Anti-symmetry consideration on the preservation of entanglement of spin system

Abstract

In this work we offer an approach to protect the entanglement based on the anti-symmetric property of the hamiltonian. Our main objective is to protect the entanglement of a given initial three-qubit state which is governed by hamiltonian of a three-spin Ising chain in site-dependent transverse fields. We show that according to anti-symmetric property of the hamiltonian with respect to some operators mimicking the time reversal operator, the dynamics of the system can be effectively reversed. It equips us to control the dynamics of the system. The control procedure is implemented as a sequence of cyclic evolution; accordingly the entanglement of the system is protected for any given initial state with any desired accuracy an long-time. Using this approach we could control not only the multiparty entanglement but also the pairwise entanglement. It is also notable that in this paper although we restrict ourselves mostly within a three-spin Ising chain in site-dependent transverse fields, our approach could be applicable to any n-qubit spin system models. *

Entanglement preservation in a system of two dipole–dipole interacting two-level atoms coupled with single mode cavity

“…To maintain and protect the entanglement of a given state in a desired value and long duration, a method has been introduced by the present author [49]. In fact, the proposed control scheme is based on the following necessary condition: the Hamiltonian H must be antisymmetric with respect to some operators, in other words, it must be at least a hermitian unitary operator, say A, which is anticommuting with…”

“…Therefore, implementation of the preservation of entanglement is a fundamental element in the realization of quantum information processing. In this paper, following the direction of [49], wherein we proposed a method for preserving entanglement in a system of spin models, and considering the work of Tores et al, [48], where they studied entanglement dynamics between two interacting two-level atoms with different species inside a cavity, we have studied and investigated the control of the dynamics of entanglement and its protection for a system of two D-D interacting TLAs , generally with different species, coupled with a single mode cavity with different couplings. The paper is organized as follows: in section two we briefly outline the approach, which is introduced in [49], to protect the entanglement of a given initial state.…”

“…In this paper, following the direction of [49], wherein we proposed a method for preserving entanglement in a system of spin models, and considering the work of Tores et al, [48], where they studied entanglement dynamics between two interacting two-level atoms with different species inside a cavity, we have studied and investigated the control of the dynamics of entanglement and its protection for a system of two D-D interacting TLAs , generally with different species, coupled with a single mode cavity with different couplings. The paper is organized as follows: in section two we briefly outline the approach, which is introduced in [49], to protect the entanglement of a given initial state. In section three we study the control of entanglement dynamics and its protection in the system of two different interacting D-D TLAs with different coupling to the single mode cavity, and implement the controlled evolutions to protect atomatom entanglement.…”