QKD: Add more text on loss mechanisms

chapter-qkd/chapter.tex

@@ -437,6 +437,7 @@ various aspects of currents in superconducters as well as phonons\cite{berriosHi
 \todoplaceholder{Something is missing here.}
 
 \subsection{Practical Challenges}
+
 The central challenge in general quantum computers is extending the lifetime of the quantum state encoding a qubit.
 Quantum states are extremely sensitive to disturbances, and despite the best efforts to shield them against external
 influence, their lifetime is still inconveniently short compared to the timescales required for quantum computation,
@@ -492,27 +493,65 @@ concern of photon number splitting attacks and because of decoherence\footnote{
     could increase the quantum state's photon number, adding entangled photons that share the original quantum state.
     Alas, doing this would not gain us much in a QKD system because an interaction of any of the quantum state's photons
     with the fiber---that is, the same loss as before---would disturb the entire entangled state.
-}, and thus the system's bit rate decreases exponentially with distance due to absorption. Some QKD systems can reach
+}, and thus the system's bit rate decreases exponentially with distance due to attenuation. Some QKD systems can reach
 ranges of several hundred kilometers, but the resulting payload data rate---usually called \emph{secret key rate}---of
 these long distance systems is measured in kilobits per second.
 
+\subsection{Loss in optical fibers}
+
 When transmitted over a fiber, there are multiple effects that degrade the quantum-optical signal of a QKD system, which
 are collectively referred to as \emph{loss}. We can coarsely classify these degrading effects into two categories:
-\emph{Decoherence}, and \emph{Absorption}. Decoherence effects result in the quantum state being changed in transit,
+\emph{decoherence}, and \emph{attenuation}. Decoherence effects result in the quantum state being changed in transit,
 which depending on the QKD implementation may mean destroying information contained within the state such as by
 disturbing the pulse's polarization, or destruction of entanglement between the in-flight state and another local state.
-In an optical channel affected by such decoherence effects, a quantum state enters the channel, and subsequently exits
-it at the other end changed. In contrast, absorption means the quantum state is not ever leaving the channel.
+In contrast, attenuation means the quantum state is not ever leaving the channel.
 
-In practice, absorption limits the length of an individual fiber run, as it becomes problematic at short distances.
-Decoherence is less relevant for the distance limitation, and mostly limits which fiber-optic technologies can be
+In practice, attenuation is the primary factor limiting the length of an individual fiber run in QKD. Even modern,
+ultra-low loss optical fiber has an attenuation in the order of \qty{0.15}{\decibel\per\kilo\meter}, resulting in a loss
+of half the signal's power, equivalent to half of all QKD pulses, in just \qty{20}{\kilo\meter}. For longer reaches,
+these losses ar multiplicative, so after only \qty{200}{\kilo\meter} only one in a thousand single-photon pulses entering
+the fiber will exit it at the other end \cite{chesnoyUnderseaFiberCommunication2015}.
+
+Decoherence effects are less relevant for the distance limitation, and mostly limit which fiber-optic technologies can be
 utilized in the first place. Due to decoherence, QKD systems usually use Single-Mode (SM) fiber over Multi-Mode (MM)
 fiber, and decoherence makes it more difficult to utilize Wavelength Division Multiplexing (xWDM) to send multiple
-either quantum or classical optical signals through a single fiber. \todo{go more into the details on xWDM, elaborate on
-decoherence mechanisms, especially crosstalk in the context of
-xWDM.}
+either quantum or classical optical signals through a single fiber. 
 
-\todo{CV-QKD}
+Attenuation in optical fibers has a number of origins. The main factor is scattering of photons on the fiber core, with
+absorbtion due to interactions between photons and the fiber core's molecular structure or embedded contaminants only
+playing a minor role. The primary component of scattering is fluctuations in the fiber core's molecular structure, with
+scattering on phonons (Brillouin scattering) or photons (Raman scattering) only adding a samll amount of
+loss\cite{wandelAttenuationSilicabasedOptical2006}.
+
+Like attenuation, decoherence can also result from a number of different mechanisms. Two optically \emph{linear}
+mechanisms, i.e.\ ones that do not depend on incident signal power, are chromatic dispersion and polarization mode
+dispersion (PMD). PMD disturbs the signal's polarization. PMD strongly depends on wavelength and is highly sensitive to
+environmental factors such as temperature or vibration \cite{brodskyPolarizationModeDispersion2006}. QKD systems
+frequently use polarization-based encodings, which are sensitive to PMD. PMD is usually mitigated by continuously
+measuring the fiber's end-to-end PMD, and adjusting a polarization controller placed
+in-line\cite{wangLongdistanceCopropagationQuantum2017, ImpactPolarizationMode,
+agnesiAllfiberSelfcompensatingPolarization2019} with the fiber to cancel out the fiber's PMD.
+
+Chromatic dispersion arises from the fiber's materials' refractive index not being perfectly constant across
+the spectral bandwidth of the optical signal, leading some frequency components of the signal to traverse the fiber
+faster than others, resulting in pulses being spread out as they continue along the fiber. Chromatic dispersion is a
+concern in some long-distance QKD systems that need to operate at a timing precision down to a few dozen picoseconds,
+but like PMD it can be compensated at the endpoint \cite{neumannExperimentallyOptimizingQKD2021,
+kiselevAnalysisChromaticDispersion2020}.
+
+Nonlinear effects such as the AC Kerr Effect, Stimulated Raman Scattering as well as Stimulated Brillouin Scattering
+can produce intermodulation when a quantum optical signal is sent through the same fiber as another, much brighter
+classical optical signal. These nonlinear effects are relevant for QKD systems that either send a reference clock
+through the same fiber as the QKD pulses, or that aim for coexistence between QKD pulses and classical optical
+networking on the same fiber, for instance in an in xWDM setup.
+
+In the AC Kerr effect, a strong optical signal influences the refractive indes of the fiber core, which modulates other
+signals propagating through the same fiber. Stimualated Brillouin Scattering arises when a high-power incident signal
+causes the emission of phonons inside the fiber core, which then act as a source of Brillouin scattering to weaker
+signals\cite{chesnoyUnderseaFiberCommunication2015}. Stimulated Raman Scattering is similar, only that the QKD signal is
+affected by direct Raman scattering on the stronger signal's photons.
+
+\todo{Some detail on CV-QKD}
 
 \subsection{Relaying}
 \todo{(one?) term of the art seems to be "repeater"}