Quantum de Finetti Theorems Under Local Measurements with Applications
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220_2017_2880_ReferencePDF.pdf
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Author(s)
Brandão, Fernando G. S. L.
Harrow, Aram W
Date Issued
April 2017
Journal
Communications in Mathematical Physics
Publisher
Springer Berlin Heidelberg
Citation
Brandão, Fernando G. S. L., and Aram W. Harrow. “Quantum de Finetti Theorems Under Local Measurements with Applications.” Communications in Mathematical Physics 353.2 (2017): 469–506.
Version
Author's final manuscript
Abstract
Quantum de Finetti theorems are a useful tool in the study of correlations in quantum multipartite states. In this paper we prove two new quantum de Finetti theorems, both showing that under tests formed by local measurements in each of the subsystems one can get an exponential improvement in the error dependence on the dimension of the subsystems. We also obtain similar results for non-signaling probability distributions. We give several applications of the results to quantum complexity theory, polynomial optimization, and quantum information theory. The proofs of the new quantum de Finetti theorems are based on information theory, in particular on the chain rule of mutual information. The results constitute improvements and generalizations of a recent de Finetti theorem due to Brandão, Christandl and Yard.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Physics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00220-017-2880-3
