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@ -496,7 +496,13 @@ concern of photon number splitting attacks and because of decoherence\footnote{
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 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.
these long distance systems is measured in kilobits per second. An interesting observation from theoretical work on
quantum key distribution algorithms is that not only is this exponential rate decay a fundamental limit for a given QKD
implementation, but it is even possible to determine a protocol-independent upper bound for a noiseless, lossy optical
channel's secret key rate. This upper bound shows the same exponentail decay and, notably, is independent of the optical
power, which is directly proportional to the repetition rate of the QKD protocol's measurements. Modulo some small,
constant factor, this upper bound cannot be circumvented with any amount of protocol engineering, or source or detector
improvements\cite{takeokaFundamentalRatelossTradeoff2014}.
\subsection{Loss in optical fibers}
@ -516,7 +522,8 @@ the fiber will exit it at the other end \cite{chesnoyUnderseaFiberCommunication2
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\cite{amitonovaQuantumKeyEstablishment2020}, 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.
Multiplexing (xWDM) to send multiple either quantum or classical optical signals through a single fiber.\todo{is this
right?}
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
@ -545,7 +552,7 @@ as well as Stimulated Brillouin Scattering can produce intermodulation and cross
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\cite{choiQuantumKeyDistribution2010}.
setup\cite{choiQuantumKeyDistribution2010, grunenfelderLimitsMultiplexingQuantum2021}.
In the AC Kerr effect, a strong optical signal influences the refractive index of the fiber core, which modulates other
signals propagating through the same fiber. Stimualated Brillouin Scattering arises when a high-power incident signal

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Subproject commit 3a7edbd1127cacc8f4c90376595b894105f3d479

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