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

ρ=ρ1⊗ρ2,

where ρ1 and ρ2 are states of the respective systems. This is a more restrictive condition than mere separability,

ρ=∑kpkρ1k⊗ρ2k.

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

S(ρ)=S(ρ1)+S(ρ2).

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