Exercise 1.We said that non-orthogonal states cannot be perfectly distinguished.Consider this ona simple example:One preparesa state l)chosen from {10),11),1+),I-)},and let you guess which one it is.Show that you cannot use any measurement to identify)with certainty Pove that theed theenityatriare hoonal toach other with the inner product defined by (A,B)=ijA Bij.Here the superscript *is the complex conjugate.Exercise 1. We said that non-orthogonal states cannot be perfectly distinguished. Consider this on a simple example: One prepares a state |𝜓〉 chosen from {|0〉,|1〉,|+〉, |−〉}, and let you guess which one it is. Show that you cannot use any measurement to identify |𝜓〉 with certainty. 2. Prove that the three Pauli matrices and the Identity matrix 𝐼 = [ 1 0 0 1 ] are orthogonal to each other with the inner product defined by 〈𝐴, 𝐵〉 = ∑ 𝐴𝑖𝑗 ∗ 𝑖𝑗 𝐵𝑖𝑗 . Here the superscript * is the complex conjugate