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Self-testing multipartite entangled states through projections onto two systems

Artykuł
Czasopismo : NEW JOURNAL OF PHYSICS   Tom: 20, Strony: 083041
Ivan Šupić [1] , Andrea Coladangelo [2] , Remigiusz Augusiak [3] , Antonio Acin [1] , [4]
  • [1]
    ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, E-08860 Castelldefels (Barcelona), Spain
  • [2]
    Department of Computing and Mathematical Sciences, California Institute of Technology, 1200 E California Blvd, Pasadena,CA 91125, United States of America
  • [3]
  • [4]
    ICREA–Institucio Catalana de Recerca i Estudis Avançats, Lluis Companys 23, E-08010 Barcelona, Spain
2018-08-28 angielski
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Finding ways to test the behaviour of quantum devices is a timely enterprise, especially in light of the rapid development of quantum technologies. Device-independent self-testing is one desirable approach, as it makes minimal assumptions on the devices being tested. In this work, we address the question of which states can be self-tested. This has been answered recently in the bipartite case (Coladangelo et al 2017 Nat. Commun. 8 15485), while it is largely unexplored in the multipartite case, with only a few scattered results, using a variety of different methods: maximal violation of a Bell inequality, numerical SWAP method, stabiliser self-testing etc. In this work, we investigate a simple, and potentially unifying, approach: combining projections onto two-qubit spaces (projecting parties or degrees of freedom) and then using maximal violation of the tiltedCHSHinequalities. This allows one to obtain self-testing of Dicke states and partially entangledGHZstates with two measurements per party, and also to recover self-testing of graph states (previously known only through stabiliser methods). Finally, we give the first self-test of a class of multipartite qudit states: we generalise the selftesting of partially entangled GHZ states by adapting techniques from (Coladangelo et al 2017 Nat. Commun. 8 15485), and show that all multipartite states which admit a Schmidt decomposition can be self-tested with few measurements.
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