A study on the relations between the topological parameter and entanglement

In this paper, some relations between the topological parameter $d$ and concurrences of the projective entangled states have been presented. It is shown that for the case with $d=n$, all the projective entangled states of two $n$-dimensional quantum systems are the maximally entangled states (i.e. $C=1$). And for another case with $d\neq n$, $C$ both approach $0$ when $d\rightarrow +\infty$ for $n=2$ and $3$. Then we study the thermal entanglement and the entanglement sudden death (ESD) for a kind of Yang-Baxter Hamiltonian. It is found that the parameter $d$ not only influences the critical temperature $T_{c}$, but also can influence the maximum entanglement value at which the system can arrive at. And we also find that the parameter $d$ has a great influence on the ESD.Comment: 8 pages, 5 figure

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

Non-adiabatic holonomic quantum computation in linear system-bath coupling

Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of $\frac{N-2}{N}$. The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities.Comment: 2 figures; accepted by Sci. Re