In the quantitative decoherence general model, calculate what will happen to (leftlanglephileft|ho_{mathcal{S}} ight| phi ightangle) if we

In the quantitative decoherence general model, calculate what will happen to \(\left\langle\phi\left|ho_{\mathcal{S}}\right| \phi\rightangle\) if we did not have \(\left\langle\epsilon_{i} \mid \epsilon_{j}\rightangle=\delta_{i j}\), and explain why that would be unsatisfactory.