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Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle
Published on: January 3, 2016
How much measurement independence is needed to demonstrate nonlocality?
Jonathan Barrett1, Nicolas Gisin
1Department of Mathematics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom.
Physical Review Letters
|April 8, 2011
Summary
Violating Bell's inequality to prove nonlocality assumes random measurement settings. This study shows partial correlations between settings and local variables can mimic nonlocality, even with independent choices.
Area of Science:
- Quantum Information Science
- Foundations of Quantum Mechanics
- Quantum Entanglement
Background:
- Inferring quantum nonlocality from Bell's inequality violations relies on the assumption of free or random choice of measurement settings.
- This assumption ensures measurement settings are uncorrelated with any hypothetical local hidden variables.
- Weakening this assumption allows for partial correlations, which may impact the interpretation of Bell test results.
Purpose of the Study:
- To investigate the connection between models that relax the free-choice assumption in Bell tests and other loopholes.
- To explore the implications of partial correlations between measurement settings and local variables on nonlocality claims.
- To determine the extent to which correlations can be reproduced under relaxed assumptions.
Main Methods:
- Analysis of theoretical models that allow for partial correlations between measurement settings and local variables.
- Examination of the relationship between these models and those incorporating classical communication or the detection loophole.
- Quantification of mutual information between observer choices and local variables for projective measurements on a singlet state.
Main Results:
- Demonstrated a link between models with partial correlations and those that allow classical communication or exploit the detection loophole.
- Showed that all correlations from projective measurements on a singlet state can be reproduced even with partial correlations.
- Found that the mutual information between Alice's choice and local variables is limited to one bit, even if Bob's choices are independent.
Conclusions:
- Relaxing the free-choice assumption in Bell tests introduces ambiguities that can be mimicked by classical communication or detection loopholes.
- The study highlights the importance of rigorously addressing the measurement independence assumption for valid nonlocality claims.
- Even under relaxed conditions, the information shared between choices and local variables is bounded, offering insights into quantum correlations.
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