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Fast generations of tree-type three-dimensional entanglement via Lewis-Riesenfeld invariants and transitionless quantum driving

View Article: PubMed Central - PubMed

ABSTRACT

Recently, a novel three-dimensional entangled state called tree-type entanglement, which is likely to have applications for improving quantum communication security, was prepared via adiabatic passage by Song et al. Here we propose two schemes for fast generating tree-type three-dimensional entanglement among three spatially separated atoms via shortcuts to adiabatic passage. With the help of quantum Zeno dynamics, two kinds of different but equivalent methods, Lewis-Riesenfeld invariants and transitionless quantum driving, are applied to construct shortcuts to adiabatic passage. The comparisons between the two methods are discussed. The strict numerical simulations show that the tree-type three-dimensional entangled states can be fast prepared with quite high fidelities and the two schemes are both robust against the variations in the parameters, atomic spontaneous emissions and the cavity-fiber photon leakages.

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(a) The fidelity of the LRI method versus δtf/tf and δε/ε; (b) the fidelity of the TQD method versus δtf/tf and δΔ/Δ. The parameters used here are same as in Fig. 5.
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f7: (a) The fidelity of the LRI method versus δtf/tf and δε/ε; (b) the fidelity of the TQD method versus δtf/tf and δΔ/Δ. The parameters used here are same as in Fig. 5.

Mentions: In the above discussion, the whole system are perfect and considered as absolutely isolated from the environment. Therefore, it is necessary to give the discussions of robustness of our schemes against the variations in the parameters and decoherence induced by the atomic spontaneous emissions and photon leakages of the cavity-fiber system. For discussing the effects of the variations in the parameters, we plot the fidelity of the LRI method versus the variations in tf and ε in Fig. 7(a) and the fidelity of the TQD method versus the variations in tf and Δ in Fig. 7(b). Here we define δx = x′ − x as the deviation of x, in which x denotes the ideal value and x′ denotes the actual value. In Fig. 7(a), the fidelity decreases with the increase of /δε/ as described in Fig. 2(b). From Eq. (25), we know that the Rabi frequencies decrease with the increase of the operation time tf. According to the limit condition , v we use, the values of the Rabi frequencies are the smaller the better, so the operation time tf is the longer the better as described in Fig. 2(a). Therefore, the fidelity of the LRI method increases with the increase of δtf in Fig. 7(a). In Fig. 7(b), we can clearly see that the effects of tf and Δ on the fidelity of the TQD method are dependent on each other and even the fidelity of the TQD method is apparently dependent on the value of Δ/tf as mentioned in the last subsection. Significantly, we notice that the fidelities of the two methods are both over 0.98 even when . Therefore, both of our schemes are robust against the variations in the parameters.


Fast generations of tree-type three-dimensional entanglement via Lewis-Riesenfeld invariants and transitionless quantum driving
(a) The fidelity of the LRI method versus δtf/tf and δε/ε; (b) the fidelity of the TQD method versus δtf/tf and δΔ/Δ. The parameters used here are same as in Fig. 5.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5036061&req=5

f7: (a) The fidelity of the LRI method versus δtf/tf and δε/ε; (b) the fidelity of the TQD method versus δtf/tf and δΔ/Δ. The parameters used here are same as in Fig. 5.
Mentions: In the above discussion, the whole system are perfect and considered as absolutely isolated from the environment. Therefore, it is necessary to give the discussions of robustness of our schemes against the variations in the parameters and decoherence induced by the atomic spontaneous emissions and photon leakages of the cavity-fiber system. For discussing the effects of the variations in the parameters, we plot the fidelity of the LRI method versus the variations in tf and ε in Fig. 7(a) and the fidelity of the TQD method versus the variations in tf and Δ in Fig. 7(b). Here we define δx = x′ − x as the deviation of x, in which x denotes the ideal value and x′ denotes the actual value. In Fig. 7(a), the fidelity decreases with the increase of /δε/ as described in Fig. 2(b). From Eq. (25), we know that the Rabi frequencies decrease with the increase of the operation time tf. According to the limit condition , v we use, the values of the Rabi frequencies are the smaller the better, so the operation time tf is the longer the better as described in Fig. 2(a). Therefore, the fidelity of the LRI method increases with the increase of δtf in Fig. 7(a). In Fig. 7(b), we can clearly see that the effects of tf and Δ on the fidelity of the TQD method are dependent on each other and even the fidelity of the TQD method is apparently dependent on the value of Δ/tf as mentioned in the last subsection. Significantly, we notice that the fidelities of the two methods are both over 0.98 even when . Therefore, both of our schemes are robust against the variations in the parameters.

View Article: PubMed Central - PubMed

ABSTRACT

Recently, a novel three-dimensional entangled state called tree-type entanglement, which is likely to have applications for improving quantum communication security, was prepared via adiabatic passage by Song et al. Here we propose two schemes for fast generating tree-type three-dimensional entanglement among three spatially separated atoms via shortcuts to adiabatic passage. With the help of quantum Zeno dynamics, two kinds of different but equivalent methods, Lewis-Riesenfeld invariants and transitionless quantum driving, are applied to construct shortcuts to adiabatic passage. The comparisons between the two methods are discussed. The strict numerical simulations show that the tree-type three-dimensional entangled states can be fast prepared with quite high fidelities and the two schemes are both robust against the variations in the parameters, atomic spontaneous emissions and the cavity-fiber photon leakages.

No MeSH data available.