Table 13 Experimental average values and theoretical results of observables for the input state\(\tfrac{1}{\sqrt{2}}(|{\overrightarrow{{\rm{e}}}}_{0})+|{\overrightarrow{{\rm{e}}}}_{1}))\). The dates behind the experimental average values in the parentheses are standard deviations.
Terms | Experimental value | Theoretical prediction | Terms | Experimental value | Theoretical prediction | Terms | Experimental value | Theoretical prediction |
|---|---|---|---|---|---|---|---|---|
\(\overline{{A^{\prime} }_{1}}\) | 0.953 (4) | 1 | \(\overline{{A^{\prime} }_{1}{A^{\prime} }_{6}}\) | 0.408 (9) | 0.5 | \(\overline{{A^{\prime} }_{5}{A^{\prime} }_{6}}\) | 0 (25) | 0 |
\(\overline{{A^{\prime} }_{2}}\) | 0.938 (1) | 1 | \(\overline{{A^{\prime} }_{1}{A^{\prime} }_{7}}\) | 0.506 (1) | 0.5 | \(\overline{{A^{\prime} }_{5}{A^{\prime} }_{11}}\) | −0.499 (9) | −0.5 |
\(\overline{{A^{\prime} }_{3}}\) | −0.344 (5) | −0.333 | \(\overline{{A^{\prime} }_{1}{A^{\prime} }_{9}}\) | −0.962 (2) | −1 | \(\overline{{A^{\prime} }_{6}{A^{\prime} }_{11}}\) | −0.501 (21) | −0.5 |
\(\overline{{A^{\prime} }_{4}}\) | −0.375 (7) | −0.333 | \(\overline{{A^{\prime} }_{2}{A^{\prime} }_{5}}\) | 0.433 (14) | 0.5 | \(\overline{{A^{\prime} }_{7}{A^{\prime} }_{8}}\) | 0.032 (7) | 0 |
\(\overline{{A^{\prime} }_{5}}\) | 0.501 (21) | 0.5 | \(\overline{{A^{\prime} }_{2}{A^{\prime} }_{8}}\) | 0.468 (3) | 0.5 | \(\overline{{A^{\prime} }_{7}{A^{\prime} }_{12}}\) | −0.505 (5) | −0.5 |
\(\overline{{A^{\prime} }_{6}}\) | 0.499 (9) | 0.5 | \(\overline{{A^{\prime} }_{2}{A^{\prime} }_{9}}\) | −0.968 (1) | −1 | \(\overline{{A^{\prime} }_{8}{A^{\prime} }_{12}}\) | −0.527 (10) | −0.5 |
\(\overline{{A^{\prime} }_{7}}\) | 0.527 (10) | 0.5 | \(\overline{{A^{\prime} }_{3}{A^{\prime} }_{5}}\) | −0.799 (3) | −0.833 | \(\overline{{A^{\prime} }_{9}{A^{\prime} }_{10}}\) | −0.991 (0) | −1 |
\(\overline{{A^{\prime} }_{8}}\) | 0.505 (5) | 0.5 | \(\overline{{A^{\prime} }_{3}{A^{\prime} }_{7}}\) | −0.826 (4) | −0.833 | \(\overline{{A^{\prime} }_{9}{A^{\prime} }_{13}}\) | −0.917 (2) | −1 |
\(\overline{{A^{\prime} }_{9}}\) | −0.907 (2) | −1 | \(\overline{{A^{\prime} }_{3}{A^{\prime} }_{10}}\) | −0.334 (12) | −0.333 | \(\overline{{A^{\prime} }_{10}{A^{\prime} }_{13}}\) | 0.907 (2) | 1 |
\(\overline{{A^{\prime} }_{10}}\) | 0.916 (2) | 1 | \(\overline{{A^{\prime} }_{4}{A^{\prime} }_{6}}\) | −0.823 (14) | −0.833 | \(\overline{{A^{\prime} }_{11}{A^{\prime} }_{12}}\) | −0.990 (0) | −1 |
\(\overline{{A^{\prime} }_{11}}\) | 0 (9) | 0 | \(\overline{{A^{\prime} }_{4}{A^{\prime} }_{8}}\) | −0.836 (11) | −0.833 | \(\overline{{A^{\prime} }_{11}{A^{\prime} }_{13}}\) | −0.010 (9) | 0 |
\(\overline{{A^{\prime} }_{12}}\) | 0.010 (9) | 0 | \(\overline{{A^{\prime} }_{4}{A^{\prime} }_{10}}\) | −0.334 (11) | −0.333 | \(\overline{{A^{\prime} }_{12}{A^{\prime} }_{13}}\) | 0 (9) | 0 |
\(\overline{{A^{\prime} }_{13}}\) | 0.990 (0) | 1 | Â | Â | Â | Â | Â | Â |
Original Yu-Oh | \(\mathop{\sum }\limits_{i=1}^{13}\overline{{A^{\prime} }_{i}}-\frac{1}{4}\mathop{\sum }\limits_{i=1}^{13}\mathop{\sum }\limits_{j=1,j\ne i}^{13}{\Gamma }_{i,j}\overline{{A^{\prime} }_{i}{A^{\prime} }_{j}}=8.246\pm 86\) | |||||||
