Publications

We consider a non-abelian leakage-free qudit system that consists of two qubits each composed of three anyons. For this system, we need to have a non-abelian four dimensional unitary representation of the braid group B6 to obtain a totally leakage-free braiding. The obtained representation is denoted by . We first prove that  is irreducible. Next, we find the points y 2 C at which the representation  is equivalent to the tensor product of a one dimensional representation (y) and ˆ 6(i), an irreducible four dimensional representation of the braid group B6. The representation ˆ 6(i) was constructed by E. Formanek to classify the irreducible representations of the braid group Bn of low degree. Finally, we prove that the representation (y) ˆ 6(i) is a unitary relative to a hermitian positive definite matrix.