More QKD WIP

chapter-qkd/Makefile

@@ -10,9 +10,9 @@ VERSION_STRING := $(shell git describe --tags --long --dirty)
 
 all: chapter.pdf
 
-%.pdf: %.tex %.bib version.tex
+%.pdf: %.tex ../main.bib version.tex
 	pdflatex -shell-escape $<
-	biber $* 
+	biber $*
 	pdflatex -shell-escape $<
 
 .PHONY: preview

chapter-qkd/chapter.tex

@@ -13,7 +13,7 @@
     doi=true,
     eprint=false
     ]{biblatex}
-\addbibresource{chapter.bib}
+\addbibresource{../main.bib}
 \usepackage{amssymb,amsmath}
 \usepackage{listings}
 \usepackage{eurosym}
@@ -240,6 +240,7 @@ limited. QKD systems always operate on photons, while general quantum computers
 implementations for their qubits that include photons and squeezed light, but extend over atom nuclei, trapped ions,
 various aspects of currents in superconducters into phonons\cite{berrios_high_2012}.
 
+\subsubsection{Practical Challenges}
 % FIXME I don't like this paragraph.
 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 their quantum states
@@ -271,8 +272,58 @@ partway through the fiber. In QKD systems however, the signal cannot be amplifie
 exponentially decreases with distance due to absorption. Some QKD systems can reach ranges of several hundred kilometer,
 but the useable data rate (here called \emph{key rate}) of these systems usually is in the kilobits per second or worse.
 
+QKD signals cannot be amplified because their security rests on the fact that each transmitted quantum state on average
+only contains on the order of one photon each. Security rests on the No-Cloning Theorem, which implies that not just
+attackers, but even the system's operators are unable to duplicate the quantum state in flight without destroying it.
+
+When transmitted over a fiber, there are multiple effects that degrade the quantum-optical signal of a QKD system. 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, 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 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
+utilized in the first place. Due to decoherence, QKD systems usually use Single-Mode (SM) fiber over Multi-Mode (MM)
+fiber, and makes it more difficult to utilize Wavelength Division Multiplexing (xWDM) to send multiple either quantum or
+classical optical signals through a single fiber.
+% FIXME go more into the details on xWDM, elaborate on decoherence mechanisms, especially crosstalk in the context of
+% xWDM.
+
+% FIXME CV-QKD
+
+\subsubsection{Relaying}
+
+The No-Cloning Theorem prevents us from using conventional optical amplifiers to extend the range of a single continuous
+QKD link. What remains as ways to extend the range of a QKD link are \emph{relaying} methods, where one QKD link is
+terminated at the relay, and another is started, with the relay proxying information between the two. We can separate
+relay implementations into two broad categories.
+
+% FIXME mention that one MDI-QKD range doubling hack
+\begin{description}
+    \item[Classical relays] encompass the trivial implementation of a relay, where the QKD link is formed by simply
+        stitching two QKD links together by connecting one link's receiver to the other link's transmitter. The key
+        characteristic of classical relays is that inside the relay, the link's cryptographic payload information is
+        handled in its classical plaintext form. Classical relays are practically feasible, but because they must handle
+        the payload in plaintext form, they are security-critical.
+
+    \item[Quantum relays] are relays that forward the QKD payload information from one link to the other in the quantum
+        realm, without translating it to classical information and back. QKD relays are currently not practically
+        feasible, but if they become available in the future, they would allow range extension without compromising the
+        QKD link's security as the same tamper-detecting properties that the QKD links provide can be extended to cover
+        the quantum forwarding process inside the relay.
+\end{description}
+
 \section{Quantum Networking}
 
+So far we have focused on the range limitation of a single QKD link with classical relays as the only practical solution
+at this point in time. Quantum Networks naturally follow from a relay-assisted QKD link, if we consider a type of
+``relay'' that is connected to more than two links. Just like switches and routers can be meshed to construct complex
+topologies in classical wide-area networks (WANs), such multi-fanout relays, or \emph{routers} can be used to provide
+QKD services over complex network topologies.
+
 \section{Securing QKD Networks with Inertial HSMs}
 
 As we discussed above, when it comes down to practical, end-to-end security properties, Quantum Key Distribution