Alice possesses two-particles A1 and A2 and Bob possesses B1 and B2. The four particle state is given as 1) A, A2B1B2 z (la) A142 la")B,B3 + 1B) 4:43 1")B, bx + c)A142\c%B,B3 +\d%A14, Id) Bybe) (1) such that |a) = cos 61 100) + sin 61 (11) 16) = cos 01|01) + sin 01 (10) c) = - sin 01/01) + cos 01 (10) |d) = sin 01 100) + cos 01|11) (2) and (a)' = cos 02|00) + sin 02 (11) lb)' = cos 02|01) + sin 02 (10) \c)' = - sin 02 (01) + cos 02 (10) \d)' = - sin 02 |00) + cos 02 (11) (3) 1. Show that the set of Eqs (2) form orthonormal basis set. Similarly the set of Eqs (3) also form orthonormal basis set (you are not required to prove it) 2. Show that Eq. (1) is a maximally entangled state between A1 A2 and B, B2 Alice possesses two-particles A1 and A2 and Bob possesses B1 and B2. The four particle state is given as 1) A, A2B1B2 z (la) A142 la")B,B3 + 1B) 4:43 1")B, bx + c)A142\c%B,B3 +\d%A14, Id) Bybe) (1) such that |a) = cos 61 100) + sin 61 (11) 16) = cos 01|01) + sin 01 (10) c) = - sin 01/01) + cos 01 (10) |d) = sin 01 100) + cos 01|11) (2) and (a)' = cos 02|00) + sin 02 (11) lb)' = cos 02|01) + sin 02 (10) \c)' = - sin 02 (01) + cos 02 (10) \d)' = - sin 02 |00) + cos 02 (11) (3) 1. Show that the set of Eqs (2) form orthonormal basis set. Similarly the set of Eqs (3) also form orthonormal basis set (you are not required to prove it) 2. Show that Eq. (1) is a maximally entangled state between A1 A2 and B, B2