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Classical command of quantum systems


Quantum computation and cryptography both involve scenarios in which a user interacts with an imperfectly modelled or ‘untrusted’ system. It is therefore of fundamental and practical interest to devise tests that reveal whether the system is behaving as instructed. In 1969, Clauser, Horne, Shimony and Holt proposed an experimental test that can be passed by a quantum-mechanical system but not by a system restricted to classical physics. Here we extend this test to enable the characterization of a large quantum system. We describe a scheme that can be used to determine the initial state and to classically command the system to evolve according to desired dynamics. The bipartite system is treated as two black boxes, with no assumptions about their inner workings except that they obey quantum physics. The scheme works even if the system is explicitly designed to undermine it; any misbehaviour is detected. Among its applications, our scheme makes it possible to test whether a claimed quantum computer is truly quantum. It also advances towards a goal of quantum cryptography: namely, the use of ‘untrusted’ devices to establish a shared random key, with security based on the validity of quantum physics.

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Figure 1: Test for quantumness.
Figure 2: Sub-protocols for verified quantum dynamics.


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We thank E. Bering, A. Broadbent, A. Chailloux, M. Christandl, R. Colbeck, T. Ito, R. König, M. McKague, V. Madhavan, R. Renner, S. Sondhi and T. Vidick for discussions. Part of this work was conducted while F.U. was at the University of California Berkeley and B.W.R. was at the Institute for Quantum Computing, University of Waterloo. B.W.R. acknowledges support from NSERC, ARO-DTO and Mitacs. U.V. acknowledges support from US NSF grant CCF-0905626 and Templeton grant 21674

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Correspondence to Ben W. Reichardt.

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Reichardt, B., Unger, F. & Vazirani, U. Classical command of quantum systems. Nature 496, 456–460 (2013).

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