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Quantum de Finetti Theorems Under Local Measurements with Applications

Brandão, Fernando G. S. L. and Harrow, Aram W. (2017) Quantum de Finetti Theorems Under Local Measurements with Applications. Communications in Mathematical Physics, 353 (2). pp. 469-506. ISSN 0010-3616. doi:10.1007/s00220-017-2880-3.

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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.

Item Type:Article
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URLURL TypeDescription Paper ReadCube access
Brandão, Fernando G. S. L.0000-0003-3866-9378
Harrow, Aram W.0000-0003-3220-7682
Additional Information:© 2017 Springer-Verlag Berlin Heidelberg. Received: 21 July 2014. Accepted: 4 March 2017. Published online: 19 April 2017. Communicated by M. M. Wolf. We are grateful to Kevin Milner, Thomas Vidick and Mark Wilde for many helpful comments on an early version of the paper, to Ashley Montanaro for explaining to us the remark at the end of Sect. 5.2, to Scott Aaronson for telling us about [3] in 2010, to Graeme Smith and Ke Li for catching a bug in an earlier version of Corollary 14 and especially to Boaz Barak, Jon Kelner and David Steurer for sharing with us an early version of [11]. We also benefited from interesting discussions with Matthias Christandl and Stephanie Wehner. Much of this work was done while FGSLB was working at the Institute for Theoretical Physics in ETH Zürich and AWH was working in the Department of Computer Science at the University of Washington. FGSLB acknowledges support from EPSRC through an Early Career Fellowship, the Polish Ministry of Science and Higher Education Grant No. IdP2011 000361, the Swiss National Science Foundation, via the National Centre of Competence in Research QSIT, the German Science Foundation (Grant CH 843/2-1), the Swiss National Science Foundation (Grants PP00P2_128455, 20CH21_138799 (CHIST-ERA project CQC)), the Swiss National Center of Competence in Research “Quantum Science and Technology (QSIT)”, and the Swiss State Secretariat for Education and Research supporting COST action MP1006. AWH was funded by NSF Grants 0916400, 0829937, 0803478, 1111382, 1452616 and 1629809, and ARO contract W911NF-12-1-0486.
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
Ministry of Science and Higher Education (Poland)IdP2011 000361
Deutsche Forschungsgemeinschaft (DFG)CH 843/2-1
Swiss National Science Foundation (SNSF)PP00P2_128455
Swiss National Science Foundation (SNSF)20CH21_138799
Swiss National Science Foundation (SNSF)CHIST-ERA project CQC
Swiss State Secretariat for Education and ResearchMP1006
Army Research Office (ARO)W911NF-12-1-0486
Issue or Number:2
Record Number:CaltechAUTHORS:20170601-151508738
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Official Citation:Brandão, F.G.S.L. & Harrow, A.W. Commun. Math. Phys. (2017) 353: 469. doi:10.1007/s00220-017-2880-3
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77900
Deposited By: Ruth Sustaita
Deposited On:01 Jun 2017 23:13
Last Modified:15 Nov 2021 17:34

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