# 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 $\rho$ 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