Quantum repeaters based on heralded qubit amplifiers

We present a quantum repeater scheme based on the recently proposed qubit amplifier [N. Gisin, S. Pironio, and N. Sangouard, Phys. Rev. Lett. 105, 070501 (2010)]. It relies on an on-demand entangled-photon-pair source which uses on-demand single-photon sources, linear optical elements, and atomic ensembles. Interestingly, the imperfections affecting the states created from this source, caused, for example, by detectors with nonunit efficiencies, are systematically purified from an entanglement swapping operation based on a two-photon detection. This allows the distribution of entanglement over very long distances with a high fidelity, that is, without vacuum components and multiphoton errors. Therefore, the resulting quantum repeater architecture does not necessitate final postselections and thus achieves high entanglement distribution rates. This also provides unique opportunities for device-independent quantum key distribution over long distances with linear optics and atomic ensembles.

Figure 1

Entanglement creation at a distance using hypothetical pair sources, producing on-demand maximally entangled states. Star: ideal source of entangled pairs, QM: quantum memories, and BM: Bell measurement.

Figure 2

Entanglement creation at a distance without heralding. Star: ideal source of entangled pairs and QM: quantum memory.

Figure 3

Heralded source of entangled pairs, QM: quantum memories and BM: Bell measurement. A pair source (star) produces a polarization entangled state in a probabilistic way in modes $in$ and $g.$ Two single-photon sources (triangles) produce a product state of two photons with orthogonal polarizations in the same spatial mode $a$. The mode $a$ is sent through a beam splitter (BS) with tunable reflectivity $R$ (in intensity) and the two photon coincidence detection $d$-$\tilde{d}$ teleports the mode $in$ to the mode $out$ (up to a unitary transformation). This leads to the entanglement between the modes $g$ and $out$ which are then stored in the memories. The BM here is inspired by [7] and consists of one PBS in the $\pm {45}^{\circ }$ basis followed by a PBS in H/V basis at each output.

Figure 4

(a) A scheme of the whole repeater consisting of $2^n$ elementary links of length $L_0.$ Blocks labeled OS represent the on site blocks presented in Fig. 3. The entanglement in each elementary link is created by converting the $out$ atomic excitations into optical modes and by performing subsequently a Bell measurement (BM). The BM is represented here by the $\otimes$ symbol. When the entanglement is succesfully created in neighboring elementary links, they are then swapped using the same BM (swapping between modes $f^{\prime }$ and $g^{\prime }$ is shown; see the text for the details). (b) Detail of the BM used in the elementary link and for the swappings. The BM consists of one PBS in the H/V basis followed by a PBS in $\pm {45}^{\circ }$ at each output.