Stronger subadditivity of entropy

Elliott H. Lieb, Robert Seiringer

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17 Scopus citations


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.

Original languageEnglish (US)
Article number062329
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number6
StatePublished - Jun 2005

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics


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