Kavli Affiliate: Stephanie Wehner
| First 5 Authors: Bethany Davies, Bethany Davies, , ,
| Summary:
In the performance analysis of quantum networks, it is common to approximate
bipartite entangled states as either being Bell-diagonal or Werner states. We
refer to these as twirled approximations because it is possible to bring any
state to such a form with a twirling map. Although twirled approximations can
simplify calculations, they can lead to an inaccuracy in performance estimates.
The goal of this work is to quantify this inaccuracy. We consider repeater
chains where end-to-end entanglement is achieved by performing an entanglement
swap at each repeater in the chain. We consider two scenarios: postselected and
non-postselected entanglement swapping, where postselection is performed based
on the Bell-state measurement outcomes at the repeaters. We show that, for
non-postselected swapping, the Bell-diagonal approximation is exact for the
computation of the Bell-diagonal elements of the end-to-end state. We also find
that the Werner approximation accurately approximates the end-to-end fidelity
when the infidelity of each initial state is small with respect to the number
of repeaters in the chain. For postselected swapping, we find bounds on the
difference in end-to-end fidelity from what is obtained with the twirled
approximation, for initial states with a general noisy form. Finally, for the
example of performing quantum key distribution over a repeater chain, we
demonstrate how our insights can be used to understand how twirled
approximations affect the secret-key rate.
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