1. Quantum Fundamentals

Density Matrices — Quiz

Test your understanding of density matrices with 5 practice questions.

Practice Questions

Question 1

Which property is NOT required for a matrix to be a valid density matrix?

Question 2

For a qubit with Bloch vector $\mathbf{r}=(0,0,1)$, which density matrix represents this state?

Question 3

Given the two-qubit product state $|+\rangle_A\otimes|0\rangle_B$, what is the reduced density matrix $\rho_A$ after tracing out system $B$?

Question 4

For the mixed qubit state $\rho=p|0\rangle\langle0|+(1-p)|1\rangle\langle1|$, what is the purity $\mathrm{Tr}(\rho^2)$?

Question 5

If a qubit is in the pure state $\rho=|1\rangle\langle1|$, what is the probability of measuring $|0\rangle$ in the computational basis?