# Product state

${\displaystyle \rho =\rho _{1}\otimes \rho _{2},}$
where ${\displaystyle \rho _{1}}$ and ${\displaystyle \rho _{2}}$ are states of the respective systems. This is a more restrictive condition than mere separability,
${\displaystyle \rho =\sum _{k}p_{k}\rho _{1}^{k}\otimes \rho _{2}^{k}.}$
${\displaystyle S(\rho )=S(\rho _{1})+S(\rho _{2}).}$