### Abstract

The strong subadditivity of entropy plays a key role in several areas of physics and mathematics. It states that the entropy S[±]=- Tr(Ï±lnÏ±) of a density matrix Ï±123 on the product of three Hilbert spaces satisfies S[Ï±123]- S[Ï±12]≤S[Ï±23]-S[Ï±2]. We strengthen this to S[Ï±123]-S[Ï±12] ≤αnα(S[Ï±23α]-S[Ï±2α]), where the nα are weights and the Ï±23α are partitions of Ï±23. Correspondingly, there is a strengthening of the theorem that the map A|Trexp[L+lnA] is concave. As applications we prove some monotonicity and convexity properties of the Wehrl coherent state entropy and entropy inequalities for quantum gases.

Original language | English (US) |
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Article number | 062329 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 71 |

Issue number | 6 |

DOIs | |

State | Published - Jun 2005 |

### All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics

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## Cite this

Lieb, E. H., & Seiringer, R. (2005). Stronger subadditivity of entropy.

*Physical Review A - Atomic, Molecular, and Optical Physics*,*71*(6), [062329]. https://doi.org/10.1103/PhysRevA.71.062329