Stronger subadditivity of entropy

É. Lieb, R. Seiringer, Physical Review A - Atomic, Molecular, and Optical Physics 71 (2005).


Journal Article | Published
Author
;
Abstract
The strong subadditivity of entropy plays a key role in several areas of physics and mathematics. It states that the entropy S[±]=- Tr(ϱlnϱ) of a density matrix ϱ123 on the product of three Hilbert spaces satisfies S[ϱ123]- S[ϱ12]≤S[ϱ23]-S[ϱ2]. We strengthen this to S[ϱ123]-S[ϱ12] ≤αnα(S[ϱ23α]-S[ϱ2α]), where the nα are weights and the ϱ23α are partitions of ϱ23. 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.
Publishing Year
Date Published
2005-06-01
Journal Title
Physical Review A - Atomic, Molecular, and Optical Physics
Volume
71
Issue
6
IST-REx-ID

Cite this

Lieb É, Seiringer R. Stronger subadditivity of entropy. Physical Review A - Atomic, Molecular, and Optical Physics. 2005;71(6). doi:10.1103/PhysRevA.71.062329
Lieb, É., & Seiringer, R. (2005). Stronger subadditivity of entropy. Physical Review A - Atomic, Molecular, and Optical Physics, 71(6). https://doi.org/10.1103/PhysRevA.71.062329
Lieb, Élliott, and Robert Seiringer. “Stronger Subadditivity of Entropy.” Physical Review A - Atomic, Molecular, and Optical Physics 71, no. 6 (2005). https://doi.org/10.1103/PhysRevA.71.062329.
É. Lieb and R. Seiringer, “Stronger subadditivity of entropy,” Physical Review A - Atomic, Molecular, and Optical Physics, vol. 71, no. 6, 2005.
Lieb É, Seiringer R. 2005. Stronger subadditivity of entropy. Physical Review A - Atomic, Molecular, and Optical Physics. 71(6).
Lieb, Élliott, and Robert Seiringer. “Stronger Subadditivity of Entropy.” Physical Review A - Atomic, Molecular, and Optical Physics, vol. 71, no. 6, American Physical Society, 2005, doi:10.1103/PhysRevA.71.062329.

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