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Asymptotically Optimal Confidences for Rejecting Local Realism



Yanbao Zhang, Scott Glancy, Emanuel Knill


Reliable experimental demonstrations of violations of local realism are highly desirable for fundamental tests of Quantum Mechanics. Such violations can be quantified in terms of a confidence for rejecting local realism. We propose a method for computing such a rejection confidence with a prediction-based ratio (PBR) test. PBR-based confidences are valid even if the prepared quantum state varies arbitrarily and the best local realistic model depends on previous measurement settings and outcomes. It is therefore not subject to loopholes such as the memory loophole [J. Barrett \emphet al.}, Phys. Rev. A \textbf66}, 042111 (2002)]. If the prepared state does not vary in time, the rejection confidence is asymptotically optimal. For comparison, we consider confidences derived from the number of standard deviations of violation of a Bell inequality and from martingale theory [R. Gill, arXiv:quant-ph/0110137]. We find that confidence values derived from the former can be too high, while those derived from the latter are pessimistic. PBR-based confidences are independent of Bell inequalities and provide an absolute measure for comparing experimental results from tests of local realism.
Physical Review A


local realism, Bell test, hypothesis test, software documentation


Zhang, Y. , Glancy, S. and Knill, E. (2011), Asymptotically Optimal Confidences for Rejecting Local Realism, Physical Review A, [online], (Accessed July 16, 2024)


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Created December 21, 2011, Updated October 12, 2021