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

$\rho = \rho_1 \otimes \rho_2 ,$

where $\rho_1$ and $\rho_2$ are states of the respective systems. This is a more restrictive condition than mere separability,

$\rho = \sum_k p_k \rho^k_1 \otimes \rho^k_2 .$