One-Shot Coherence Distillation

Bartosz Regula, Kun Fang, Xin Wang, and Gerardo Adesso
Phys. Rev. Lett. 121, 010401 – Published 3 July 2018
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Abstract

We characterize the distillation of quantum coherence in the one-shot setting, that is, the conversion of general quantum states into maximally coherent states under different classes of quantum operations. We show that the maximally incoherent operations (MIO) and the dephasing-covariant incoherent operations (DIO) have the same power in the task of one-shot coherence distillation. We establish that the one-shot distillable coherence under MIO and DIO is efficiently computable with a semidefinite program, which we show to correspond to a quantum hypothesis testing problem. Further, we introduce a family of coherence monotones generalizing the robustness of coherence as well as the modified trace distance of coherence, and show that they admit an operational interpretation in characterizing the fidelity of distillation under different classes of operations. By providing an explicit formula for these quantities for pure states, we show that the one-shot distillable coherence under MIO, DIO, strictly incoherent operations, and incoherent operations is equal for all pure states.

  • Received 5 December 2017
  • Revised 18 April 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.010401

© 2018 American Physical Society

Physics Subject Headings (PhySH)

General PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Bartosz Regula1,*, Kun Fang2,†, Xin Wang2,‡, and Gerardo Adesso1,§

  • 1School of Mathematical Sciences and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
  • 2Centre for Quantum Software and Information, School of Software, Faculty of Engineering and Information Technology, University of Technology Sydney, New South Wales 2007, Australia

  • *bartosz.regula@gmail.com
  • kun.fang-1@student.uts.edu.au
  • xin.wang-8@student.uts.edu.au
  • §gerardo.adesso@nottingham.ac.uk

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Issue

Vol. 121, Iss. 1 — 6 July 2018

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