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arXiv:1907.05033 · New Journal of Physics

Engineering optical hybrid entanglement between discrete- and continuous-variable states

Kun Huang, Hanna Le Jeannic, Olivier Morin, Tom Darras, Giovanni Guccione, Adrien Cavaillès, Julien Laurat

Published Aug 1, 2019• 48 citations
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Abstract

Abstract The generation and manipulation of hybrid entanglement of light involving discrete- and continuous-variable states have recently appeared as essential resources towards the realization of heterogeneous quantum networks. Here we investigate a scheme for the remote generation of hybrid entanglement between particle-like and wave-like optical qubits based on a non-local heralding photon detection. We also extend this scheme with additional local or non-local detections. An additional local heralding allows the resulting state to exhibit a higher fidelity with the targeted entangled qubits while a two-photon non-local heralding detection gives access to a higher dimensionality in the discrete-variable subspace, resulting thereby in the generation of hybrid entangled qutrits. The implementation of the presented schemes, in combination with ongoing works on high-fidelity quantum state engineering, will provide novel non-classical light sources for the development of optical hybrid architectures.

DOI
10.1088/1367-2630/ab34e7

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Abstract The generation and manipulation of hybrid entanglement of light involving discrete- and continuous-variable states have recently appeared as essential resources towards the realization of heterogeneous quantum networks. Here we investigate a scheme for the remote generation of hybrid entanglement between particle-like and wave-like optical qubits based on a non-local heralding photon detection. We also extend this scheme with additional local or non-local detections. An additional local heralding allows the resulting state to exhibit a higher fidelity with the targeted entangled qubits while a two-photon non-local heralding detection gives access to a higher dimensionality in the discrete-variable subspace, resulting thereby in the generation of hybrid entangled qutrits. The implementation of the presented schemes, in combination with ongoing works on high-fidelity quantum state engineering, will provide novel non-classical light sources for the development of optical hybrid architectures.
By coherently combining advantages while largely avoiding limitations of two mainstream platforms, optical hybrid entanglement involving both discrete and continuous variables has recently garnered widespread attention and emerged as a promising idea for building heterogenous quantum networks. In contrast to previous results, here we propose a new scheme to remotely generate hybrid entanglement between discrete polarization and continuous quadrature optical qubits heralded by two-photon Bell-state measurement. As a novel nonclassical light resource, we further use it to discuss two examples of ways—entanglement swapping and quantum teleportation—in which quantum information processing and communications could make use of this hybrid technique.
The wave-particle duality of light has led to two different encodings of optical quantum information. One approach, refered as the discrete-variable (DV) one, relies on finite dimensional quantum systems, while the other one, refered as the continuous-variable (CV) one, is based on wave-like states belonging to an infinite dimensional Hilbert space. These two encodings have historically been separated, but recently, new hybrid protocols which aim at combining the two complementary encodings have emerged [1]. In that prospect our recent demonstration of the measurement-induced generation of hybrid entanglement between discrete and continuous-variable quantum states generated using optical parametric oscillators [2], located at distant places and connected by a lossy channel, has opened the way to the implementation of hybrid protocols and heterogeneous quantum networks. Here we will report the first protocols based on this resource: the remote preparation of continuous-variable qubits [3], and a violation of an Einstein-Podolosky-Rosen steering inequality [4].
The wave-particle duality of light has led to two different encodings of optical quantum information. One approach, referred to as the discrete-variable (DV) one, relies on finite dimensional quantum systems, while the other one, referred to as the continuous-variable (CV) one, is based on wave-like states belonging to an infinite dimensional Hilbert space. These two encodings have historically been separated, but recently, new hybrid protocols which aim at combining the advantages of the two encodings have emerged [1] . In that prospect our recent demonstration of the measurement-induced generation of hybrid entanglement between discrete- and continuous-variable quantum states [2] , [3] , located at distant places and connected by a lossy channel, has opened the way to the implementation of hybrid protocols and heterogeneous quantum networks. Following the first protocols based on this resource, such as the remote preparation of continuous-variable qubits [4] , or a violation of an Einstein-Podolsky-Rosen steering inequality [5] , we will here report our latest experimental results on entanglement swapping and quantum teleportation protocols using hybrid entangled states based on different encodings [6] .
In optical quantum information, one can distinguish two approaches: the discrete-variable (DV), involving single photons, for example c0|0〉 + c1|1〉, and the continuous-variable alternative (CV) encoding information into the quadrature components of the light field. In this CV approach, qubits can be implemented as superposition of coherent states of opposite phases, |cat ±〉 = |α〉 ± |−α〉, also called optical Schrodinger cat states. Combining these two approaches has recently led to a so-called optical hybrid quantum information aiming at merging the properties of both [1]. As both encodings have their own advantages and drawbacks, transferring information between them is a requirement which can be fulfill by teleportation using hybrid entanglement between particle-like qubits and wave-like qubits, i.e. entanglement of the form |0〉|α〉 + |1〉|−α〉.
There are two traditionally-separated approaches to optical quantum information: the continuous- and discrete-variable strategies respectively linked to the wave-like and particle-like nature of light. This thesis work is focused on the novel hybrid approach aiming to join the capabilities of both strategies into single systems. Using hybrid methods, we report on the use of optical parametric oscillators and superconducting-nanowire single-photon detectors to generate highly non-classical non-Gaussian states such as high-purity single-photons, Schr\"odinger cat states and finally hybrid entanglement of light between continuous- and discrete-variable encoding. The potential of this resource is studied in a number of protocols. We first consider non-locality tests with hybrid entanglement such as Bell inequality violation and experimentally demonstrate the violation of Einstein-Podolsky-Rosen steering inequalities. We finally report on the progress made towards the implementation of a new setup for the demonstration of hybrid quantum teleportation between continuous and discrete-variable encodings. Our demonstrations prove the versatility of this hybrid resource and open the possibility of implementing scalable quantum networks linking systems of dissimilar nature.
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- 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.