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

main.bib

@@ -70,6 +70,26 @@
   file = {/home/jaseg/Zotero/storage/2EYFTVCY/Amiri et al. - 2018 - Efficient Unconditionally Secure Signatures Using .pdf}
 }
 
+@article{amitonovaQuantumKeyEstablishment2020,
+  title = {Quantum Key Establishment via a Multimode Fiber},
+  author = {Amitonova, Lyubov V. and Tentrup, Tristan B. H. and Vellekoop, Ivo M. and Pinkse, Pepijn W. H.},
+  date = {2020-03-02},
+  journaltitle = {Optics Express},
+  shortjournal = {Opt. Express, OE},
+  volume = {28},
+  number = {5},
+  pages = {5965--5981},
+  publisher = {Optica Publishing Group},
+  issn = {1094-4087},
+  doi = {10.1364/OE.380791},
+  url = {https://opg.optica.org/oe/abstract.cfm?uri=oe-28-5-5965},
+  urldate = {2024-09-04},
+  abstract = {Quantum communication aims to provide absolutely secure transmission of secret information. State-of-the-art methods encode symbols into single photons or coherent light with much less than one photon on average. For long-distance communication, typically a single-mode fiber is used and significant effort has been devoted already to increase the data carrying capacity of a single optical line. Here we propose and demonstrate a fundamentally new concept for remote key establishment. Our method allows high-dimensional alphabets using spatial degrees of freedom by transmitting information through a light-scrambling multimode fiber and exploiting the no-cloning theorem. Eavesdropper attacks can be detected without using randomly switched mutually unbiased bases. We prove the security against a common class of intercept-resend and beam-splitting attacks with single-photon Fock states and with weak coherent light. Since it is optical fiber based, our method allows to naturally extend secure communication to larger distances. We experimentally demonstrate this new type of key exchange method by encoding information into a few-photon light pulse decomposed over guided modes of an easily available multimode fiber.},
+  langid = {english},
+  keywords = {Multicore fibers,Multimode fibers,Quantum communications,Quantum key distribution,Single mode fibers,Space division multiplexing},
+  file = {/home/jaseg/Sync/Research/Zotero/2020_Amitonova et al_Quantum key establishment via a multimode fiber.pdf}
+}
+
 @online{AntimatterAlgorithmThat,
   title = {Antimatter: An Algorithm That Prunes {{CRDT}}/{{OT}} History},
   url = {https://braid.org/antimatter},
@@ -775,6 +795,26 @@
   file = {/home/jaseg/Zotero/storage/VI2VBKAG/Choi et al. - 2010 - Halbach Magnetic Circuit for Voice Coil Motor in H.pdf}
 }
 
+@article{choiQuantumKeyDistribution2010,
+  title = {Quantum Key Distribution on a {{10Gb}}/s {{WDM-PON}}},
+  author = {Choi, Iris and Young, Robert J. and Townsend, Paul D.},
+  date = {2010-04-26},
+  journaltitle = {Optics Express},
+  shortjournal = {Opt. Express, OE},
+  volume = {18},
+  number = {9},
+  pages = {9600--9612},
+  publisher = {Optica Publishing Group},
+  issn = {1094-4087},
+  doi = {10.1364/OE.18.009600},
+  url = {https://opg.optica.org/oe/abstract.cfm?uri=oe-18-9-9600},
+  urldate = {2024-09-04},
+  abstract = {We present the first demonstration of quantum key distribution (QKD) on a multi-user wavelength division multiplexed passive optical network (WDM-PON) with simultaneous, bidirectional 10Gb/s classical channel transmission. The C-Band QKD system operates at a clock rate of 10GHz and employs differential phase shift keying (DPSK). A dual feeder fiber and band filtering scheme is used to suppress classical to quantum channel cross-talk generated by spontaneous Raman scattering, which would otherwise prevent secure key distribution. Quantum keys were distributed to 4 users with negligible Raman cross-talk penalties. The mean QBER value for 4 users was 3.5\% with a mean raw key distribution rate of 1.3Mb/s, which decreased to 696kb/s after temporal windowing to reduce inter-symbol interference due to single photon detector timing jitter.},
+  langid = {english},
+  keywords = {Passive optical networks,Quantum cryptography,Quantum key distribution,Raman scattering,Stimulated Raman scattering,Wavelength division multiplexing},
+  file = {/home/jaseg/Sync/Research/Zotero/2010_Choi et al_Quantum key distribution on a 10Gb-s WDM-PON.pdf}
+}
+
 @incollection{choudhuriComplexitySecureComputation2020,
   title = {The {{Round Complexity}} of {{Secure Computation Against Covert Adversaries}}},
   booktitle = {Security and {{Cryptography}} for {{Networks}}},