Abstract:
Entanglement distribution in multi node networks can become the backbone for a
future quantum internet, it will become a widely accepted phenomenon as quantum
repeater networks become more and more efficient. Graph theoretic approaches to
make a feasible multi-node quantum network for secure communication and
distributed quantum computation are of particular interest as the classical internet
was built on such theories. Unlike today’s classical internet, quantum internet will
most likely rely on more than one path between the source and destination. This
multi-path routing paradigm allows the user-pair to establish entanglement, and send
their Bell-pairs through paths other than shortest path and still get a single high
fidelity Bell-pair at the end via entanglement purification. This study encompasses a
quintessential comparative analysis of having more than the minimum required edges
in networks to support multi-path routing with an added advantage of temporal layers
from utilizing quantum memories. We provide an explanation for benefits of having
redundant edges in tree networks by adding rings of edges at each level and compare
the idea of cost distances with lattice networks. our analysis provides an
understanding of fidelity-efficiency trade-offs in the context of user competition and
path finding probabilities. We make an argument for network topologies playing an
important role in serving the purpose whether it is for distributed quantum
computation or for quantum key distribution. To show deployability of entanglement
distribution networks with extra edges we present a wide area network for 14 selected
universities in Islamabad in two different fiber-optic based network topologies. One
being minimal spanning tree network that costs around $61, 370.00 and the other
being completely connected network which costs about $1, 109, 670.00. Regardless of
the monetary cost a clear advantage is shown in key generation rates for ideal nodes.
