Quantifying Operations with an Application to Coherence

Thomas Theurer, Dario Egloff, Lijian Zhang, and Martin B. Plenio
Phys. Rev. Lett. 122, 190405 – Published 17 May 2019
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Abstract

To describe certain facets of nonclassicality, it is necessary to quantify properties of operations instead of states. This is the case if one wants to quantify how well an operation detects nonclassicality, which is a necessary prerequisite for its use in quantum technologies. To do so rigorously, we build resource theories on the level of operations, exploiting the concept of resource destroying maps. We discuss the two basic ingredients of these resource theories, the free operations and the free superoperations, which are sequential and parallel concatenations with free operations. This leads to defining properties of functionals that are well suited to quantify the resources of operations. We introduce these concepts at the example of coherence. In particular, we present two measures quantifying the ability of an operation to detect, i.e., to use, coherence, one of them with an operational interpretation, and provide methods to evaluate them.

  • Received 23 June 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.190405

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyGeneral Physics

Authors & Affiliations

Thomas Theurer1,*, Dario Egloff1,4,*, Lijian Zhang2,3, and Martin B. Plenio1

  • 1Institute of Theoretical Physics and IQST, Universität Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany
  • 2National Laboratory of Solid State Microstructures and College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
  • 3Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
  • 4Technical University Dresden, Institute of Theoretical Physics, D-01062 Dresden, Germany

  • *These two authors contributed equally to this work.

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Issue

Vol. 122, Iss. 19 — 17 May 2019

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