### Abstract

Collective operations on a network of spatially-separated
quantum systems can be carried out using local quantum
(LQ) operations, classical communication (CC) and shared
entanglement (SE). Such operations can also be used to communicate classical information and establish entanglement between distant parties. We show how these facts lead to measures of the inseparability of quantum operations, and argue that a maximally-inseparable operation on 2 qubits is the SWAP operation. The generalisation of our argument to N qubit operations leads to the conclusion that permutation operations
are maximally-inseparable. For even N, we find the
minimum SE and CC resources which are sufficient to perform
an arbitrary collective operation. These minimum resources
are 2(N − 1) ebits and 4(N − 1) bits, and these limits can
be attained using a simple teleportation-based protocol. We
also obtain lower bounds on the minimum resources for the
odd case. For all N4, we show that the SE/CC resources
required to perform an arbitrary operation are strictly greater than those that any operation can establish/communicate.

Original language | English |
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Article number | 032314 |

Number of pages | 17 |

Journal | Physics Letters A |

Volume | 63 |

Issue number | 3 |

DOIs | |

Publication status | Published - 15 Feb 2001 |

### Keywords

- entanglement
- quantum physics
- multiparticle quantum operations
- teleportation

## Cite this

Chefles, A., Gilson, C. R., & Barnett, S. M. (2001). Entanglement, information and multiparticle quantum operations.

*Physics Letters A*,*63*(3), [032314]. https://doi.org/10.1103/PhysRevA.63.032314