Quantum relative Lorenz curves

Francesco Buscemi, Gilad Gour

Research output: Contribution to journalArticlepeer-review


The theory of majorization and its variants, including thermomajorization, have been found to play a central role in the formulation of many physical resource theories, ranging from entanglement theory to quantum thermodynamics. Here we formulate the framework of quantum relative Lorenz curves, and show how it is able to unify majorization, thermomajorization, and their noncommutative analogs. In doing so, we define the family of Hilbert α divergences and show how it relates with other divergences used in quantum information theory. We then apply these tools to the problem of deciding the existence of a suitable transformation from an initial pair of quantum states to a final one, focusing in particular on applications to the resource theory of athermality, a precursor of quantum thermodynamics.

Original languageEnglish
Article number012110
JournalPhysical Review A
Issue number1
StatePublished - 9 Jan 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics


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