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arXiv:1011.5352 · International Journal of Quantum Information

QUANTUM ENTANGLEMENT TRANSFER BETWEEN SPIN PAIRS

QING-YOU MENG, FU-LIN ZHANG, JING-LING CHEN

Published Oct 1, 2010• 2 citations
arXivHTMLPDF

Abstract

The transfer of entanglement from source particles (SPs) to target particles (TPs) via the Heisenberg interaction H = s1 ⋅ s2 has been investigated. In our research, TPs are two qubits and SPs are two qubits or qutrits. When TPs are two qubits, we find that no matter what state the TPs are initially prepared in, at the specific time t = π the quantity of entanglement of the TPs can attain 1 after interaction with the SPs which stay on the maximally entangled state. When TPs are two qutrits, the maximal quantity of entanglement of the TPs is proportional to the quantity of entanglement of the initial state of the TPs and cannot attain 1 for almost all the initial states of the TPs. Here we propose an iterated operation which can make the TPs go to the maximal entangled state.

DOI
10.1142/s0219749910006824

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The transfer of entanglement from source particles (SPs) to target particles (TPs) via the Heisenberg interaction H = s1 ⋅ s2 has been investigated. In our research, TPs are two qubits and SPs are two qubits or qutrits. When TPs are two qubits, we find that no matter what state the TPs are initially prepared in, at the specific time t = π the quantity of entanglement of the TPs can attain 1 after interaction with the SPs which stay on the maximally entangled state. When TPs are two qutrits, the maximal quantity of entanglement of the TPs is proportional to the quantity of entanglement of the initial state of the TPs and cannot attain 1 for almost all the initial states of the TPs. Here we propose an iterated operation which can make the TPs go to the maximal entangled state.
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.
The problem of a controlled transfer of an entanglement initially encoded into two two-level atoms that are successively sent through two single-mode cavities is investigated. The atoms and the cavity modes form a four-qubit system and we demonstrate the conditions under which the initial entanglement encoded into the atoms can be completely transferred to other pairs of qubits. We find that in the case of non-zero detuning between the atomic transition frequencies and the cavity mode frequencies, no complete transfer of the initial entanglement is possible to any of the other pairs of qubits. In the case of exact resonance and equal coupling strengths of the atoms to the cavity modes, an initial maximally entangled state of the atoms can be completely transferred to the cavity modes. Complete transfer of the entanglement is restricted to the cavity modes, with transfer to the other pairs being limited to 50%. We find that complete transfer of an initial entanglement to other pairs of qubits may take place if the initial state is not the maximally entangled state and the atoms couple to the cavity modes with unequal strengths. Depending on the ratio between the coupling strengths, optimal entanglement can be created between the atoms and one of the cavity modes.
We study the relation between energy and entanglement in an entanglement transfer problem. We first analyze the general setup of two entangled qubits (``aaa'' and ``bbb'') exchanging this entanglement with two other independent qubits (``AAA'' and ``BBB''). Qubit ``aaa'' (``bbb'') interacts with qubit ``AAA'' (``BBB'') via a spin-exchange-like unitary evolution. A physical realization of this scenario could be the problem of two-level atoms transferring entanglement to resonant cavities via independent Jaynes-Cummings interactions. We study the dynamics of entanglement and energy for the second pair of qubits (tracing out the originally entangled ones) and show that these quantities are closely related. For example, the allowed quantum states occupy a restricted area in a phase diagram entanglement vs energy. Moreover, the curve which bounds this area is exactly the one followed if both interactions are equal and the entire four qubit system is isolated. We also consider the case when the target pair of qubits is subjected to losses and can spontaneously decay.