Comparison of incoherent operations and measures of coherence

Eric Chitambar, Gilad Gour

Research output: Contribution to journalArticlepeer-review


A resource theory of quantum coherence attempts to characterize the quantum coherence that exists in a given quantum system. Many different approaches to a resource theory of coherence have recently been proposed, with their differences lying primarily in the identification of "free" or "incoherent" operations. In this article, we compare a number of these operational classes. In particular, the recently introduced class of dephasing-covariant operations is analyzed, and we characterize the Kraus operators of such maps. A number of coherence measures are introduced based on relative Rényi entropies, and we study incoherent state transformations under different operational classes. In particular, we show that the incoherent Schmidt rank can be increased arbitrarily large by certain noncoherence generating operations. The distinction between asymmetry-based versus basis-dependent notions of coherence theory is clarified, and we further develop the resource theory of N asymmetry, where N is the group of all diagonal incoherent unitaries.

Original languageEnglish (US)
Article number052336
JournalPhysical Review A
Issue number5
StatePublished - Nov 30 2016
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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