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arXiv:1207.6008 · Physical Review A

High-fidelity entanglement purification using chains of atoms and optical cavities

Denis Gonţa, Peter van Loock

Published Nov 9, 2012• 25 citations
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Abstract

In our previous paper [D. Gon\ifmmode \mbox{\c{t}}\else \c{t}\fi{}a and P. van Loock, Phys. Rev. A 84, 042303 (2011)], we proposed an efficient scheme to purify dynamically a bipartite entangled state using short chains of atoms coupled to high-finesse optical cavities. In contrast to conventional entanglement purification protocols, we avoid controlled-not gates and thus reduce complicated pulse sequences and superfluous qubit operations. In this paper, we significantly improve the output fidelity of remotely entangled atoms by introducing one additional entanglement protocol in each of the repeater nodes and by optimizing the laser beams required to control the entire scheme. Our improved distillation scheme yields an almost-unit output fidelity that, together with the entanglement distribution and swapping, opens an attractive route towards an efficient and experimentally feasible quantum repeater for long-distance quantum communication.

DOI
10.1103/physreva.86.052312

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In our previous paper [D. Gon\ifmmode \mbox{\c{t}}\else \c{t}\fi{}a and P. van Loock, Phys. Rev. A 84, 042303 (2011)], we proposed an efficient scheme to purify dynamically a bipartite entangled state using short chains of atoms coupled to high-finesse optical cavities. In contrast to conventional entanglement purification protocols, we avoid controlled-not gates and thus reduce complicated pulse sequences and superfluous qubit operations. In this paper, we significantly improve the output fidelity of remotely entangled atoms by introducing one additional entanglement protocol in each of the repeater nodes and by optimizing the laser beams required to control the entire scheme. Our improved distillation scheme yields an almost-unit output fidelity that, together with the entanglement distribution and swapping, opens an attractive route towards an efficient and experimentally feasible quantum repeater for long-distance quantum communication.
In the framework of cavity QED, we propose a practical scheme to purify dynamically a bipartite entangled state using short chains of atoms coupled to high-finesse optical cavities. In contrast to conventional entanglement purification protocols, we avoid controlled-not gates, thus reducing complicated pulse sequences and superfluous qubit operations. Our interaction scheme works in a deterministic way and, together with entanglement distribution and swapping, opens a route toward efficient quantum repeaters for long-distance quantum communication.
In the framework of cavity QED, we propose a quantum repeater scheme that uses coherent light and atoms coupled to optical cavities. In contrast to conventional schemes, we exploit solely the cavity QED evolution for the entire quantum repeater scheme and, thus, avoid any explicit execution of quantum logical gates. The entanglement distribution between the repeater nodes is realized with the help of pulses of coherent light interacting with the atom-cavity system in each repeater node. In our previous paper [D. Gonta and P. van Loock, Phys. Rev. A 86, 052312 (2012)], we already proposed a dynamical protocol to purify a bipartite entangled state using the evolution of atomic chains coupled to optical cavities. Here, we incorporate parts of this protocol in our repeater scheme, combining it with dynamical versions of entanglement distribution and swapping.
We present an efficient entanglement purification protocol (EPP) with controlled-not (CNOT) gates and linear optics. With the CNOT gates, our EPP can reach a higher fidelity than the conventional one. Moreover, it does not require the fidelity of the initial mixed state to satisfy F > 1/2. If the initial state is not entangled, it still can be purified. With the linear optics, this protocol can get pure maximally entangled pairs with some probabilities. Meanwhile, it can be used to purify the entanglement between the atomic ensembles in distant locations. This protocol may be useful in long-distance quantum communication.
Quantum repeaters create long-distance entanglement between quantum systems while overcoming difficulties such as the attenuation of single photons in a fiber. Recently, an implementation of a repeater protocol based on single qubits in atomic ensembles and linear optics has been proposed [Duan et al., Nature (London) 414, 413 (2001)]. Motivated by rapid experimental progress towards implementing that protocol, here we develop a more efficient scheme compatible with active purification of arbitrary errors. Using similar resources as the earlier protocol, our approach intrinsically purifies leakage out of the logical subspace and all errors within the logical subspace, leading to greatly improved performance in the presence of experimental inefficiencies. Our analysis indicates that our scheme could generate approximately one pair per 3min3\phantom{\rule{0.3em}{0ex}}\mathrm{min}3min over 1280km1280\phantom{\rule{0.3em}{0ex}}\mathrm{km}1280km distance with fidelity $(F\ensuremath{\geqslant}78%)$ sufficient to violate Bell's inequality.
Individual atoms in optical cavities can provide an efficient interface between stationary qubits and flying qubits (photons), which is an essential building block for quantum communication. Furthermore, cavity-assisted controlled-not (cnot) gates can be used for swapping entanglement to long distances in a quantum repeater setup. Nonetheless, dissipation introduced by the cavity during the cnot may increase the experimental difficulty in obtaining long-distance entanglement distribution using these systems. We analyze and compare a number of cavity-based repeater schemes combining various entanglement generation schemes and cavity-assisted cnot gates. We find that a scheme, where high-fidelity entanglement is first generated in a two-photon detection scheme and then swapped to long distances using a recently proposed heralded controlled-ZZZ (cz) gate, exhibits superior performance compared to the other schemes. The heralded gate moves the effect of dissipation from the fidelity to the success probability of the gate thereby enabling high-fidelity entanglement swapping. As a result, high-rate entanglement distribution can be achieved over long distances even for low cooperativities of the atom-cavity systems. This high-fidelity repeater is shown to outperform the other cavity-based schemes by up to two orders of magnitude in the rate for realistic parameters and large distances (1000 km).
High-quality long-distance entanglement is essential for both quantum communication and scalable quantum networks. Entanglement purification is to distill high-quality entanglement from low-quality entanglement in a noisy environment and it plays a key role in quantum repeaters. The previous significant entanglement purification experiments require two pairs of low-quality entangled states and were demonstrated in tabletop. Here we propose and report a high-efficiency and long-distance entanglement purification using only one pair of hyperentangled state. We also demonstrate its practical application in entanglement-based quantum key distribution (QKD). One pair of polarization spatial-mode hyperentanglement was distributed over 11 km multicore fiber (noisy channel). After purification, the fidelity of polarization entanglement arises from 0.771 to 0.887 and the effective key rate in entanglement-based QKD increases from 0 to 0.332. The values of Clauser-Horne-Shimony-Holt inequality of polarization entanglement arises from 1.829 to 2.128. Moreover, by using one pair of hyperentanglement and deterministic controlled-NOT gates, the total purification efficiency can be estimated as 6.6×10^{3} times than the experiment using two pairs of entangled states with spontaneous parametric down-conversion sources. Our results offer the potential to be implemented as part of a full quantum repeater and large-scale quantum network.