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Journal of Air Force Engineering University

Research on Clock Synchronization between Satellite and Ground Station Based on Second-order Correlation of the Quantum Entangled Photons

Yuan Bo-ru

Published Jan 1, 2014• 1 citation
OpenAlex

Abstract

The time synchronization accuracy on the order of nanoseconds can be provided using the conventional methods of time synchronization,a higher measurement accuracy on the order of femto-seconds can be reached by quantum measurement which employs entangled photon pairs in order to break the limit of measurement accuracy of conventional methods.The second-order correlation function of the entangled photon pairs which produced in a spontaneous type?Ⅱparametric down-conversion is investigated by integral transforming in the nonlinear crystal and substituting the first order expand of the wave vector.The relation between the second-order correlation function and temporal difference.A quantum method in clock synchronization between satellite and ground station is proposed based on the temporal correlation.The simulation indicates that the measurement accuracy provided by the second-order correlation function can be 70femto-seconds and the synchronization accuracy in the scheme can be 140femto-seconds in the ideal case.

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The time synchronization accuracy on the order of nanoseconds can be provided using the conventional methods of time synchronization,a higher measurement accuracy on the order of femto-seconds can be reached by quantum measurement which employs entangled photon pairs in order to break the limit of measurement accuracy of conventional methods.The second-order correlation function of the entangled photon pairs which produced in a spontaneous type?Ⅱparametric down-conversion is investigated by integral transforming in the nonlinear crystal and substituting the first order expand of the wave vector.The relation between the second-order correlation function and temporal difference.A quantum method in clock synchronization between satellite and ground station is proposed based on the temporal correlation.The simulation indicates that the measurement accuracy provided by the second-order correlation function can be 70femto-seconds and the synchronization accuracy in the scheme can be 140femto-seconds in the ideal case.
Based on the quantum feature and the quantum coherent principle of the entangled photon pairs produced with the spontaneous parametric down-conversion,a measurement method of the distant clock synchronization is studied.This method can not only be used in studying the distant clock synchronization and the quantum positioning,but is useful in measuring the time difference of a pair of entangled photon passing the nonlinear crystal.The results show that the shorter the time difference is,the better the coherence and synchronization of the two probed events are.
Accurate timekeeping is essential for scientific and technological advancements, particularly in areas of communication, networking, navigation, and high precision measurements. While many methods of time resolution are already established using classical resources, they fail to combine high precision outcomes with large-scale implementations. Additionally, numerous quantum networking architectures using satellite-assisted methods have demonstrated quantum communication on scales exceeding ground-based methods. For these reasons, we propose the use of a time synchronization method by which pairs of highly time-correlated photons are exchanged between clocks on satellites and clocks on Earth, al- lowing users to reconstruct the time offsets between their clocks. This is known as Quantum Clock Synchronization (QCS). We analyze global time synchronization, via numerical simulation, using a network of satellites equipped with quantum resources, such as entangled photon sources (SPDC) and single photon detectors. We find that for satellites in low-earth orbits, a configuration of 50 evenly-space satellites provides constant visibility and sub-nanosecond time synchronization to any location on Earth. Due to practical constraints, clocks available for use on satellites are often of lesser quality than those available for ground use. However, by allowing the satellites in our network to synchronize among themselves, we overcome this limitation, forming a highly precise “master clock” capable of global, high precision time synchronization. We then examine the amount of quantum security provided by polarization-entangled photon sources as a potential way to protect an experimental implementation of QCS from attacks such as signal spoofing. To do this, we identify regions on Earth where Bell violations between exchanged entangled photons can ensure quantum security at various confidence vii levels. Combined with similar insights gained from determining the network scale of our QCS protocol at the single-link level, we demonstrate the potential for highly precise, global, and potentially quantum-secure clock synchronization. Finally, we modify our QCS protocol to support frequency, or tick-rate, offsets in addition to constant time offsets. We motivate this by presenting some relativistic effects that can introduce frequency differences between clocks in space and on Earth. Provided that relative velocities between clocks are corrected for, we identify constant and variable clock defects through numerical simulations.
Based on the second-order quantum interference between frequency entangled photons that are generated by parametric down conversion, a quantum strategic algorithm for synchronizing two spatially separated clocks has been recently presented. In the reference frame of a Hong-Ou-Mandel (HOM) interferometer, photon correlations are used to define simultaneous events. Once the HOM interferometer is balanced by use of an adjustable optical delay in one arm, arrival times of simulta- neously generated photons are recorded by each clock. The clock offset is determined by correlation measurement of the recorded arrival times. Utilizing this algorithm, we demonstrate a proof-of-principle experiment for synchronizing two clocks separated by 4 km fiber link. A minimum timing stability of 0.44 ps at averaging time of 16000 s is achieved with an absolute time accuracy of 73.2 ps. The timing stability is verified to be limited by the correlation measurement device and ideally can be better than 10 fs. Such results shine a light to the application of quantum clock synchronization in the real high-accuracy timing system.
We propose a practical scheme of satellite-based quantum clock synchronization with atmospheric dispersion cancellation and by taking into account spacetime background of the Earth. Two frequency entangled pulses are employed to synchronize two clocks, one at a ground station and the other at a satellite. The time discrepancy of the two clocks is introduced into the pulses by moving mirrors and is extracted by measuring the coincidence rate of the pulses in the interferometer. We find that the pulses are distorted due to effects of gravity when they propagate between the Earth and the satellite, resulting in coincidence rate are remarkably affected. We also find that the precision of the clock synchronization are sensitive to the source parameters and the altitude of the satellite. Our proposal can be realized with current technology.
Clock synchronization between the ground and satellites is a fundamental issue in future quantum telecommunication, navigation, and global positioning systems. Here, we propose a scheme of near-Earth orbit satellite-based quantum clock synchronization with atmospheric dispersion cancellation by taking into account the spacetime background of the Earth. Two frequency entangled pulses are employed to synchronize two clocks, one at a ground station and the other at a satellite. The time discrepancy of the two clocks is introduced into the pulses by moving mirrors and is extracted by measuring the coincidence rate of the pulses in the interferometer. We find that the pulses are distorted due to effects of gravity when they propagate between the Earth and the satellite, resulting in remarkably affected coincidence rates. We also find that the precision of the clock synchronization is sensitive to the source parameters and the altitude of the satellite. The scheme provides a solution for satellite-based quantum clock synchronization with high precision, which can be realized, in principle, with current technology.