Table 3 The parameters f and e keep \({\hat{P}}_{{\bf{0}},{\boldsymbol{f}}}\), \({\hat{P}}_{{\boldsymbol{e}},{\bf{0}}}\). In Eqs (38) and (39), constant coefficients \({\sum }_{\bar{{\boldsymbol{x}}},{\boldsymbol{f}}}{(-1)}^{\bar{{\boldsymbol{x}}}\cdot {\boldsymbol{f}}}\) equal to 0 as the cancellation coefficient leading some \({\hat{P}}_{{\bf{0}},{\boldsymbol{f}}}\), \({\hat{P}}_{{\boldsymbol{e}},{\bf{0}}}\) cancelled. Take \({\boldsymbol{f}}\mathrm{=11100000}\) and \(01100000\) for example which are belong and not belong to Table 3. \({\sum }_{\bar{{\boldsymbol{x}}}}{(-1)}^{\bar{{\boldsymbol{x}}}\cdot \mathrm{(11100000)}}={2}^{4}\) and \({\sum }_{\bar{{\boldsymbol{x}}}}{(-\mathrm{1)}}^{\bar{{\boldsymbol{x}}}\cdot \mathrm{(01100000)}}=0\).

From: The solvability of quantum k-pair network in a measurement-based way