Quantifying Quantum Resources with Conic Programming

Roope Uola, Tristan Kraft, Jiangwei Shang, Xiao-Dong Yu, and Otfried Gühne
Phys. Rev. Lett. 122, 130404 – Published 2 April 2019
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Abstract

Resource theories can be used to formalize the quantification and manipulation of resources in quantum information processing such as entanglement, asymmetry and coherence of quantum states, and incompatibility of quantum measurements. Given a certain state or measurement, one can ask whether there is a task in which it performs better than any resourceless state or measurement. Using conic programming, we prove that any general robustness measure (with respect to a convex set of free states or measurements) can be seen as a quantifier of such outperformance in some discrimination task. We apply the technique to various examples, e.g., joint measurability, positive operator valued measures simulable by projective measurements, and state assemblages preparable with a given Schmidt number.

  • Figure
  • Received 9 January 2019
  • Corrected 16 April 2019

DOI:https://doi.org/10.1103/PhysRevLett.122.130404

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyGeneral Physics

Corrections

16 April 2019

Correction: Missing information in Refs. [14] and [31] has been inserted.

Authors & Affiliations

Roope Uola1,2,*, Tristan Kraft1,3, Jiangwei Shang4, Xiao-Dong Yu1, and Otfried Gühne1

  • 1Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Str. 3, D-57068 Siegen, Germany
  • 2Département de Physique Appliquée, Université de Genève, CH-1211 Genève, Switzerland
  • 3SUPA and Department of Physics, University of Strathclyde, G40NG Glasgow, United Kingdom
  • 4Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing 100081, China

  • *roope.uola@gmail.com

See Also

Quantum Incompatibility Witnesses

Claudio Carmeli, Teiko Heinosaari, and Alessandro Toigo
Phys. Rev. Lett. 122, 130402 (2019)

All Sets of Incompatible Measurements give an Advantage in Quantum State Discrimination

Paul Skrzypczyk, Ivan Šupić, and Daniel Cavalcanti
Phys. Rev. Lett. 122, 130403 (2019)

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Vol. 122, Iss. 13 — 5 April 2019

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