An early telecom fibre has attenuation and is driven by a pulsed source.

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Quantum Information and Technology, Ch Quantum key distribution and quantum networks

Problem

An early telecom fibre has attenuation

0.25\,\mathrm{dB\,km^{-1}}

and is driven by a

100\,\mathrm{MHz}

pulsed source. ((a)) Estimate the fibre length at which the repeaterless bound falls to

1\,\mathrm{bit\,s^{-1}}

, using

-\log_2(1-\eta)\approx1.44\eta

and

\eta = 10^{-\alpha L/10}

. ((b)) For a modern fibre with

0.2\,\mathrm{dB\,km^{-1}}

attenuation and a

1\,\mathrm{GHz}

source, estimate the length at which the repeaterless bound falls to

1\,\mathrm{kbit\,s^{-1}}

, and compare it with the

1200\,\mathrm{km}

range over which the 2017 Micius satellite delivered keys at roughly kilohertz rates. Comment on why the fibre bound cannot be beaten by better detectors alone.

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