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@ -496,7 +496,13 @@ concern of photon number splitting attacks and because of decoherence\footnote{
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with the fiber---that is, the same loss as before---would disturb the entire entangled state.
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}, and thus the system's bit rate decreases exponentially with distance due to attenuation. Some QKD systems can reach
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ranges of several hundred kilometers, but the resulting payload data rate---usually called \emph{secret key rate}---of
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these long distance systems is measured in kilobits per second.
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these long distance systems is measured in kilobits per second. An interesting observation from theoretical work on
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quantum key distribution algorithms is that not only is this exponential rate decay a fundamental limit for a given QKD
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implementation, but it is even possible to determine a protocol-independent upper bound for a noiseless, lossy optical
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channel's secret key rate. This upper bound shows the same exponentail decay and, notably, is independent of the optical
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power, which is directly proportional to the repetition rate of the QKD protocol's measurements. Modulo some small,
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constant factor, this upper bound cannot be circumvented with any amount of protocol engineering, or source or detector
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improvements\cite{takeokaFundamentalRatelossTradeoff2014}.
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\subsection{Loss in optical fibers}
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@ -516,7 +522,8 @@ the fiber will exit it at the other end \cite{chesnoyUnderseaFiberCommunication2
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Decoherence effects are less relevant for the distance limitation, and mostly limit which fiber-optic technologies can be
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utilized in the first place. Due to decoherence, QKD systems usually use Single-Mode (SM) fiber over Multi-Mode (MM)
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fiber\cite{amitonovaQuantumKeyEstablishment2020}, and decoherence makes it more difficult to utilize Wavelength Division
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Multiplexing (xWDM) to send multiple either quantum or classical optical signals through a single fiber.
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Multiplexing (xWDM) to send multiple either quantum or classical optical signals through a single fiber.\todo{is this
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right?}
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Attenuation in optical fibers has a number of origins. The main factor is scattering of photons on the fiber core, with
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absorbtion due to interactions between photons and the fiber core's molecular structure or embedded contaminants only
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@ -545,7 +552,7 @@ as well as Stimulated Brillouin Scattering can produce intermodulation and cross
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sent through the same fiber as another, much brighter classical optical signal. These nonlinear effects are relevant for
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QKD systems that either send a reference clock through the same fiber as the QKD pulses, or that aim for coexistence
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between QKD pulses and classical optical networking on the same fiber, for instance in an in xWDM
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setup\cite{choiQuantumKeyDistribution2010}.
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setup\cite{choiQuantumKeyDistribution2010, grunenfelderLimitsMultiplexingQuantum2021}.
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In the AC Kerr effect, a strong optical signal influences the refractive index of the fiber core, which modulates other
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signals propagating through the same fiber. Stimualated Brillouin Scattering arises when a high-power incident signal
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@ -1 +1 @@
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Subproject commit 601159904f4269366e29d85c2e90cbf000157f4f
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Subproject commit 3a7edbd1127cacc8f4c90376595b894105f3d479
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