## Abstract

Recently, an interesting quantity called the quantum Rényi divergence (or 'sandwiched' Rényi relative entropy) was defined for pairs of positive semi-definite operators ρ and σ. It depends on a parameter and acts as a parent quantity for other relative entropies which have important operational significance in quantum information theory: the quantum relative entropy and the min- and max-relative entropies. There is, however, another relative entropy, called the 0-relative Rényi entropy, which plays a key role in the analysis of various quantum information-processing tasks in the one-shot setting. We prove that the 0-relative Rényi entropy is obtainable from the quantum Rényi divergence only if ρ and σ have equal supports. This, along with existing results in the literature, suggests that it suffices to consider two essential parent quantities from which operationally relevant entropic quantities can be derived - the quantum Rényi divergence with parameter 1/2, and the -relative Rényi entropy with∈ [0, 1).

Original language | English (US) |
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Article number | 045304 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 47 |

Issue number | 4 |

DOIs | |

State | Published - Jan 31 2014 |

Externally published | Yes |

## Keywords

- 0-relative Rényi entropy
- one-shot information theory
- quantum Rényi divergence

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modeling and Simulation
- Mathematical Physics
- General Physics and Astronomy