Physics:Product state

Short description: Separable quantum state with no classical correlation or entanglement

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,

$\rho =\sum _k{p}_k{\rho }_1^k\otimes {\rho }_2^k.$

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

$S(\rho )=S({\rho }_1)+S({\rho }_2).$