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[Steffen et al., 2006] (the details of which are beyond the scope of this thesis) to
measure not just the fractional populations of the possible states, but the entire
density matrix. The result is shown in Table 11.1 for the entangled pair created
using the resonator coupling scheme.
Comparing this density matrix to the ideal Bell singlet state | 10 〉−| 01 〉 yields
a trace-fidelity of F(ρ raw ) = √ Tr(〈 Singlet |ρ raw | Singlet 〉) = 88.3%. Calculating
the “Entanglement of Formation” [Hill and Wootters, 1997] (EoF) of the state
yields a value of EoF(ρ raw ) = 0.378. The EoF gives a monotonic measure of the
entanglement shown by the coupled quantum state. It ranges from 0 for classical
states to 1 for maximally entangled states. Intuitively, it gives the inverse of the
number of identical copies of the state needed that would allow a purification
protocol to combine the copies into a maximally entangled state.
To get a better understanding of the true state of the coupled pair, the data can
be corrected for measurement visibilities to obtain the result shown in Table 11.2.
This state shows a trace-fidelity of F(ρ corr ) = √ Tr(〈 Singlet |ρ corr | Singlet 〉) =
92.1% and an entanglement of formation of EoF(ρ corr ) = 0.449.
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