We derive the exact reduced dynamics of a central two-qubit system in a spin star configuration. The exact evolution of the reduced system density matrix is obtained and we compute the limit of an infinite number of environment spins. Initially pure states of the central system evolve into mixed ones and we determine the decoherence-free states of the model. The long-time behavior is studied, partial decoherence is shown to be a result of the coupling of the qubits to the environment, and entanglement evolution of the central system is investigated.
We consider a generalized spin star system which can be solved exactly, with the central spin- system embedded in a bath of N spin- particles. In this system, in addition to the central–outer couplings, each pair of nearest neighbours of the bath spins interacts within themselves. The general expressions of the eigenstates as well as the eigenvalues of the model are derived with the use of symmetries of the system. We then investigate the quantum phase transitions in some limiting cases and show that the occurrence of the quantum phase transitions can be obtained by varying the external control parameters. We further analyse the properties of quantum communication in this model. In the time evolution, some simple and interesting results are discovered concerning transfer fidelity, cloning fidelity, as well as entanglements created.
This paper considers a generalized spin star system which can be solved exactly, with the central spin-½ system embedded in an outer ring of N spin-½ particles(denoted as spin bath). In this model, in addition to the central-outer interaction, each pair of nearest neighbour of the bath interacts within themselves. The general expressions of the eigenstates as well as the eigenvalues of the model are derived with the use of the symmetries of system. It analyses the quantum state transfer and the dynamical behaviour of entanglement created during quantum communication. It also analyses the efficiency of the configuration regarded as quantum phase covariant clone or decoherence model. Some interesting results are discovered concerning the properties of quantum communication in this model.
Simple physical interactions between spin-
1∕2 particles may result in quantum states that exhibit exotic correlations that are difficult to find if one simply explores state spaces of multipartite systems. In particular, we present a detailed investigation of the well-known Ising model of a chain (ring) of spin-
1∕2 particles (qubits) in a transverse magnetic field. We present explicit expressions for eigenstates of the model Hamiltonian for arbitrary number of spin-
1∕2 particles in the chain in the standard (computer) basis, and we investigate quantum entanglement between individual qubits. We analyze bipartite as well as multipartite entanglement in the ground state of the model. In particular, we show that bipartite entanglement between pairs of qubits of the Ising chain (measured in terms of a concurrence) as a function of the parameter $\ensuremath{\lambda}$ has a maximum around the point $\ensuremath{\lambda}=1$, and it monotonically decreases for large values of $\ensuremath{\lambda}$. We prove that in the limit $\ensuremath{\lambda}\ensuremath{\rightarrow}\ensuremath{\infty}$ this state is locally unitary equivalent to an
N-partite Greenberger-Horn-Zeilinger state. We also analyze a very specific eigenstate of the Ising Hamiltonian with a zero eigenenergy (we denote this eigenstate as the
X-state). This
X-state exhibits the ``extreme'' entanglement in a sense that an arbitrary subset
A of $k\ensuremath{\leqslant}n$ qubits in the Ising chain composed of
N=2n+1 qubits is maximally entangled with the remaining qubits (set
B) in the chain. In addition, we prove that by performing a local operation just on the subset
B, one can transform the
X-state into a direct product of
k singlets shared by the parties
A and
B. This property of the
X-state can be utilized for new secure multipartite communication protocols.