Week assignment 09 (Homework vault part)
Deadline: 13. 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).
In all exercises we will use the same state of Alice-Bob system,
|ψ =
1
3
√
3 |00 − 2i |10 + (1 − i) |11 .
Exercise 1. [3pt] Suppose Bob performs measurement in computational basis. Compute probabilities pj for
particular outcomes j ∈ {0, 1}, determine corresponding conditional states of Alice φj and compute
ρ1
A = p0 |φ0 φ0| + p1 |φ1 φ1| .
Exercise 2. [2pts] Compute reduced density matrix for Alice, ρ2
A = TrB[|ψ ψ|].
Exercise 3. [2pts] From states ρ1,2
A compute probabilities with which Alice measures outcomes + and − if
she performs measurement in the Hadamard basis.