## Abstract

The stabilizer group of an n-qubit state ψ is the set of all matrices of the form g = g1⊗..otimes;gn, with g1,..,gn being any 2×2 invertible complex matrices that satisfy gj i = j i. We showthat for 5 or more qubits, except for a set of states of zero measure, the stabilizer group of multipartite entangled states is trivial, that is, containing only the identity element. We use this result to show that for 5 or more qubits, the action of deterministic local operations and classical communication (LOCC) can almost always be simulated simply by local unitary (LU) operations. This proves that almost all n-qubit states with n≥5 can neither be reached nor be converted into any other (n-partite entangled), LU-inequivalent state via deterministic LOCC. We also find a simple and elegant expression for the maximal probability to convert one multi-qubit entangled state to another for this generic set of states.

Original language | English |
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Article number | 092204 |

Journal | Journal of Mathematical Physics |

Volume | 58 |

Issue number | 9 |

DOIs | |

State | Published - 1 Sep 2017 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics