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. 2023 Jul 19;9(29):eadd7131. doi: 10.1126/sciadv.add7131

Table 1. The summary of the mutual information quantification from incomplete measurements consisting of one-fourth of all possible Pauli projectors in each case.

The MaxLik and the measurement-specific DNNs are compared up to five-qubit quantum systems. The ratio of the mean absolute errors (MAEs) of the methods shows an increasing improvement in the performance of the DNN approach for entanglement quantification in higher-dimensional systems.

Number of qubits MAE Ratio of MaxLik and DNN MAEs
MaxLik DNN
2 0.20 ± 0.16 0.09 ± 0.09 2.2
3 0.068 ± 0.055 0.023 ± 0.020 3.0
4 0.019 ± 0.014 0.005 ± 0.001 3.8
5 0.039 ± 0.032 0.009 ± 0.001 4.3