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Gaussian hypothesis testing and quantum illumination

Wilde, Mark M. and Tomamichel, Marco and Lloyd, Seth and Berta, Mario (2017) Gaussian hypothesis testing and quantum illumination. Physical Review Letters, 119 (12). Art. No. 120501. ISSN 0031-9007. https://resolver.caltech.edu/CaltechAUTHORS:20170817-110500251

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevLett.119.120501DOIArticle
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.120501PublisherArticle
https://arxiv.org/abs/1608.06991arXivDiscussion Paper
ORCID:
AuthorORCID
Tomamichel, Marco0000-0001-5410-3329
Berta, Mario0000-0002-0428-3429
Additional Information:© 2017 American Physical Society. Received 7 September 2016; published 18 September 2017. We are grateful to Nilanjana Datta, Saikat Guha, Stefano Pirandola, and Kaushik Seshadreesan for discussions and to Jeffrey H. Shapiro and Quntao Zhuang for feedback on our manuscript. M. T., S. L., and M. B. acknowledge the Hearne Institute for Theoretical Physics at Louisiana State University for hosting them for a research visit. M. B. acknowledges funding by the SNSF through a fellowship, funding by the Institute for Quantum Information and Matter (IQIM), a NSF Physics Frontiers Center (NSF Grant No. PHY-1125565) with support of the Gordon and Betty Moore Foundation (Grant No. GBMF-12500028), and funding support from the ARO grant for Research on Quantum Algorithms at the IQIM (Grant No. W911NF-12-1-0521). S. L. acknowledges ARO, AFOSR, and IARPA. M. T. is funded by an ARC Discovery Early Career Researcher Award fellowship (Grant No. DE160100821). M. M. W. acknowledges the NSF Grant No. CCF-1350397.
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Swiss National Science Foundation (SNSF)UNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSFPHY-1125565
Gordon and Betty Moore FoundationGBMF-12500028
Army Research Office (ARO)W911NF-12-1-0521
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Intelligence Advanced Research Projects Activity (IARPA)UNSPECIFIED
Australian Research CouncilDE160100821
NSFCCF-1350397
Issue or Number:12
Record Number:CaltechAUTHORS:20170817-110500251
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170817-110500251
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80557
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:17 Aug 2017 18:19
Last Modified:03 Oct 2019 18:32

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