### Abstract

We present two general approaches to obtain the strong converse exponent of simple quantum hypothesis testing for correlated quantum states. One approach requires that the states satisfy a certain factorization property; typical examples of such states are the temperature states of translation-invariant finite-range interactions on a spin chain. The other approach requires the differentiability of a regularized Rényi α-divergence in the parameter α; typical examples of such states include temperature states of non-interacting fermionic lattice systems, and classical irreducible Markov chains. In all cases, we get that the strong converse exponent is equal to the Hoeffding anti-divergence, which in turn is obtained from the regularized Rényi divergences of the two states.

Original language | English |
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Article number | 7298426 |

Pages (from-to) | 6975-6994 |

Number of pages | 20 |

Journal | IEEE Transactions on Information Theory |

Volume | 61 |

Issue number | 12 |

DOIs | |

Publication status | Published - Dec 2015 |

### Keywords

- Hypothesis testing
- Rényi divergences
- correlated quantum states

### ASJC Scopus subject areas

- Information Systems
- Computer Science Applications
- Library and Information Sciences

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## Cite this

*IEEE Transactions on Information Theory*,

*61*(12), 6975-6994. [7298426]. https://doi.org/10.1109/TIT.2015.2489259