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Physical Review A

Entanglement transfer from entangled two-mode fields to a pair of separable and mixed qubits

Jian Zou, Jun Gang Li, Bin Shao, Jian Li, Qian ShuLi

Published Apr 24, 2006• 40 citations
Publisher

Abstract

We consider the entanglement of two remote qubits induced by local interaction with the two-mode nonclassical state fields. We investigate the transfer of entanglement from different two-mode nonclassical state fields to a pair of separable and mixed qubits. We find that no matter what state the qubit subsystem is initially prepared in, at the specific time $gt\ensuremath{\simeq}11.07$ the entanglement of the Bell state fields can be almost completely transferred to the qubit subsystem, i.e., the Bell state fields can drive an initially separable and very mixed state of qubits into an almost pure highly entangled state suitable for quantum information processing. For the entangled coherent state fields $\ensuremath{\mid}u⟩={N}_{1}(\ensuremath{\mid}\ensuremath{\alpha},\ensuremath{-}\ensuremath{\alpha}⟩+\ensuremath{\mid}\ensuremath{-}\ensuremath{\alpha},\ensuremath{\alpha}⟩)$ and $\ensuremath{\mid}{u}^{\ensuremath{'}}⟩={N}_{2}(\ensuremath{\mid}\ensuremath{\alpha},\ensuremath{-}\ensuremath{\alpha}⟩\ensuremath{-}\ensuremath{\mid}\ensuremath{-}\ensuremath{\alpha},\ensuremath{\alpha}⟩)$ we find that when $\ensuremath{\mid}\ensuremath{\alpha}\ensuremath{\mid}$ is small, the dynamic behaviors of the entanglement between two qubits are quite different. For $\ensuremath{\mid}u⟩$ there is almost no entanglement between two qubits while for $\ensuremath{\mid}{u}^{\ensuremath{'}}⟩$ the dynamic behavior of the entanglement between two qubits is very similar to that of the Bell state field. For large $\ensuremath{\mid}\ensuremath{\alpha}\ensuremath{\mid}$ we find that the dynamic behaviors of entanglement between two qubits are almost the same for these two fields, and when $gt\ensuremath{\sim}\ensuremath{\mid}\ensuremath{\alpha}\ensuremath{\mid}\ensuremath{\pi}$ the entanglement between two qubits reaches its maximum and is almost independent of initial mixedness of the qubit subsystem. For the two-mode squeezed vacuum state field we find that when $r\ensuremath{\sim}0.86$ and $gt\ensuremath{\simeq}11.07$ the entanglement transfer reaches its maximum which also almost does not depend on the initial mixedness of the qubit subsystem.

DOI
10.1103/physreva.73.042319

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Entanglement transfer from the superposition states of the pair coherent states or the SU(1,1) coherent states to two initially separable qubits is investigated. The entropy of the superposition states has a novel property: there exists a maximum value when the phase difference between the two 2-mode coherent states is π. In the process of entanglement transfer from these superposition states to qubits, it is found that the qubits have the largest possible entanglement at the maximum of the entropy of the initial field, which shows a relationship between the entanglement of the initial field and that of the qubits. The concurrence of the qubits can periodically approach unity when the parameters of the initial field are properly chosen and the two qubits are initially at the ground states.
We study entanglement transfer from even and odd two-mode nonlinear coherent states to two separable qubits. The separable qubits are assumed to be in the following three states: both of the qubits are in the ground state, one qubit is in the ground state and the other is in a mixed state, and both of them are in a mixed state. The interaction between the field states and the system of qubits is considered under the Jaynes–Cummings model. We use negativity to evaluate the entanglement transfer to the system of qubits after interaction with the field states. The conditions for the production of the maximum amount of entanglement between qubits will be discussed. We observe that the maximum value of entanglement transfer is related to the interaction of odd nonlinear coherent states with the qubits when both of the latter are in the ground state.
We consider an entangled but non-interacting qubit pair a 1 and b 1 that is independently coupled to a set of local qubit systems, a I and b J , of 0 bit value, respectively. We derive rules for the transfer of entanglement from the pair a 1 – b 1 to an arbitrary pair a I – b J , for the case of qubit-number conserving local interactions. It is shown that the transfer rule depends strongly on the initial entangled state. If the initial entanglement is in the form of the Bell state corresponding to anti-correlated qubits, the sum of the square of the nonlocal pairwise concurrences is conserved. If the initial state is the Bell state with correlated qubits, this sum can be reduced, even to zero in some cases, to reveal a complete and abrupt loss of all nonlocal pairwise entanglement. We also identify that for the nonlocal bipartitions A – b J involving all qubits at one location, with one qubit b J at the other location, the concurrences satisfy a simple addition rule for both cases of the Bell states that the sum of the square of the nonlocal concurrences is conserved.
The dynamics of entanglement and fidelity for a subsystem of two separate spin-1∕21∕21∕2 qubits prepared in Bell states is investigated. One of the subsystem qubit labeled AAA is under the influence of a Heisenberg XYXYXY spin bath, while another one labeled BBB is uncoupled with that. We discuss two cases: (i) the number of bath spins is infinite, $N\ensuremath{\rightarrow}\ensuremath{\infty}$, and (ii) NNN is finite, N=40N=40N=40. In both cases, the bath is initially prepared in a thermal equilibrium state. It is shown that the time dependence of the concurrence and the fidelity of the two subsystem qubits can be controlled by tuning the parameters of the spin bath, such as the anisotropic parameter, the temperature, and the coupling strength with qubit AAA. It is interesting to find that the dynamics of the concurrence is independent of four different initial Bell states and that of the fidelity is divided into two groups.