Quantum entanglement was termed "spooky action at a distance" in the well-known paper by Einstein, Podolsky, and Rosen. Entanglement is expected to be distributed over longer and longer distances in both practical applications and fundamental research into the principles of nature. Here, we present a proposal for distributing entangled photon pairs between Earth and the Moon using a Lagrangian point at a distance of 1.28 light seconds. One of the most fascinating features in this long-distance distribution of entanglement is as follows. One can perform the Bell test with human supplying the random measurement settings and recording the results while still maintaining spacelike intervals. To realize a proof-of-principle experiment, we develop an entangled photon source with 1 GHz generation rate, about 2 orders of magnitude higher than previous results. Violation of Bell's inequality was observed under a total simulated loss of 103 dB with measurement settings chosen by two experimenters. This demonstrates the feasibility of such long-distance Bell test over extremely high-loss channels, paving the way for one of the ultimate tests of the foundations of quantum mechanics.
Long-distance entanglement distribution is essential for both foundational tests of quantum physics and scalable quantum networks. Owing to channel loss, however, the previously achieved distance was limited to ~100 kilometers. Here we demonstrate satellite-based distribution of entangled photon pairs to two locations separated by 1203 kilometers on Earth, through two satellite-to-ground downlinks with a summed length varying from 1600 to 2400 kilometers. We observed a survival of two-photon entanglement and a violation of Bell inequality by 2.37 ± 0.09 under strict Einstein locality conditions. The obtained effective link efficiency is orders of magnitude higher than that of the direct bidirectional transmission of the two photons through telecommunication fibers.
It is commonly accepted that the results of measurements simultaneously realized over two entangled subsystems are statistically correlated instantaneously regardless of the distance between them. In accordance with Bell theorem, everything happens in such measurements as if there was a correlation propagating at infinite speed between the two subsystems.These correlations have been so far verified experimentally up to a distance of 1200 km. We discuss the interest and feasibility of extending this distance to 390,000 km, thus gaining a factor of 300. The idea is to install one of the polarimeters on the Moon, with the other on Earth. Such an experiment would provide a new test of Quantum Physics and allow to put higher constraints on alternative theories and interpretations. We also discuss the possibility to violate Bell inequalities beyond Earth-Moon distance.
Quantum entanglement is a non-classical correlation between quantum systems that cannot be accounted for by any local hidden-variable theory. Since its articulation in the Einstein-Podolsky-Rosen paper of 1935 and its formal testability through Bell's theorem in 1964, entanglement has evolved from a philosophical puzzle into the central resource of quantum information science. This review surveys the conceptual foundations of entanglement, the experimental record culminating in loophole-free Bell tests, and applications including quantum key distribution, quantum teleportation, and measurement-based quantum computation. We summarise quantitative results of representative Bell experiments, discuss entanglement measures for mixed states, and outline recent developments in long-distance entanglement distribution via satellites and quantum repeaters. Persistent challenges decoherence, certification of high-dimensional entanglement, and scalable distribution are identified as active frontiers of research.
Verifying the violation of Bell's inequality is one of the most representative methods to demonstrate that entangled photon pairs prepared in a quantum optics-based system exhibit quantum properties. While experiments on Bell inequality violations have been theoretically well-established and extensively conducted to implement various quantum information technologies in laboratory settings, mathematical modeling for systematically describing the distribution of high-brightness entangled photon pairs in high-loss environments remains an issue that requires further research. As the brightness of the entangled photon pairs increases, the influence of multi-photon effects becomes more significant, leading to a decrease in the CHSH value
Sand also a reduction in the standard deviation of the CHSH value
ΔS. Therefore, a new analysis of the
(S−2)/ΔSvalue is required to more precisely confirm the degree of CHSH inequality violation including the reliability of
S. In this paper, we propose a mathematical model to predict the
(S−2)/ΔSvalue as a function of the brightness of the entangled photon pair source, and we also suggest the need to optimize the brightness of this source. Additionally, we provide experimental evidence supporting this model. The experiment confirms that when the mean photon number is
μ=0.026in an entanglement distribution setup with a total loss of
−19.03dB, the CHSH value drops to 2.69, while the
(S−2)/ΔSvalue increases to 60.95.
Verifying the violation of Bell's inequality is one of the most representative methods to demonstrate that entangled photon pairs prepared in a quantum optics-based system exhibit quantum properties. While experiments on Bell inequality violations have been theoretically well-established and extensively conducted to implement various quantum information technologies in laboratory settings, mathematical modeling for accurately predicting the distribution of high-intensity entangled photon pairs in high-loss environments remains an issue that requires further research. As the brightness of the entangled photon pairs increases, the influence of multi-photon effects becomes more significant, leading to a decrease in the CHSH value
S and also a reduction in the standard deviation of the CHSH value
ΔS. Therefore, a new analysis of the
(S−2)/ΔS value is required to more precisely confirm the degree of CHSH inequality violation including the reliability of
S. In this paper, we propose a mathematical model to predict the
(S−2)/ΔS value as a function of the brightness of the entangled photon pair source, and we also suggest the need to optimize the brightness of this source. Additionally, we provide experimental evidence supporting this model. The experiment confirms that when the mean photon number is
μ=0.026 in an entanglement distribution setup with a total loss of
−19.03 dB, the CHSH value drops to 2.69, while the
(S−2)/ΔS value increases to 60.95.