QKD: add part on MDI-QKD

chapter-qkd/chapter.tex

@@ -434,7 +434,8 @@ No-Cloning Theorem and sometimes quantum entanglement in their operation, the sc
 limited. QKD systems always operate on photons, while general quantum computers use a variety of physical
 implementations for their qubits that include photons and squeezed light, but extend over atom nuclei, trapped ions,
 various aspects of currents in superconducters as well as phonons\cite{berriosHighFidelityQuantum2012}.
-\todoplaceholder{Something is missing here.}
+
+\todoplaceholder{Add concrete description of at least one QKD protocol (BB84?)}
 
 \subsection{Practical Challenges}
 
@@ -514,8 +515,8 @@ 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, 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. 
+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. 
 
 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
@@ -539,29 +540,31 @@ concern in some long-distance QKD systems that need to operate at a timing preci
 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.
+Besided linear Brillouin and Raman Scattering, nonlinear effects such as the AC Kerr Effect, Stimulated Raman Scattering
+as well as Stimulated Brillouin Scattering can produce intermodulation and crosstalk 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\cite{choiQuantumKeyDistribution2010}.
 
-In the AC Kerr effect, a strong optical signal influences the refractive indes of the fiber core, which modulates other
+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
-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.
+causes the emission of phonons inside the fiber core, which then act as a source of Brillouin scattering. Stimulated
+Raman Scattering is a similar effect based on Raman scattering\cite{chesnoyUnderseaFiberCommunication2015}. When a fiber
+is shared between weak QKD and bright classical signals, both Brillouin and Raman scattering introduce noise in the QKD
+channel as photons from the classical signal change their wavelength, and might end up inside the QKD channel's
+bandwidth\cite{choiQuantumKeyDistribution2010}.
 
 \todo{Some detail on CV-QKD}
 
 \subsection{Relaying}
 \todo{(one?) term of the art seems to be "repeater"}
 
-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.
+We cannot use conventional optical amplifiers to extend the range of a single continuous QKD link lest we destroy the
+signal or we might enable attacks. What remains as ways to extend the range of a QKD link are \emph{relaying} methods,
+where one QKD link is terminated at a relay station partway to its destination, and another is started, with the relay
+proxying information between the two. We can separate relay implementations into two broad categories.
 
-\todo{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
@@ -576,6 +579,29 @@ relay implementations into two broad categories.
         the quantum forwarding process inside the relay.
 \end{description}
 
+For practical purposes, classical relays are the only relevant option. A long-range QKD system employing classical
+relays would be able to cover arbitrary distances, trading off reliance upon physical security of the trusted relay
+stations. Academic work on QKD recognizes this limitation, but few proposals to its solution have been put forth.
+
+\subsection{Range extension in Measurement Device Independent (MDI)-QKD}
+
+One technology closest to a solution on the trusted relay issue is Measurement Device Independent (MDI)-QKD. Broadly
+speaking, in an MDI-QKD system two QKD endpoints are connected through exactly one relay (or router). The key idea of
+MDI-QKD is to move all trusted components of the protocol out of this central relay, and into the trusted nodes at both
+ends of the link. Instead of directly measuring the photons sent by both endpoints, the relay node has them interfere
+and measures the result of this interference. This measurement result does not allow the relay to draw any conclusions
+on the individual qubits that the endpoints exchange, but when the relay communicates these measurements to the
+endpoints, the endpoints can reconstruct their shared secret key bits. Although in MDI-QKD the relay node still performs
+quantum measurements and participates in the overall QKD protocol, the protocol guarantees that even a malicious relay
+cannot learn anything about the exchanged keys from its limited vantage point.
+
+MDI-QKD effectively doubles the range of a QKD system. Unfortunately, the approach from MDI-QKD cannot be adapted to
+multiple chained relays, and thus it is mostly interesting for hub and spoke-style quantum network topologies. In a
+relay-assisted long-range QKD system, MDI-QKD could only be used to eliminate trust in half of the relays, which in the
+grand scheme of things does not reduce attack surface by much.
+
+\todo{Mention entanglement swapping range extension}
+
 \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