In [[Quantum information science - theory|quantum information theory]], '''separable operations''' on a general multipartite [[states|quantum state]] is an operations with product [[Kraus decomposition|Kraus operators]].
Abstract mathematical definition for the case of $K$-partite quantum state $\rho$ 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 following 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.
Separable operations play a big role in [[state distinguishability and state discrimination]].
= References =
*V. Gheorghiu, R. B. Griffiths, ''Phys. Rev. A'' '''78''', 020304 (R) (2008)
*V. Gheorghiu, R. B. Griffiths, ''Phys. Rev. A'' '''76''', 032310 (2007)
*R. Duan, Y. Feng, Y. Xin, M. Ying, '''arXiv:0705.0795 [quant-ph]'''
[[Category:Handbook of Quantum Information]]
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