Efficient Quantum Pseudorandomness
Name
PhysRevLett.116.170502.pdf
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207.83 KB
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Adobe PDF
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Author(s)
Brandão, Fernando G. S. L.
Horodecki, Michał
Harrow, Aram W
Date Issued
April 2016
Journal
Physical Review Letters
Publisher
American Physical Society (APS)
Citation
Brandão, Fernando G. S. L., et al. “Efficient Quantum Pseudorandomness.” Physical Review Letters, vol. 116, no. 17, Apr. 2016. © 2016 American Physical Society
Version
Final published version
Abstract
Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g., in computation, communication, and control. Fully random transformations require exponential time for either classical or quantum systems, but in man y cases pseudorandom operations can emulate certain properties of truly random ones. Indeed, in the classical realm there is by now a well-developed theory regarding such pseudorandom operations. However, the construction of such objects turns out to be much harder in the quantum case. Here, we show that random quantum unitary time evolutions ("circuits") are a powerful source of quantum pseudorandomness. This gives for the first time a polynomial-time construction of quantum unitary designs, which can replace fully random operations in most applications, and shows that generic quantum dynamics cannot be distinguished from truly random processes. We discuss applications of our result to quantum information science, cryptography, and understanding the self-equilibration of closed quantum dynamics.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PHYSREVLETT.116.170502
