TY - JOUR

T1 - Robust self-testing of two-qubit states

AU - Coopmans, Tim

AU - Kaniewski, Jȩdrzej

AU - Schaffner, Christian

PY - 2019

Y1 - 2019

N2 - It is well known that observing nonlocal correlations allows us to draw conclusions about the quantum systems under consideration. In some cases this yields a characterisation which is essentially complete, a phenomenon known as self-testing. Self-testing becomes particularly interesting if we can make the statement robust, so that it can be applied to a real experimental setup. For the simplest self-testing scenarios the most robust bounds come from the method based on operator inequalities. In this work we elaborate on this idea and apply it to the family of tilted Clauser-Horne-Shimony-Holt (CHSH) inequalities. These inequalities are maximally violated by partially entangled two-qubit states and our goal is to estimate the quality of the state based only on the observed violation. For these inequalities we have reached a candidate bound and while we have not been able to prove it analytically, we have gathered convincing numerical evidence that it holds. Our final contribution is a proof that in the usual formulation, the CHSH inequality only becomes a self-test when the violation exceeds a certain threshold. This shows that self-testing scenarios fall into two distinct classes depending on whether they exhibit such a threshold or not.

AB - It is well known that observing nonlocal correlations allows us to draw conclusions about the quantum systems under consideration. In some cases this yields a characterisation which is essentially complete, a phenomenon known as self-testing. Self-testing becomes particularly interesting if we can make the statement robust, so that it can be applied to a real experimental setup. For the simplest self-testing scenarios the most robust bounds come from the method based on operator inequalities. In this work we elaborate on this idea and apply it to the family of tilted Clauser-Horne-Shimony-Holt (CHSH) inequalities. These inequalities are maximally violated by partially entangled two-qubit states and our goal is to estimate the quality of the state based only on the observed violation. For these inequalities we have reached a candidate bound and while we have not been able to prove it analytically, we have gathered convincing numerical evidence that it holds. Our final contribution is a proof that in the usual formulation, the CHSH inequality only becomes a self-test when the violation exceeds a certain threshold. This shows that self-testing scenarios fall into two distinct classes depending on whether they exhibit such a threshold or not.

UR - http://www.scopus.com/inward/record.url?scp=85066856272&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.99.052123

DO - 10.1103/PhysRevA.99.052123

M3 - Article

VL - 99

JO - Physical Review A: covering atomic, molecular, and optical physics and quantum information

JF - Physical Review A: covering atomic, molecular, and optical physics and quantum information

SN - 2469-9926

IS - 5

M1 - 052123

ER -