Week assignment 08 (Homework vault part)
Deadline: 09. 12. 2020
Upload scan, photograph, or a typesetted pdf of computation to the corresponding homework vault. Do
not forget to include your name and personal ID number (uˇco) on the page(s).
Exercise 1. [1pt] Determine the probabilities with which Bob measures 0 and 1 and in both cases describe
the conditional state of Alice. Their joint state is
|ψ AB =
1
√
6
|00 AB +
√
2 |01 AB − i
√
3 |10 AB .
Exercise 2. [2pts] Using the ABC method find decomposition for a controlled U operation, where
U =
1
√
2
i 1
1 i
Exercise 3. [3pts] Let us have matrix
A =
1
2
−1 −i
√
3
i
√
3 1
.
Find its egenvalues and corresponding eigenvectors and decide whether the matrix is unitary, Hermitian,
positive semi-definite, and/or a projection.