density matrix
The sum occurs over 




N

B


:=
dim
⁡
(

H

B


)


{\displaystyle N_{B}:=\dim(H_{B})}

 and 




I

A




{\displaystyle I_{A}}

 the identity operator in 




H

A




{\displaystyle H_{A}}

. ρA is sometimes called the reduced density matrix of ρ on subsystem A. Colloquially, we "trace out" system B to obtain the reduced density matrix on A.
