ising theory (or the closely related $SU(2)_2$), $SO(N)_2$ for $N$ odd, and $SU(3)_3$. The solution from the Jones-Kauffman theory at a $6^{th}$ root of unity, which is closely related to $SO(3)_2$ or $SU(2)_4$, is explicitly described in the end.Comment: Some minor change

Quantum entanglement, supersymmetry, and the generalized Yang-Baxter equation

Entangled states, such as the Bell and GHZ states, are generated from separable states using matrices known to satisfy the Yang-Baxter equation and its generalization. This remarkable fact hints at the possibility of using braiding operators as quantum entanglers, and is part of a larger speculated connection between topological and quantum entanglement. We push the analysis of this connection forward, by showing that supersymmetry algebras can be used to construct large families of solutions of the spectral parameter-dependent generalized Yang-Baxter equation. We present a number of explicit examples and outline a general algorithm for arbitrary numbers of qubits. The operators we obtain produce, in turn, all the entangled states in a multi-qubit system classified by the Stochastic Local Operations and Classical Communication protocol introduced in quantum information theory

Quantum Computing via The Bethe Ansatz

We recognize quantum circuit model of computation as factorisable scattering model and propose that a quantum computer is associated with a quantum many-body system solved by the Bethe ansatz. As an typical example to support our perspectives on quantum computation, we study quantum computing in one-dimensional nonrelativistic system with delta-function interaction, where the two-body scattering matrix satisfies the factorisation equation (the quantum Yang--Baxter equation) and acts as a parametric two-body quantum gate. We conclude by comparing quantum computing via the factorisable scattering with topological quantum computing.Comment: 6 pages. Comments welcom

Method of constructing braid group representation and entanglement in a Yang-Baxter sysytem

In this paper we present reducible representation of the $n^{2}$ braid group representation which is constructed on the tensor product of n-dimensional spaces. By some combining methods we can construct more arbitrary $n^{2}$ dimensional braiding matrix S which satisfy the braid relations, and we get some useful braiding matrix S. By Yang-Baxteraition approach, we derive a $9\times9$ unitary $\breve{R}$ according to a $9\times9$ braiding S-matrix we have constructed. The entanglement properties of $\breve{R}$-matrix is investigated, and the arbitrary degree of entanglement for two-qutrit entangled states can be generated via $\breve{R}(\theta, \phi_{1},\phi_{2})$-matrix acting on the standard basis.Comment: 9 page