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European Quantum Electronics Conference (EQEC)

Testing Bell's inequality with independent observers

Gregor Weihs, Thomas D. Jennewein, Christoph Simon, Harald Weinfurter, Anton Zeilinger

Published Jan 1, 1998• 0 citations
Publisher
DOI
10.1109/eqec.1998.714875

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Self-testing refers to the strongest device-independent (DI) certification method that validates the nature of a quantum system and devices solely based on the observed statistics. We demonstrate the self-testing of state and measurements based on the Gisin Bell inequality (GBI) featuring arbitrary inputs for both parties. We introduce a systematic and elegant sum-of-squares (SOS) approach that enables the dimension-independent derivation of the optimal quantum violation of GBI. We derive the state and the interrelation between the local observables directly from the optimization condition. Since the practical experimental scenario involves inevitable noise and imperfection, we present a comprehensive strategy for robust self-testing.
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Quantum theory is inconsistent with any local hidden variable model as was first shown by Bell. To test Bell inequalities two separated observers extract correlations from a common ensemble of identical systems. Since quantum theory does not allow simultaneous measurements of noncommuting observables, on each system every party measures a single randomly chosen observable out of a given set. Here we suggest a different approach for testing Bell inequalities that is experimentally realizable by current methods. We show that Bell inequalities can be maximally violated even when all observables are measured on each member of the ensemble. This is possible by using weak measurements that produce small disturbance, at the expense of accuracy. However, our approach does not constitute an independent test of quantum nonlocality since the local hidden variables may correlate the noise of the measurement instruments. Nevertheless, by adding a randomly chosen precise measurement at the end of every cycle of weak measurements, the parties can verify that the hidden variables were not interfering with the noise, and thus validate the suggested test.
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