A submarine fibre link runs with attenuation

PHYSICS · Multi-part · Fermi University Physics · Quantum Information & Technology · Quantum information theory and communication · Quantum information theory and communication

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

Problem

A submarine fibre link runs

L = 300\,\mathrm{km}

with attenuation

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

, fed by a

500\,\mathrm{MHz}

pulsed source. ((a)) Estimate the repeaterless bound on the secret-key rate for this link, in bits per second, using

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

and

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

for small

\eta

. ((b)) An engineer proposes splitting the link into three equal segments with a quantum memory at each intermediate node, so that entanglement swapping can be attempted once both flanking segments have succeeded. Estimate the minimum time a memory must hold its qubit, taking the light speed in fibre to be

c_{\rm fibre} = 2\times10^5\,\mathrm{km\,s^{-1}}

and using the memory-time estimate

L/c_{\rm fibre}

for the full link length. ((c)) State briefly, using no-cloning, why inserting an optical amplifier mid-link cannot be used to beat the bound found in part (a).

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