arXiv:2007.11711 Quantum hypothesis testing in many-body systems Jan de Boera, Victor Godeta, Jani Kastikainenb;d, Esko Keski-Vakkurib;c a Institute for Theoretical Physics, University of Amsterdam, PO Box 94485, 1090 GL Amsterdam, The Netherlands bDepartment of Physics, P.O.Box 64, FIN-00014 University of Helsinki, Finland cHelsinki Institute of Physics, P.O.Box 64, FIN-00014 University of Helsinki, Finland dAPC, AstroParticule et Cosmologie, Universit´ede Paris, CNRS/IN2P3, CEA/IRFU, Observatoire de Paris, 10, rue Alice Domon et L´eonieDuquet, 75205 Paris Cedex 13, France
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[email protected] ABSTRACT One of the key tasks in physics is to perform measurements in order to determine the state of a system. Often, measurements are aimed at determining the values of physical parameters, but one can also ask simpler questions, such as \is the system in state A or state B?". In quantum mechanics, the latter type of measurements can be studied and optimized using the framework of quantum hypothesis testing. In many cases one can explicitly find the optimal measurement in the limit where one has simultaneous access to a large number n of identical copies of the system, arXiv:2007.11711v3 [quant-ph] 28 Jun 2021 and estimate the expected error as n becomes large. Interestingly, error estimates turn out to involve various quantum information theoretic quantities such as relative entropy, thereby giving these quantities operational meaning. In this paper we consider the application of quantum hypothesis testing to quantum many-body systems and quantum field theory.