Analytic and nearly optimal self-testing bounds for the Clauser-Horne-Shimony-Holt and Mermin inequalities
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Analytic and nearly optimal self-testing bounds for the Clauser-Horne-Shimony-Holt and Mermin inequalities. / Kaniewski, Jedrzej.
I: Physical Review Letters, Bind 117, Nr. 7, 070402, 11.08.2016.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Analytic and nearly optimal self-testing bounds for the Clauser-Horne-Shimony-Holt and Mermin inequalities
AU - Kaniewski, Jedrzej
PY - 2016/8/11
Y1 - 2016/8/11
N2 - Self-testing refers to the phenomenon that certain extremal quantum correlations (almost) uniquely identify the quantum system under consideration. For instance, observing the maximal violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality certifies that the two parties share a singlet. While self-testing results are known for several classes of states, in many cases they are only applicable if the observed statistics are almost perfect, which makes them unsuitable for practical applications. Practically relevant self-testing bounds are much less common and moreover they all result from a single numerical method (with one exception which we discuss in detail). In this work we present a new technique for proving analytic self-testing bounds of practically relevant robustness. We obtain improved bounds for the case of self-testing the singlet using the CHSH inequality (in particular we show that nontrivial fidelity with the singlet can be achieved as long as the violation exceeds β∗=(16+142√)/17≈2.11). In the case of self-testing the tripartite Greenberger-Horne-Zeilinger state using the Mermin inequality, we derive a bound which not only improves on previously known results but turns out to be tight. We discuss other scenarios to which our technique can be immediately applied.
AB - Self-testing refers to the phenomenon that certain extremal quantum correlations (almost) uniquely identify the quantum system under consideration. For instance, observing the maximal violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality certifies that the two parties share a singlet. While self-testing results are known for several classes of states, in many cases they are only applicable if the observed statistics are almost perfect, which makes them unsuitable for practical applications. Practically relevant self-testing bounds are much less common and moreover they all result from a single numerical method (with one exception which we discuss in detail). In this work we present a new technique for proving analytic self-testing bounds of practically relevant robustness. We obtain improved bounds for the case of self-testing the singlet using the CHSH inequality (in particular we show that nontrivial fidelity with the singlet can be achieved as long as the violation exceeds β∗=(16+142√)/17≈2.11). In the case of self-testing the tripartite Greenberger-Horne-Zeilinger state using the Mermin inequality, we derive a bound which not only improves on previously known results but turns out to be tight. We discuss other scenarios to which our technique can be immediately applied.
U2 - 10.1103/PhysRevLett.117.070402
DO - 10.1103/PhysRevLett.117.070402
M3 - Journal article
C2 - 27563939
VL - 117
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 7
M1 - 070402
ER -
ID: 164495232