\section{Full setup description}
\label{appendix:setup}
\label{appendix:copropagation}

\graphic[wide,label=schematic]{figures/schematics/20260129_source_copropagating.eps}{
  Full schematic of the experimental setup.
  Schematic of the QKD setup with the non-degenerate entangled photon pair source scheme per construction in \cite{shenDistributingPolarizationEntangled2022}.
  405\,nm pump light is split into two paths and undergoes Type-0 SPDC in a ppKTP crystal, generating photon pairs of non-degenerate wavelengths at 586\,nm (signal) and 1310\,nm (idler).
  A pair of $\alpha{}$-BBO crystals separately recombine the signal and idler to create the polarization-entangled state $\ket{\Phi{}^{+}} = \frac{1}{\sqrt{2}}\left(\ket{HH} + \ket{VV}\right)$. DM:~Dichroic mirror; LP:~Longpass filter; BP:~Bandpass filter.
  Each photon is sent through a passive beamsplitter array consisting of 50:50 and polarizing beamsplitters (PBS) for measurement along the rectilinear (HV) and diagonal (DA) polarization bases. Detection events from the individual APDs are registered on corresponding time taggers. A classical authenticated communication channel is used for photon pair coincidence tracking and frequency compensation.
}

% Description of QKD scheme and key points that make the protocol work
We perform entanglement distribution as per the BBM92 QKD protocol:
the $\ket{\Phi^+}$ maximally-entangled state in the polarization degree of freedom is distributed between two parties, one situated locally (Alice) and the other situated remotely (Bob).


% Overall description of source
Highly wavelength-asymmetric photon pairs are generated by Type-0 spontaneous parametric downconversion (SPDC) in a periodically-poled potassium titanyl phosphate (ppKTP) crystal, following the scheme
$$
405\,\text{nm} \rightarrow 586\,\text{nm} + 1310\,\text{nm}.
$$
This is illustrated in Fig.~\ref{schematic}.
The linear displacement interformetric configuration of the pair source generates the $\ket{\Phi^+}$ state, by spatially overlapping two downconversion beams from the same nonlinear crystal to yield the $(\ket{HH} + e^{i\theta}\ket{VV})/\sqrt{2}$ state, with phase compensation achieved by tilts in the half-wave plate (HWP).
The signal 586\,nm and idler 1310\,nm photons are wavelength-separated with a dichroic mirror, the former measured locally by Alice and the latter remotely by Bob.
Figure~\ref{schematic} illustrates the aforementioned pair source setup, and a more complete description of the setup can be found in \cite{shenDistributingPolarizationEntangled2022}.


% Source operating parameters and output properties
We measured 150,000\,photon pairs/s using a pair of APDs, using an input pump power of 8.1\,mW.
A plot of the source visibility is shown in Fig.~\ref{source:visibility}.
The high asymmetry in downconversion wavelengths results in an instrincally narrow bandwidth of 0.7\,nm (120\,GHz) for the 1310\,nm idler light, without the use of additional spectral filtering optics.

Each photon of the pair is projected into either the rectilinear (HV) or diagonal (DA) polarization bases using a passive beamsplitter array, and detection events are timestamped on free-running time taggers. A motorised polarization controller (MPC) performs active polarization compensation for rotations in the fiber.

\section{Photon pair source}
\label{appendix:source}

 ( 405\,nm ), 405\,nm pump light
   is split into two paths and undergoes Type-0 SPDC in a ppKTP crystal, generating photon pairs of non-degenerate wavelengths at 586\,nm (signal) and 1310\,nm (idler).
  A pair of $\alpha{}$-BBO crystals separately recombine the signal and idler to create the polarization-entangled state $\ket{\Phi{}^{+}} = \frac{1}{\sqrt{2}}\left(\ket{HH} + \ket{VV}\right)$. DM:~Dichroic mirror; LP:~Longpass filter; BP:~Bandpass filter. TODO

\graphic[label=source:visibility]{figures/plots/sourcevisibility.eps}{
  Visibility of the pair source. Visibility is at least XXX.
  Pair source visibility as a metric of entanglement fidelity.
  Each curve is obtained by projecting the polarization for 586\,nm light, and scanning the polarization of 1310\,nm light using a rotating HWP.
}

\section{Clock synchronization}
\label{appendix:clocksync}

\graphic[label=sync:correlation]{figures/plots/sync_freqcorrelation.png}{
  \textbf{Top:} Frequency stability plot. Green shows actual frequency.
  \textbf{Bottom:} Plot of temperature at Clementi. No correlation with temperature observed.
}

Whenever costream drops (on average every 5 minutes), readevents will be killed (blue), which results in the timestamp card cooling down. Restarting the timestamp card causes it to warm up again, with a time constant of 12 minutes (orange).
The green is the true frequency drift.

Calculations on the frequency stability are based on this green curve.

\todo{Condense the appendix to just mention that costream drops events regularly, and there are knock-on effects on frequency stability, coincidence rate.}


\section{OSA}
\label{appendix:osa}

\graphic[label=osa]{figures/plots/transceiver_1550nm.png}{
  Spectral density of the 1550\,nm transceiver measured by using an optical spectrum analyzer (Yokogawa AQ6370E) at 0.1\,nm resolution, with the inset showing the spectrum peak offset by 1550.2\,nm.
}

The spectrum of the C-band transceiver is shown in Fig.~\ref{osa}, measured by tapping one of the dual-simplex channel with a 50:50 fiber beamsplitter. The maximum power of the transceiver is -0.7\,dBm. It has a -30\,dB bandwidth of 0.4\,nm and sidebands at -43.2\,dB.

Significant light leakage is present in the laser, measuring at -83\,dBm/nm at the 1310\,nm wavelength.
This is easily suppressed by \todo{XXX} orders of magnitude using another inline WDM (not depicted in Fig.~\ref{schematic}), such that no excess O-band light from the laser contributes to the noise counts.

% Possibly add scaling of attenuation with dark counts in the receiver boxes


\section{Deployed fiber OTDR}
\label{appendix:otdr:semb}

% and possibly co-propagation setup description here.

\begin{figure}
  \centering
  \includegraphics[width=\linewidth]{figures/fiber_otdr_semb.png}
  \caption{\label{system:otdr:semb}
    \textbf{Top:} Optical time-domain reflectometry (OTDR) measurement of deployed fiber link between S15, CQT and NetLink Trust Sembawang Central Office. Fiber is a G.652 telecommunications fiber [TODO: Check this] spanning 29.5\,km with 11.5\,dB loss at 1310\,nm transmission wavelength.
    \textbf{Bottom:} Map showing the corresponding QKD node locations, with straight-line distance of XXX\,km.
  }
\end{figure}


\section{Temperature correlations}
\label{appendix:correlations}
\graphic[label=appendix:comp]{figures/plots/result_qber_comp.png}{
  No correlation with temperature and rainfall observed.
}


\section{SUTD}
\label{appendix:sutd}

\begin{figure*}
  \centering
  \begin{minipage}[t]{0.5\textwidth}
    \includegraphics[width=\textwidth]{figures/sketches/nussutdfiber_reduced.pdf}
  \end{minipage}
  \begin{minipage}[t]{0.45\textwidth}
    \includegraphics{figures/fiber2.eps}
  \end{minipage}
  \caption{\label{otdr}
    \textbf{Left:} QKD node locations in Singapore, with a straight-line distance of 21\,km between the two nodes. \todo{Add SUTD node as well}
    \textbf{Right:} Optical time-domain reflectometry (OTDR) measurement of the deployed fiber link between NUS and SUTD. The measured distance is 46.4\,km with 19.20\,dB cumulative loss for 1310\,nm light. Reflection spikes and dips occur at fiber patching points.
  }
\end{figure*}


Telecommunication fiber is deployed between Center for Quantum Technologies, National University of Singapore (NUS), and Future Communications Connectivity Lab, Singapore University of Technology and Design (SUTD), with a total fiber length of 46.4\,km as shown in Fig.~\ref{otdr}.
The entanglement pair source is situated in NUS with the 586\,nm photons measured locally, while the 1310\,nm photons are sent over the fiber to SUTD for remote measurement.


\section{Loss budget}
\label{appendix:loss}


\setlength{\tabcolsep}{0.5em}% for horizontal padding
{\renewcommand{\arraystretch}{1.2}% for vertical padding
\begin{table}
  \begin{tabular}{|l|c|}
    \hline \textbf{Cause} & \textbf{T (dB)} \\
    \hline Coupling into deployed fiber & -0.1 \\
    \hline Deployed fiber & -19.2 \\
    \hline LCVR transmission & -2.2 \\
    \hline Fiber-fiber coupling in free space & -1.0 \\
    \hline Detector efficiency & -9.2 \\
    \hline
  \end{tabular}
  \caption{\label{losses} Transmission loss contributions from different components in the 1310\,nm channel. }
\end{table}
}
