A limit of the quantum Rényi divergence

Nilanjana Datta, Felix Leditzky

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Article number045304
JournalJournal of Physics A: Mathematical and Theoretical
Issue number4
StatePublished - Jan 31 2014
Externally publishedYes


  • 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
  • Physics and Astronomy(all)


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