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Separable operations

In quantum information theory, separable operations on a general multipartite quantum state is an operations with product Kraus operators.

Abstract mathematical definition for the case of $K$ -partite quantum state $ρ$ can be formulated as

$\rho\mapsto\rho^{\prime}=\Lambda(\rho)=\sum_{k=1}^N A_k\rho A_k^{\dagger}$ ,

with operators $A k$ satisfying followimg conditions:

$\sum_{k=1}^N A_k^{\dagger}A_k=\mathbb{I}$

$A_k=\otimes_{l=1}^K A_{k_l}$

LOCC operations are subclass of separable operations.

References

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