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 Ak 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.

Separable operations play a big role in state distinguishability and state discrimination.


References

  • V. Gheorghiu, R. B. Griffiths, Phys. Rev. A 76, 032310 (2007)
  • R. Duan, Y. Feng, Y. Xin, M. Ying, quant-ph/0705.0795
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