Density operators are an alternative to the state vector formalism of quantum mechanics. They are commonly used in many scenarios but of course have their trade offs. Due to the fact that many state vectors can lead to the same density operators, some view the density matrix for a quantum system as more fundamental to reality, claimimg differentiating between state vectors is perhaps less important. In Chapter 29.5 of "The Road to Reality", Roger Penrose argues against this view point however, stating that the inability to keep track of relative phase factors and global phase factors in the density matrix formalism is a bug and not a feature. However, he also explains there are some who believe that loss of information of the phase factors may actually occur near the Planck length or at times close to the Planck time, where quantum fluctuations die to gravity may cause this information to be lost.
In this notebook, we give examples using Python and Qiskit of the density matrix formalism. Exercises are included at the end.
