Table 3 The values of AoF1 and AoF2 between Eq. 27 (the ideal output states from \({\hat{\text{R}}}_{1}^{{{\text{Id}}}}\) and \({\hat{\text{R}}}_{2}^{{{\text{Id}}}}\)) and Eq. 28 (the practical output state from \({\hat{\text{R}}}^{{\Pr}}\)) are listed. The values were calculated using Eq. 29, with consideration to the coupling strength \(g/\kappa\) and the side-leakage rate \(\kappa_{s} /\kappa\), with \(\gamma /\kappa = 0.1\) and \(\omega_{{{\text{X}}^{ - } }} = \omega_{c}\).

From: Encoding scheme using quantum dots for single logical qubit information onto four-photon decoherence-free states

\(\gamma /\kappa = 0.1\)

\(\kappa_{s} /\kappa\)

AoF1 \(\left( {\omega - \omega_{c} = \kappa /2} \right)\)

AoF2 \(\left( {\omega - \omega_{c} = 0} \right)\)

\(g/\kappa = 2.4\)

0.01

0.9967

0.9997

1.00

0.9381

0.9989

2.00

0.8983

0.9688

\(g/\kappa = 0.1\)

0.01

0.7598

0.8906

1.00

0.7652

0.5816

2.00

0.7654

0.6163