Chapter 4

The problems in this chapter are focused on density operators.

Background material

The most frequent use of density operators/matrices is describing the statistical state of a quantum systems. In other words given all possible pure states whats the probability of any given state.

The expectation of a hermitian matrix corresponding to an observable corresponds to the average given by:

where $\rho$ is the density matrix that can describe a pure or mixed state. In the case of a pure state its simply given by $\rho=\ket{\psi}\bra{\psi}$ and has the property that $\rho^2 = \rho$, i.e., idempotent.

Problems

Programing Problems

• Problem 1

• Problem 2

• Problem 3