## Question

# 5. (20 points) In the product Hilbert space C4 C2C2, the Bell states are given by 1 (10) & (0) + | 1) >

## 5. (20 points) In the product Hilbert space C4 C2C2, the Bell states are given by 1 (10) & (0) + | 1) > 1)) 10+) = (11) 1 |0) = =(|0) |0) |1)|1)) - (12) 2 14+) = (|0) |1) + |1) |0)) (13) 1 |V-) = (|0) |1) |1) |0)), (14) which form an orthonormal basis in C4. Here, {|0), 11)} is an arbitrary orthonormal basis in the Hilbert space C. Let (i) Find |+), |0) = (ete cos(6), sin(0) |1) e = sin(0) cos(0) ), |+), and V) for this basis. (ii) Find the above states when = 0 and 0 = 0. (15)

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