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 _{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}).

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