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Quantum-limited measurements of optical signals from a geostationary satellite
Kevin Günthner, Imran Khan, Dominique Elser, Birgit Stiller, Ömer Bayraktar, Christian R. Müller, Karen Saucke, Daniel Tröndle, Frank Heine, Stefan Seel, Peter Greulich, Herwig Zech, Björn Gütlich, Sabine Philipp-May, Christoph Marquardt, Gerd Leuchs
TL;DR
The paper examines whether quantum coherence properties remain preserved after optical signals travel 38,600 km from geostationary orbit through Earth’s gravitational potential and atmosphere. It measures satellite-to-ground signals and finds nearly vacuum-limited received states, while bounding possible excess noise in the link.
Problem
Whether quantum coherence properties are preserved after propagation over 38,600 km through Earth’s gravitational potential is a question relevant to testing quantum mechanics and quantum communication.
Source: p. 1Method
The authors make phase-space measurements of binary phase-modulated coherent optical signals sent from a geostationary satellite to an optical ground station.
Source: pp. 1–2Results
The received signal variance is 1.01 ± 0.03 times the vacuum quantum uncertainty, and the bound on excess noise is below 65 dB despite 85 dB overall loss.
Source: pp. 3–4Takeaways & Limitations
The measurements are a first step toward quantum communication from geostationary orbit, with existing coherent-communication hardware offering technological proximity to a global quantum network.
Source: p. 4Security proofs for continuous-variable discrete-modulation protocols still need improvement to support quantum channels with higher losses.
Source: p. 3
Abstract
from arXiv · showhide
The measurement of quantum signals that traveled through long distances is of fundamental and technological interest. We present quantum-limited coherent measurements of optical signals, sent from a satellite in geostationary Earth orbit to an optical ground station. We bound the excess noise that the quantum states could have acquired after having propagated 38600 km through Earth's gravitational potential as well as its turbulent atmosphere. Our results indicate that quantum communication is feasible in principle in such a scenario, highlighting the possibility of a global quantum key distribution network for secure communication.
Detailed description of signal analysis
The analysis recovers pulse centers from an asynchronous BPSK trace, then bins amplitude-modulated samples to estimate signal amplitudes and excess noise against vacuum noise. It limits fits to the receiver’s linear range and estimates uncertainty from fit and binning errors.
Detailed description of signal analysis
- 50 million samples at 40 GS/s span the 1.25 ms trace used for analysis.The trace was recorded while the satellite sent amplitude-modulated BPSK signals.Source: Detailed description of signal analysis · p. 5
- 5.2380(5) samples is the recovered clock offset, and 14.2222731533(3) samples per pulse corresponds to 2.81249(1) GHz.One sample is taken at each pulse center, where the measured X quadrature can determine the amplitude because ⟨P⟩=0.Source: Detailed description of signal analysis · p. 5
- 2,197 repetitions of the 0.568890(3) µs modulation period are superimposed before binning the trace into 50 amplitude segments.The channel transmission is treated as stationary over the 1.25 ms superposition.Source: Detailed description of signal analysis · p. 6
- The BPSK histograms are fit with a double Gaussian assuming equal variances for |+α⟩ and |−α⟩, while vacuum and dark-noise traces use single-Gaussian fits.Dark noise is subtracted from both vacuum and signal variances before excess noise is calculated relative to vacuum uncertainty.Source: Detailed description of signal analysis · pp. 6–7
- 13 segments with received amplitude below 2 are analyzed because the receiver becomes nonlinear at α ≥2.The fitted curves agree well with the measurements in the retained range.Source: Detailed description of signal analysis · p. 6, Figure S3 · p. 6
- 95% confidence intervals and a worst-case calculation bound excess-noise errors, with an additional error estimate for amplitude binning.A sinusoidal fit estimates the binning error from slightly different amplitudes grouped in each bin.Source: Detailed description of signal analysis · p. 7
Detector characterization
The detector characterization verifies linear vacuum-noise scaling with local-oscillator power and establishes the vacuum reference used for satellite signal measurements.
Detector characterization
- The vacuum noise power scales linearly with local-oscillator power under step-wise attenuation.The measurements use the same processing routine for vacuum and satellite signals, with single- and double-Gaussian fits, respectively.Source: Detector characterization · p. 7
- Telemetry records the detector DC outputs at 5 kHz and provides the local-oscillator power used to select the corresponding vacuum variance for each signal run.The measured power values calibrate the summed detector DC outputs in milliwatts.Source: Detector characterization · p. 7
- 6 dB is the clearance of measured vacuum quantum noise above detector electronic noise.The vacuum variance corresponding to each signal run is determined using ground-station telemetry.Source: Detector characterization · p. 7
Amplifier noise behavior
The satellite-terminal amplifier adds thermal excess noise to the BPSK signals before transmission, quantified from its noise figure and gain.
Amplifier noise behavior
- 33 dB above vacuum uncertainty is the quadrature variance associated with the amplified thermal quantum states.This value follows from the amplifier’s 6.4 dB noise figure and 27 dB gain.Source: Amplifier noise behavior · p. 7
- 6.4 dB is the amplifier noise figure, expressed as the ratio between input and amplified-signal signal-to-noise ratios.The noise figure is reported as NF.Source: Amplifier noise behavior · p. 7
- 27 dB of amplifier gain accompanies the reported 6.4 dB noise figure in the satellite signal chain.Together, these amplifier characteristics correspond to thermal states with a quadrature variance about 33 dB above vacuum uncertainty.Source: Amplifier noise behavior · p. 7
Virtual aperture concept
A virtual aperture at the exosphere estimates how much sender excess noise remains after diffraction, separating it from noise added later by the atmosphere or ground station. Under this model, the sender contribution is negligible at the virtual aperture, and the atmosphere’s added excess noise is bounded.
Virtual aperture concept
- An aperture smaller than the beam diameter sees reduced excess noise; to bound atmospheric excess noise, the analysis considers a virtual aperture in the exosphere 1000 km above ground.The beam waist is 6 cm, and the spot radius is evaluated at 38,600 km from the satellite.Source: Virtual aperture concept · p. 8
- The estimate approximates the Airy-pattern center as Gaussian and integrates the intensity ratio over the virtual aperture.Propagation from GEO to the exosphere is assumed quasi-vacuum and to add no noise.Source: Virtual aperture concept · p. 8
- 0.8 ± 2.4 is the estimated atmospheric excess-noise bound after scaling for station technical losses and 3 dB of atmospheric losses.The estimate conservatively assumes the receiving station operates noiselessly.Source: Virtual aperture concept · p. 8
- Scaling the 33 dB initial excess noise by diffraction loss leaves -28 dB, or 0.001 units above vacuum uncertainty, at the virtual aperture.The resulting states there are treated as quantum noise limited for practical purposes.Source: Virtual aperture concept · p. 8
- At the ground aperture, detected excess noise is attributed to the atmosphere and/or technical noise inside the TAOGS.The atmospheric bound is obtained by conservatively assuming no noise from the receiving station.Source: Virtual aperture concept · p. 8