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Every Quantum Helps: Operational Advantage of Quantum Resources beyond Convexity

Kohdai Kuroiwa1,2, Ryuji Takagi3, Gerardo Adesso4, and Hayata Yamasaki5

  • 1Institute for Quantum Computing and Department of Combinatorics and Optimization, University of Waterloo, Ontario N2L 3G1, Canada
  • 2Perimeter Institute for Theoretical Physics, Ontario N2L 2Y5, Canada
  • 3Department of Basic Science, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
  • 4School of Mathematical Sciences and Centre for the Mathematical and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
  • 5Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

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Phys. Rev. Lett. 132, 150201 – Published 8 April, 2024

DOI: https://doi.org/10.1103/PhysRevLett.132.150201

Abstract

Identifying what quantum-mechanical properties are useful to untap a superior performance in quantum technologies is a pivotal question. Quantum resource theories provide a unified framework to analyze and understand such properties, as successfully demonstrated for entanglement and coherence. While these are examples of convex resources, for which quantum advantages can always be identified, many physical resources are described by a nonconvex set of free states and their interpretation has so far remained elusive. Here we address the fundamental question of the usefulness of quantum resources without convexity assumption, by providing two operational interpretations of the generalized robustness measure in general resource theories. First, we characterize the generalized robustness in terms of a nonlinear resource witness and reveal that any state is more advantageous than a free one in some multicopy channel discrimination task. Next, we consider a scenario where a theory is characterized by multiple constraints and show that the generalized robustness coincides with the worst-case advantage in a single-copy channel discrimination setting. Based on these characterizations, we conclude that every quantum resource state shows a qualitative and quantitative advantage in discrimination problems in a general resource theory even without any specification on the structure of the free states.

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Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories

Kohdai Kuroiwa, Ryuji Takagi, Gerardo Adesso, and Hayata Yamasaki
Phys. Rev. A 109, 042403 (2024)

Article Text

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Phys. Rev. Lett. 132, 150201– Published 8 April, 2024
  • Received 2 December 2023
  • Accepted 5 February 2024
Article part of CHORUS
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