The mutual information between two discrete random variables 
and 
is defined to be
 |
(1)
|
bits. Additional properties are
 |  |  |
(2)
|
 |  |  |
(3)
|
and
 |
(4)
|
where 
is the Shannon entropy of the random
variable 
and 
is the joint entropy of these variables.
For a joint density matrix 
, the quantum analogue is
 |
(5)
|
where 
is von Neumann entropy, 
is quantum relative
entropy, and 
and 
are the reduced density matrices. All logarithms
must use the same base. This quantity measures total correlations, including classical
correlations, and is not by itself a measure of quantum
entanglement (Watrous 2018).
