Energy-Constrained Discrimination of Unitaries, Quantum Speed Limits, and a Gaussian Solovay-Kitaev Theorem

Simon Becker, Nilanjana Datta, Ludovico Lami, and Cambyse Rouzé
Phys. Rev. Lett. 126, 190504 – Published 13 May 2021
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Abstract

We investigate the energy-constrained (EC) diamond norm distance between unitary channels acting on possibly infinite-dimensional quantum systems, and establish a number of results. First, we prove that optimal EC discrimination between two unitary channels does not require the use of any entanglement. Extending a result by Acín, we also show that a finite number of parallel queries suffices to achieve zero error discrimination even in this EC setting. Second, we employ EC diamond norms to study a novel type of quantum speed limits, which apply to pairs of quantum dynamical semigroups. We expect these results to be relevant for benchmarking internal dynamics of quantum devices. Third, we establish a version of the Solovay-Kitaev theorem that applies to the group of Gaussian unitaries over a finite number of modes, with the approximation error being measured with respect to the EC diamond norm relative to the photon number Hamiltonian.

  • Received 20 July 2020
  • Accepted 31 March 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.190504

© 2021 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Simon Becker1,*, Nilanjana Datta1,†, Ludovico Lami2,‡, and Cambyse Rouzé3,§

  • 1Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
  • 2Institut für Theoretische Physik und IQST, Universität Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany
  • 3Zentrum Mathematik, Technische Universität München, 85748 Garching, Germany

  • *simon.becker@damtp.cam.ac.uk
  • n.datta@damtp.cam.ac.uk
  • ludovico.lami@gmail.com
  • §rouzecambyse@gmail.com

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Issue

Vol. 126, Iss. 19 — 14 May 2021

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