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arXiv:1406.0381 · New Journal of Physics

Witnessing single-photon entanglement with local homodyne measurements: analytical bounds and robustness to losses

Melvyn Ho, Olivier Morin, Jean-Daniel Bancal, Nicolas Gisin, Nicolas Sangouard, Julien Laurat

Published Oct 24, 2014• 12 citations
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Abstract

Single-photon entanglement is one of the primary resources for quantum networks, including quantum repeater architectures. Such entanglement can be revealed with only local homodyne measurements through the entanglement witness presented in Morin et al (2013 Phys. Rev. Lett. 110 130401 ). Here, we provide an extended analysis of this witness by introducing analytical bounds and by reporting measurements confirming its great robustness with regard to losses. This study highlights the potential of optical hybrid methods, where discrete entanglement is characterized through continuous-variable measurements.

DOI
10.1088/1367-2630/16/10/103035

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Single-photon entanglement is one of the primary resources for quantum networks, including quantum repeater architectures. Such entanglement can be revealed with only local homodyne measurements through the entanglement witness presented in Morin et al (2013 Phys. Rev. Lett. 110 130401 ). Here, we provide an extended analysis of this witness by introducing analytical bounds and by reporting measurements confirming its great robustness with regard to losses. This study highlights the potential of optical hybrid methods, where discrete entanglement is characterized through continuous-variable measurements.
Single-photon entangled states constitute the simplest form of entanglement, yet they provide a valuable resource in quantum information sciences. Specifically, they lie at the heart of quantum networks, as they can be used for quantum teleportation, swapped and purified with linear optics. The main drawback of such resource is the difficulty in measuring it. Here, we present and experimentally test the first operational witness suited for single-photon entanglement which relies only on local homodyning and does not require post-selection. Our results highlight the potential of hybrid methods, where discrete entanglement is characterized through continuous-variable measurements, in verifying the proper functioning of future quantum networks.
Single-photon entangled states, i.e. states describing two optical paths sharing a single-photon, constitute the simplest form of entanglement. Yet they provide a valuable resource in quantum information science. Specifically, they lie at the heart of quantum networks, as they can be used for quantum teleportation, swapped and purified with linear optics. The main drawback of such entanglement is the difficulty in measuring it. Here, we present and experimentally test an entanglement witness [1] allowing one not only to say whether a given state is path-entangled but also that entanglement lies in the subspace where the optical paths are each filled with one photon at most, i.e. refers to single-photon entanglement. It uses local homodyning only and relies on no assumption about the Hilbert space dimension of the measured system, as explained in the following.
Single-photon entangled states, i.e., states describing two optical paths sharing a single photon, constitute the simplest form of entanglement. Yet they provide a valuable resource in quantum information science. Specifically, they lie at the heart of quantum networks, as they can be used for quantum teleportation, swapped, and purified with linear optics. The main drawback of such entanglement is the difficulty in measuring it. Here, we present and experimentally test an entanglement witness allowing one to say whether a given state is path entangled and also that entanglement lies in the subspace, where the optical paths are each filled with one photon at most, i.e., refers to single-photon entanglement. It uses local homodyning only and relies on no assumption about the Hilbert space dimension of the measured system. Our work provides a simple and trustworthy method for verifying the proper functioning of future quantum networks.
Hybrid encoding of quantum information is a promising approach towards the realization of optical quantum protocols. It combines advantages of continuous variables encoding, such as high efficiencies, with those of discrete variables, such as high fidelities. In particular, entangled hybrid states were shown to be a valuable resource for quantum information protocols. In this work we present a hybrid entanglement witness that can be implemented on available experiments and is robust to noise currently observed in quantum optical setups. The proposed witness is based on measurements of genuinely hybrid observables. The noise model we consider is general. It is formally characterized with Kraus operators since the considered hybrid system can be expressed in a finite dimension basis. A practical advantage of the witness is that it can be tested by measuring just a few experimentally available observables.
Entanglement does not always require one particle per party. It was predicted some thirty years ago that a single photon traversing a beam splitter could violate a Bell inequality. Although initially debated, single-photon nonlocality was eventually demonstrated via homodyne measurements. Here, we present an alternate realisation that avoids the complexity of homodyne measurements and potential loopholes in their implementation. We violate a Bell inequality by performing joint measurements on two copies of the same single-photon entangled state, where one photon acts as a phase reference for the other, making it self-referential. We observe CHSH parameters of 2.71±0.092.71\pm 0.092.71±0.09 and 2.23±0.072.23\pm 0.072.23±0.07, depending on the joint measurements implemented. This offers a new perspective on single-photon nonlocality and a more accessible experimental route, potentially applicable to general mode-entangled states in diverse platforms.