Maximal coherence and the resource theory of purity

Year: 2018

Authors: Streltsov A., Kampermann H., Wolk S., Gessner M., Bruss D.

Autors Affiliation: Gdansk Univ Technol, Fac Appl Phys & Math, PL-80233 Gdansk, Poland; Natl Quantum Informat Ctr Gdansk, PL-81824 Sopot, Poland; Free Univ Berlin, Dahlem Ctr Complex Quantum Syst, D-14195 Berlin, Germany; Heinrich Heine Univ Dusseldorf, Inst Theoret Phys 3, D-40225 Dusseldorf, Germany; Univ Innsbruck, Inst Theoret Phys, Technikerstr 25, A-6020 Innsbruck, Austria; Univ Siegen, Nat Wissensch Lich Tech Fak, Walter Flex Str 3, D-57072 Siegen, Germany; INO CNR, QSTAR, Largo Enrico Fermi 2, I-50125 Florence, Italy; LENS, Largo Enrico Fermi 2, I-50125 Florence, Italy; Ist Nazl Ric Metrol, Str Cacce 91, I-10135 Turin, Italy.

Abstract: The resource theory of quantum coherence studies the off-diagonal elements of a density matrix in a distinguished basis, whereas the resource theory of purity studies all deviations from the maximally mixed state. Weestablish a direct connection between the two resource theories, by identifying purity as the maximal coherence which is achievable by unitary operations. The states that saturate this maximum identify a universal family of maximally coherent mixed states. These states are optimal resources under maximally incoherent operations, and thus independent of the way coherence is quantified. For all distance-based coherence quantifiers the maximal coherence can be evaluated exactly, and is shown to coincide with the corresponding distance-based purity quantifier. We further show that purity bounds the maximal amount of entanglement and discord that can be generated by unitary operations, thus demonstrating that purity is the most elementary resource for quantum information processing.

Journal/Review: NEW JOURNAL OF PHYSICS

Volume: 20      Pages from: 53058-1  to: 53058-14

More Information: We thank Gerardo Adesso, Kaifeng Bu, Dario Egloff, Xueyuan Hu, Martin Plenio, and Alexey Rastegin for discussions. We acknowledge financial support by the Alexander von Humboldt-Foundation, Bundesministerium fur Bildung und Forschung, the National Science Center in Poland (POLONEZUMO-2016/21/P/ST2/04054), and the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 665778.
KeyWords: quantum coherence; quantum entanglement; resource theories; quantum; entanglement
DOI: 10.1088/1367-2630/aac484

Citations: 101
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