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Connecting heterogeneous quantum networks by hybrid entanglement swapping

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 Added by Julien Laurat
 Publication date 2020
  fields Physics
and research's language is English




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Recent advances in quantum technologies are rapidly stimulating the building of quantum networks. With the parallel development of multiple physical platforms and different types of encodings, a challenge for present and future networks is to uphold a heterogeneous structure for full functionality and therefore support modular systems that are not necessarily compatible with one another. Central to this endeavor is the capability to distribute and interconnect optical entangled states relying on different discrete and continuous quantum variables. Here we report an entanglement swapping protocol connecting such entangled states. We generate single-photon entanglement and hybrid entanglement between particle-like and wave-like optical qubits, and then demonstrate the heralded creation of hybrid entanglement at a distance by using a specific Bell-state measurement. This ability opens up the prospect of connecting heterogeneous nodes of a network, with the promise of increased integration and novel functionalities.



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Hyper-hybrid entanglement for two indistinguishable bosons has been recently proposed by Li textit{et al.} [Y. Li, M. Gessner, W. Li, and A. Smerzi, href{https://doi.org/10.1103/PhysRevLett.120.050404}{Phys. Rev. Lett. 120, 050404 (2018)}]. In the current paper, we show that this entanglement exists for two indistinguishable fermions also. Next, we establish two {em no-go} results: no hyper-hybrid entanglement for two {em distinguishable} particles, and no unit fidelity quantum teleportation using {em indistinguishable} particles. If either of these is possible, then the {em no-signaling principle} would be violated. While several earlier works have attempted extending many results on distinguishable particles to indistinguishable ones, and vice versa, the above two no-go results establish a nontrivial separation between the two domains. Finally, we propose an efficient entanglement swapping using only two indistinguishable particles, whereas a minimum number of either three distinguishable or four indistinguishable particles is necessary for existing protocols.
We propose the use of hybrid entanglement in an entanglement swapping protocol, as means of distributing a Bell state with high fidelity to two parties, Alice and Bob. The hybrid entanglement used in this work is described as a discrete variable (Fock state) and a continuous variable (cat state superposition) entangled state. We model equal and unequal levels of photonic loss between the two propagating continuous variable modes, before detecting these states via a projective vacuum-one-photon measurement, and the other mode via balanced homodyne detection. We investigate homodyne measurement imperfections, and the associated success probability of the measurement schemes chosen in this protocol. We show that our entanglement swapping scheme is resilient to low levels of photonic losses, as well as low levels of averaged unequal losses between the two propagating modes, and show an improvement in this loss resilience over other hybrid entanglement schemes using coherent state superpositions as the propagating modes. Finally, we conclude that our protocol is suitable for potential quantum networking applications which require two nodes to share entanglement separated over a distance of 5-10 km when used with a suitable entanglement purification scheme.
We formulate the problem of finding the optimal entanglement swapping scheme in a quantum repeater chain as a Markov decision process and present its solution for different repeaters sizes. Based on this, we are able to demonstrate that the commonly used doubling scheme for performing probabilistic entanglement swapping of probabilistically distributed entangled qubit pairs in quantum repeaters does not always produce the best possible raw rate. Focussing on this figure of merit, without considering additional probabilistic elements for error suppression such as entanglement distillation on higher nesting levels, our approach reveals that a power-of-two number of segments has no privileged position in quantum repeater theory; the best scheme can be constructed for any number of segments. Moreover, classical communication can be included into our scheme, and we show how this influences the raw waiting time for different number of segments, confirming again the optimality of non-doubling in some relevant parameter regimes. Thus, our approach provides the minimal possible waiting time of quantum repeaters in a fairly general physical setting.
Photonic entanglement swapping, the procedure of entangling photons without any direct interaction, is a fundamental test of quantum mechanics and an essential resource to the realization of quantum networks. Probabilistic sources of non-classical light can be used for entanglement swapping, but quantum communication technologies with device-independent functionalities demand for push-button operation that, in principle, can be implemented using single quantum emitters. This, however, turned out to be an extraordinary challenge due to the stringent requirements on the efficiency and purity of generation of entangled states. Here we tackle this challenge and show that pairs of polarization-entangled photons generated on-demand by a GaAs quantum dot can be used to successfully demonstrate all-photonic entanglement swapping. Moreover, we develop a theoretical model that provides quantitative insight on the critical figures of merit for the performance of the swapping procedure. This work shows that solid-state quantum emitters are mature for quantum networking and indicates a path for scaling up.
We report entanglement swapping with time-bin entangled photon pairs, each constituted of a 795 nm photon and a 1533 nm photon, that are created via spontaneous parametric down conversion in a non-linear crystal. After projecting the two 1533 nm photons onto a Bell state, entanglement between the two 795 nm photons is verified by means of quantum state tomography. As an important feature, the wavelength and bandwidth of the 795 nm photons is compatible with Tm:LiNbO3-based quantum memories, making our experiment an important step towards the realization of a quantum repeater.
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