Generation of pure, ionic entangled states via linear optics

In this paper, we propose a novel scheme to generate two-ion maximally entangled states from either pure product states or mixed states using linear optics. Our new scheme is mainly based on the ionic interference. Because the proposed scheme can generate pure maximally entangled states from mixed states, we denote it as purification-like generation scheme. The scheme does not need a Bell state analyzer as the existing entanglement generation schemes do, it also avoids the difficulty of synchronizing the arrival time of the two scattered photons faced by the existing schemes, thus the proposed new entanglement generation scheme can be implemented more easily in practice.Comment: 6 pages, 4 figure

Entanglement in the anisotropic Heisenberg XYZ model with different Dzyaloshinskii-Moriya interaction and inhomogeneous magnetic field

We investigate the entanglement in a two-qubit Heisenberg XYZ system with different Dzyaloshinskii-Moriya(DM) interaction and inhomogeneous magnetic field. It is found that the control parameters ($D_{x}$, $B_{x}$ and $b_{x}$) are remarkably different with the common control parameters ($D_{z}$,$B_{z}$ and $b_{z}$) in the entanglement and the critical temperature, and these x-component parameters can increase the entanglement and the critical temperature more efficiently. Furthermore, we show the properties of these x-component parameters for the control of entanglement. In the ground state, increasing $D_{x}$ (spin-orbit coupling parameter) can decrease the critical value $b_{xc}$ and increase the entanglement in the revival region, and adjusting some parameters (increasing $b_{x}$ and $J$, decreasing $B_{x}$ and $\Delta$) can decrease the critical value $D_{xc}$ to enlarge the revival region. In the thermal state, increasing $D_{x}$ can increase the revival region and the entanglement in the revival region (for $T$ or $b_{x}$), and enhance the critical value $B_{xc}$ to make the region of high entanglement larger. Also, the entanglement and the revival region will increase with the decrease of $B_{x}$ (uniform magnetic field). In addition, small $b_{x}$ (nonuniform magnetic field) has some similar properties to $D_{x}$, and with the increase of $b_{x}$ the entanglement also has a revival phenomenon, so that the entanglement can exist at higher temperature for larger $b_{x}$.Comment: 8 pages, 8 figure

Conjugacy Classes of Renner Monoids

In this paper we describe conjugacy classes of a Renner monoid $R$ with unit group $W$, the Weyl group. We show that every element in $R$ is conjugate to an element $ue$ where $u\in W$ and $e$ is an idempotent in a cross section lattice. Denote by $W(e)$ and $W_*(e)$ the centralizer and stabilizer of $e\in \Lambda$ in $W$, respectively. Let $W(e)$ act by conjugation on the set of left cosets of $W_*(e)$ in $W$. We find that $ue$ and $ve$ ($u, v\in W$) are conjugate if and only if $uW_*(e)$ and $vW_*(e)$ are in the same orbit. As consequences, there is a one-to-one correspondence between the conjugacy classes of $R$ and the orbits of this action. We then obtain a formula for calculating the number of conjugacy classes of $R$, and describe in detail the conjugacy classes of the Renner monoid of some $\cal J$-irreducible monoids. We then generalize the Munn conjugacy on a rook monoid to any Renner monoid and show that the Munn conjugacy coincides with the semigroup conjugacy, action conjugacy, and character conjugacy. We also show that the number of inequivalent irreducible representations of $R$ over an algebraically closed field of characteristic zero equals the number of the Munn conjugacy classes in $R$.Comment: A reference ([13]) and Corollary 4.5 are added to show the connection between the result in Theorem 4.4 of the previous version and the results in [13]. A paragraph on page 12 is new to show that Theorem 4.4 can also be deduced from the results in [13]. Two necessary concepts from [13] to describe the connection are inserted in Section 2.