Table 1 Summary of the four overlap estimation strategies

Measurement

\({\hat{\sigma }}_{i},\,{\hat{\sigma }}_{i}\)

\(\,{\hat{\sigma }}_{i},|\widetilde{\phi }\rangle \langle \widetilde{\phi }|\)

\({\hat{E}}_{-}=|{\Psi }_{-}{{\rangle }}{{\langle }}{\Psi }_{-}|\)

HOMI, PPNRD

Estimator \(\widetilde{c}\)

\({|\langle \widetilde{\psi }|\widetilde{\phi }\rangle |}^{2}\)

k/N

1 − 2k/N

(1 − 2k/N)/Γ

v(c, N)

4κc(1 − c)/N

(2κ + 1)c(1 − c)/N

(1 − c²)/N

(3 − Γc)(1 − Γ² c²)/2NΓ²