Title | Keyring models: an approach to steerability |

Publication Type | Journal Article |

Year of Publication | 2018 |

Authors | Miller, C, Colbeck, R, Shi, Y |

Journal | Journal of Mathematical Physics |

Volume | 59 |

Pages | 022103 |

Date Published | 2018/01/02 |

Abstract | If a measurement is made on one half of a bipartite system then, conditioned on the outcome, the other half has a new reduced state. If these reduced states defy classical explanation — that is, if shared randomness cannot produce these reduced states for all possible measurements — the bipartite state is said to be steerable. Determining which states are steerable is a challenging problem even for low dimensions. In the case of two-qubit systems a criterion is known for T-states (that is, those with maximally mixed marginals) under projective measurements. In the current work we introduce the concept of keyring models — a special class of local hidden state model. When the measurements made correspond to real projectors, these allow us to study steerability beyond T-states. Using keyring models, we completely solve the steering problem for real projective measurements when the state arises from mixing a pure two-qubit state with uniform noise. We also give a partial solution in the case when the uniform noise is replaced by independent depolarizing channels. Our results imply that Werner states, which are a special case of the previous states, are unsteerable under real projective measurements if and only if their efficiency is at most 2/π. |

URL | http://aip.scitation.org/doi/full/10.1063/1.5006199 |

DOI | 10.1063/1.5006199 |