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

[math]\displaystyle{ \rho = \rho_1 \otimes \rho_2 , }[/math]

where [math]\displaystyle{ \rho_1 }[/math] and [math]\displaystyle{ \rho_2 }[/math] are states of the respective systems. This is a more restrictive condition than mere separability,

[math]\displaystyle{ \rho = \sum_k p_k \rho^k_1 \otimes \rho^k_2 . }[/math]

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

[math]\displaystyle{ S(\rho) = S(\rho_1) + S(\rho_2). }[/math]

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