## Abstract

We demonstrate the distribution of quantum entanglement via optical free-space links to independent receivers separated by 600 m, with no line of sight between each other. A Bell inequality between those receivers is violated by more than four standard deviations, confirming the quality of the entanglement. This outdoor experiment represents a step toward satellite-based distributed quantum entanglement.

Quantum entanglement is a fundamental feature of quantum mechanics and is central to most advanced quantum communication applications (*1, 2*). At present, most realizations of quantum communication schemes are based on entangled photon pairs, which are shared over long distances with the use of optical-fiber links. In these experiments, entanglement has been distributed over distances ranging from several hundred meters up to 10 km (*3*–*5*). In all cases, violation of a Bell inequality was used as the experimental measure for proving that entanglement was indeed shared between the separate observers. On the basis of present fiber and detector technology, it has been determined that absorptive losses limit the distances over which entanglement can be shared to the order of 100 km (*6, 7*). Without the addition of (as-yet undemonstrated) quantum repeaters (*8*), the extent over which one can quantum communicate is restricted to this distance over which entanglement can be distributed. Free-space optical links provide a way to overcome these limitations. Earth-based free-space links are also limited in distance due to obstructing objects in the line of sight, atmospheric attenuation because of weather conditions and aerosols (*9*) and, ultimately, the curvature of Earth. The use of satellite technology will permit those distances to be bridged beyond the capability of Earth-based stations, eventually leading to a truly global distribution of entangled photons and thus to novel possibilities for fundamental quantum physics research and quantum communication applications. Recently, several groups have succeeded in distributing faint classical laser pulses via free-space links over distances up to several kilometers to demonstrate free-space quantum cryptography (*10, 11, 12*). We have taken the next step and demonstrated the free-space distribution of entangled photons over long distances between two independent receiver stations.

In our setup, the two receivers were located at different sides of the Danube River in Vienna, Austria, on the rooftops of two buildings approximately 600 m apart. The actual measurements took place during night at outside temperatures around 0° C and wind strengths up to 50 km/h, thereby demonstrating the robustness of our source and links against less than ideal environmental conditions. The receiver stations were located at distances of 150 and 500 m, respectively, from the entangled photon source and did not have a direct line of sight to one another due to obstruction from trees and power lines (Fig. 1).

Each photon from the entangled pair emitted by the source was coupled into a single-mode optical fiber. The fibers were connected to independent sending telescopes that consisted of a single-mode fiber coupler located approximately in the focal plane of a 5-cm-diameter lens. Each receiver terminal was equipped with a similar telescope (with the addition of a polarizer), which was aligned to couple the incoming entangled photons back into single-mode fibers for detection in single-photon–counting avalanche photo diodes with a detection efficiency of about 40%. Due to the spatial selectivity of the single-mode fibers (*13*), no bandpass filters were required at the source or at the receivers to discriminate the signal from the background light during night operation. However, the end of a measurement run was sharply marked by the onset of sunrise, which increased the background from almost zero to several thousands per second in only a few minutes.

As a source for polarization-entangled photons, we used type II spontaneous parametric down-conversion (SPDC) (*14*), pumped by a violet laser diode operating at 405 nm to produce nearly energy degenerate pairs at 810 nm. With a pump power of 18 mW, we measured ∼120,000 s^{–}^{1} single photons in each arm of the source and approximately 20,000 polarization entangled photon pairs per s, which were coupled into single-mode fibers to the telescopes. Visibilities of the polarization correlations, which indicate the quality of the entanglement, were found to be larger than 97% in the 0°/90° basis and larger than 94% in the 45°/135° basis, before coupling them to the long-distance free-space telescope links. The setup for the source has been miniaturized to fit on a small optical breadboard, and it could easily be transported from the laboratory to the outdoor field site, where it was kept in a small shielded container. Electrical power for the source was provided by a gasoline-driven power generator, which makes it completely independent from an ideal laboratory environment.

The attenuation in each of the links was about 12 dB (6% transmission) without taking into account the efficiency of the detectors (*15*). In total, local single count rates of ∼4000 s^{–}^{1} (including background) and a maximum coincidence rate of 15 s^{–}^{1} could be observed. The local singles background rates were 650 s^{–}^{1} and 750 s^{–}^{1} at receivers A and B, respectively. The background was almost entirely due to the dark count rates of the detectors, while other background was highly suppressed by the spatial selectivity of the single-mode fibers and by the nighttime operation (*16*).

Our SPDC source was aligned to produce the singlet state which is one of the four maximally entangled Bell states. *H* and *V* denote horizontal and vertical polarization, respectively, and *A* and *B* indicate the different spatial modes in which the photons are collected. To show the quality of the distributed entanglement between the separate observers, we measured a series of polarization correlations that was eventually used to show a violation of a Bell inequality. The polarization correlation coefficients are given by (1) where N is the number of coincident detection events between the observers when the polarizers are set to ϕ_{A} (denoted by “+”) or the corresponding orthogonal (denoted by “–”) at receiver A and ϕ_{B} (denoted by “+”) or (denoted by “–”) at receiver B. In general, the coincidence count rate is given by *N*(ϕ_{A},ϕ_{B}) = 1/2 sin^{2}(ϕ_{A}–ϕ_{B}). The experimental data exhibit this behavior (Fig. 2). The quality of the state ρ observed at the receiver stations can be defined by the fidelity *F* = 〈Ψ^{–}|ρ|Ψ^{–}〉. The correlation coefficient can be calculated from *F* = [3*E*(ϕ,ϕ)+1]/4, where *E*(ϕ,ϕ) is the two-photon visibility for orthogonal polarization. With a visibility of 0.81 ± 0.02 in the H/V-basis and 0.85±0.02 in the 45°/135° basis, we obtain an average fidelity of (87 ± 3)%, which clearly overcomes the critical limit of 78% necessary to violate a Bell inequality (*17*). This fidelity was preserved over more than 2 hours, indicating the stability of the source and the links at the field site.

Further correlation coefficients were measured for a test of the Clauser-Horne-Shimony-Holt (CHSH) inequality (*18*), which, in contrast to the original Bell inequality (*19*), allows for nonperfect correlations by introducing experimentally accessible expectation values *E*(ϕ_{1},ϕ_{2}). We used single-output analyzers, i.e., a polarizer, instead of two-output analyzers such as a polarizing beamsplitter. The CHSH-inequality has the form (2) where *S* is the “Bell parameter.” The quantum-mechanical prediction for photon pairs in the singlet state is *E*(ϕ_{A},ϕ_{B}) = –cos[2(ϕ_{A} – ϕ_{B})]. The value for *S* is maximized for the set of angles = {0°,45°,22.5°,67.5°} to , which violates the limit of 2 and thus leads to a contradiction between local realistic theories and quantum mechanics. The experimentally obtained correlation coefficients are shown in Table 1. Using those values, we find *S* = 2.41 ± 0.10, demonstrating the violation of a Bell inequality by 4.1 standard deviations. Due to the low background level, no additional data correction was necessary. These results clearly demonstrate that the two separated receiver stations share an entangled quantum state distributed to them via free-space optical links.

(φ_{A},φ_{B}) | E(φ_{A},φ_{B}) |
---|---|

(0°,22.5°) | -0.509 ± 0.057 |

(0°,67.5°) | +0.643 ± 0.042 |

(45°,22.5°) | -0.558 ± 0.055 |

(45°,67.5°) | -0.702 ± 0.046 |

One of the benefits of a free-space distribution of quantum entanglement is the possibility of bridging large distances by additional use of space infrastructure such as satellites. Free-space links will provide a unique means to study fundamental limits due to long-distance deterioration of quantum correlations because of decoherence. In contrast, free-space quantum channels may provide the means to build truly global quantum communication networks. In the specific example of quantum cryptography, quantum entanglement enables secure key generation between the parties sharing entanglement (*20*), whereas the violation of a Bell inequality can provide a security test of the protocol (*21*). Although we did not intend to establish a cryptographic protocol, we can estimate the results for a cryptographic scheme based on entangled photons (*22*,*23*). A raw key is established by the anti-correlated detection events, which are obtained when both receivers randomly choose the same basis. A cryptographic system based on our setup would have shown a total raw key generation rate of a few tens of bits per second and an estimated quantum bit error rate (QBER) of ∼8.4%. We believe that these numbers can be improved significantly through improvements in telescope design.

Our link attenuation of 12 dB corresponds to a value that might be achievable with state-of-the-art space technology when establishing a free-space optical link between an Earth-based receiver telescope of 100 cm diameter and a satellite-based transmitter telescope of 20 cm diameter orbiting earth at a distance of ∼600 km (*24*). Typical losses in an actual satellite experiment might vary, depending on the link optics and on the performance of satellite pointing and tracking (*25*,*26*). Even then, our results represent an encouraging basis for future space experiments with entangled photons.