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Table 1 List of parameters and values for which we assigned fixed values. Justification of these values is given in Sect. 3

From: Q3Sat: quantum communications uplink to a 3U CubeSat—feasibility & design

Symbol Parameter Value
\(d_{B}\) Diameter of active detector area on CubeSat 20 μm
\(D_{A}\) OGS telescope diameter 30 cm
\(D_{B}\) CubeSat telescope diameter 10 cm
\(e_{0}\) Probability of noise count to be correct 50%
\(e_{d}\) Probability of erroneous detection 2%
\(E^{\mathit {max}}_{\mathit {E}91/\mathit {DSP}}\) Maximum tolerable QBER for E91/DSP 10.2% /6.2%
\(\eta_{A}\) OGS multiplexed SNSPD efficiency (E91 only) 70% (−1.5 dB)
\(\eta_{B}\) CubeSat detector efficiency 15% (−8.2 dB)
f Error correction protocol efficiency 1.1
\(f_{B}\) Effective focal length CubeSat telescope 40 cm
\(f_{\mathit {SYN}}\) Repetition rate of OGS’s beacon laser 10 MHz
FoV Field of view CubeSat (full angle) 50 μrad
λ Signal photon wavelength 810 nm
Λ Total loss −62.7 dB (max)
\(\Lambda_{A}\) Total loss OGS arm (source to detector) (E91 only) 60% (−2.3 dB)
\(\Lambda_{H}\) Heralding efficiency (E91 only) 85% (−0.7 dB)
\(\Lambda_{\mathit {TA}}\) OGS telescope loss (only E91) −1.0 dB
\(\Lambda_{\mathit {TB}}\) CubeSat telescope loss −1.5 dB
\(\Lambda_{\mathit {OB}}\) CubeSat optical elements loss −1.0 dB
\(\Lambda_{\mathit {PB}}\) CubeSat pointing loss −2.5 dB
\(\Lambda_{\mathit {SB}}\) CubeSat basis switch loss −0.5 dB
\(\Lambda_{\mathit {SYN}}\) Loss due to errors in clock sync. −0.5 dB
\(\mu_{\mathit {DSP}}\) Mean photon number per signal pulse (DSP only) 0.64
\(\mu_{\mathit {E}91}\) Mean photon number per coincidence window (E91 only) 0.01
\(r_{0}\) Fried parameter 5 cm–40 cm
\(R_{A}\) OGS count rate (E91 only) 60 Mcps
\(R_{B}\) CubeSat count rate (including noise) 3 kcps (max)
\(R_{B}^{\mathit {max}}\) CubeSat detectors’ maximum count rate 100 kHz
\(R_{\mathit {BG}}\) CubeSat background counts (total) 80–180 cps
\(R_{\mathit {DC}}\) CubeSat dark count rate (per detector) 200 cps
\(R_{B+D}\) CubeSat total noise counts 480–580 cps
\(R^{P}_{\mathit {DSP}}\) Effective signal photon rate (DSP only) 315 Mcps
\(R^{P}_{\mathit {E}91}\) Pair rate of entangled photon source (E91 only) 100 Mcps
\(R_{\mathit {rep}}\) Repetition rate of single photon source (DSP only) 1 GHz
\(\sigma_{A}\) OGS pointing precision (rms, full angle) 2.4 μrad
\(\sigma_{B}\) CubeSat pointing precision (rms, full angle) 40 μrad
\(t_{A}\) Combined OGS detectors + time tagging jitter 16 ps
\(t_{B}\) CubeSat detector + time tagging jitter 37 ps
τ Coincidence window 80 ps
\(t_{\mathit {SB}}\) CubeSat basis switching time 100 μs
\(t_{\mathit {TT}}\) Time tagging resolution (on board CubeSat) 10 ps
\(t_{\mathit {MD}}\) Measurement duration of each chunk for clock sync. 100 ms
\(t_{\mathit {QC}}\) Maximum duration of quantum connection per pass 220 s