Product state

In quantum mechanics, a product state, or simply separable state, is a special type of separable state in which there are neither classical nor quantum correlations. Precisely, it is a joint state of two systems which can be expressed as

${\displaystyle \rho =\rho _{1}\otimes \rho _{2},}$

where ${\displaystyle \rho _{1}}$ and ${\displaystyle \rho _{2}}$ are states of the respective systems. This is a more restrictive condition than mere separability,

${\displaystyle \rho =\sum _{k}p_{k}\rho _{1}^{k}\otimes \rho _{2}^{k}.}$

One property of the product state is that in terms of entropy,

${\displaystyle S(\rho )=S(\rho _{1})+S(\rho _{2}).}$