Quantum key distribution allows for the generation of a secret key between distant parties connected by a quantum channel such as optical fibre or free space. Unfortunately, the rate of generation of a secret key by direct transmission is fundamentally limited by the distance. This limit can be overcome by the implementation of so-called quantum repeaters. Here, we assess the performance of a specific but very natural setup called a single sequential repeater for quantum key distribution. We offer a fine-grained assessment of the repeater by introducing a series of benchmarks. The benchmarks, which should be surpassed to claim a working repeater, are based on finite-energy considerations, thermal noise and the losses in the setup. In order to boost the performance of the studied repeaters we introduce two methods. The first one corresponds to the concept of a cut-off, which reduces the effect of decoherence during storage of a quantum state by introducing a maximum storage time. Secondly, we supplement the standard classical post-processing with an advantage distillation procedure. Using these methods, we find realistic parameters for which it is possible to achieve rates greater than each of the benchmarks, guiding the way towards implementing quantum repeaters. * These authors contributed equally; f.d.rozpedek@tudelft.nl arXiv:1705.00043v2 [quant-ph]
How can one detect entanglement between multiple optical paths sharing a single photon? We address this question by proposing a scalable protocol, which only uses local measurements where single photon detection is combined with small displacement operations. The resulting entanglement witness does not require postselection, nor assumptions about the photon number in each path. Furthermore, it guarantees that entanglement lies in a subspace with at most one photon per optical path and reveals genuinely multipartite entanglement. We demonstrate its scalability and resistance to loss by performing various experiments with two and three optical paths. We anticipate applications of our results for quantum network certification.
Photons of a laser beam driving the upper motional sideband of an optomechanical cavity can decay into photon-phonon pairs by means of an optomechanical parametric process. The phononic state can subsequently be mapped to a photonic state by exciting the lower sideband, hence creating photon-photon pairs out of an optomechanical system. Here we show that these pairs can violate a Bell inequality when they are measured with photon counting techniques preceded by small displacement operations in phase space. The consequence of such a violation as well as the experimental requirements are intensively discussed. DOI: 10.1103/PhysRevLett.116.070405 Introduction.-Cavity optomechanics, which describes a mechanical oscillator controlled by an electromagnetic cavity mode via a generalized radiation pressure force, is the subject of intense research [1][2][3]. Most recent progress includes the cooling of mechanical oscillators down to the ground state [4][5][6], the readout of the mechanical position with a readout imprecision below the standard quantum limit [7] as well as optomechanical squeezing [8,9] and entanglement [10]. Reciprocally, the mechanical degrees of freedom can be used to control the cavity light, e.g., for fast and slow light [11,12], frequency conversions [13,14], squeezing [15], and information storage in long-lived mechanical oscillations [10,16].Optomechanical systems are also envisioned as test benches for physical theories [17][18][19][20][21][22][23]. As a step in this direction, quantum correlations between light and mechanics have been observed recently [10]. In this experiment, quantum features have been detected through an entanglement witness where one assumes that the measurement devices are well characterized and where quantum theory is used to predict the results of these measurements on separable states. It is interesting to wonder whether the nonclassical behavior of optomechanical systems can be certified outside of the quantum formalism, i.e., from a Bell test [24]. This is particularly relevant to test postquantum theories including explicit collapse models [25][26][27][28], where the assumption that the system behaves quantum mechanically may be questionable [29].In this Letter, we show how to perform such a Bell test in the experimentally relevant weak-optomechanical coupling and sideband-resolved regime. Our proposal, which starts with a mechanical oscillator close to its ground state, consists of two steps. First, the optomechanical system is excited by a laser tuned to the upper motional sideband of the cavity to create photon-phonon pairs via optomechanical parametric conversion. Second, a laser resonant with
Motivated by very recent experiments, we consider a scenario "à la Bell" in which two protagonists test the Clauser-Horne-Shimony-Holt (CHSH) inequality using a photon-pair source based on spontaneous parametric down conversion and imperfect photon detectors. The conventional wisdom says that (i) if the detectors have unit efficiency, the CHSH violation can reach its maximum quantum value 2 √ 2. To obtain the maximal possible violation, it suffices that the source emits (ii) maximally entangled photon pairs (iii) in two well defined single modes. Through a non-perturabive calculation of non-local correlations, we show that none of these statements are true. By providing the optimal pump parameters, measurement settings and state structure for any detection efficiency and dark count probability, our results give the recipe to close all the loopholes in a Bell test using photon pairs.
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