Consider a system that is in a mixed state. The system has 0.3 of probability in a pure state and 0.7 of probability in another pure state
. Then the density matrix
is
In the most general cases, neither nor
is an eigenstate. So we cannot expect that
is diagonal.
For example, if each of the pure state and
is a superposition of two eigenstates
, then
and
.
For simplicity, assume that the eigenstates form a complete orthonormal set.
If we use as basis,
— Me@2018.03.12 11:51 AM
.
.
2018.03.14 Wednesday (c) All rights reserved by ACHK