Gaussian Hypothesis Testing and Quantum Illumination

Mark M. Wilde, Marco Tomamichel, Seth Lloyd, and Mario Berta
Phys. Rev. Lett. 119, 120501 – Published 18 September 2017
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Abstract

Quantum hypothesis testing is one of the most basic tasks in quantum information theory and has fundamental links with quantum communication and estimation theory. In this paper, we establish a formula that characterizes the decay rate of the minimal type-II error probability in a quantum hypothesis test of two Gaussian states given a fixed constraint on the type-I error probability. This formula is a direct function of the mean vectors and covariance matrices of the quantum Gaussian states in question. We give an application to quantum illumination, which is the task of determining whether there is a low-reflectivity object embedded in a target region with a bright thermal-noise bath. For the asymmetric-error setting, we find that a quantum illumination transmitter can achieve an error probability exponent stronger than a coherent-state transmitter of the same mean photon number, and furthermore, that it requires far fewer trials to do so. This occurs when the background thermal noise is either low or bright, which means that a quantum advantage is even easier to witness than in the symmetric-error setting because it occurs for a larger range of parameters. Going forward from here, we expect our formula to have applications in settings well beyond those considered in this paper, especially to quantum communication tasks involving quantum Gaussian channels.

  • Figure
  • Received 7 September 2016

DOI:https://doi.org/10.1103/PhysRevLett.119.120501

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

Mark M. Wilde1, Marco Tomamichel2, Seth Lloyd3, and Mario Berta4

  • 1Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803, USA
  • 2Centre for Quantum Software and Information and School of Software, University of Technology Sydney, Broadway NSW 2007, Australia
  • 3Research Laboratory of Electronics and the Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 4Department of Computing, Imperial College London, 180 Queen’s Gate Kensington, London SW7 2AZ, United Kingdom and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA

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Issue

Vol. 119, Iss. 12 — 22 September 2017

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