# The Significance of Measurement Independence for Bell Inequalities and Locality

@article{Hall2016TheSO, title={The Significance of Measurement Independence for Bell Inequalities and Locality}, author={Michael J. W. Hall}, journal={arXiv: Quantum Physics}, year={2016}, pages={189-204} }

A local and deterministic model of quantum correlations is always possible, as shown explicitly by Brans in 1988: one simply needs the physical systems being measured to have a suitable statistical correlation with the physical systems performing the measurement, via some common cause. Hence, to derive no-go results such as Bell inequalities, an assumption of measurement independence is crucial. It is a surprisingly strong assumption—less than 1 / 15 bits of prior correlation suffice for a…

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## References

SHOWING 1-10 OF 37 REFERENCES

Optimal free will on one side in reproducing the singlet correlation

- Physics
- 2012

Bell’s theorem teaches us that there are quantum correlations that cannot be simulated by just shared randomness (local hidden variable). There are some recent results which simulate the singlet…

Relaxed Bell inequalities and Kochen-Specker theorems

- Mathematics
- 2011

The combination of various physically plausible properties, such as no signaling, determinism, and experimental free will, is known to be incompatible with quantum correlations. Hence, these…

Local deterministic model of singlet state correlations based on relaxing measurement independence.

- PhysicsPhysical review letters
- 2010

A simple measure of the degree of measurement independent is defined for correlation models, and it is shown that all spin correlations of a singlet state can be modeled via giving up just 14% of measurement independence.

Arbitrarily small amount of measurement independence is sufficient to manifest quantum nonlocality.

- MathematicsPhysical review letters
- 2014

It is proved that even in the simplest Bell test-one involving 2 parties each performing 2 binary-outcome measurements-an arbitrarily small amount of measurement independence is sufficient to manifest quantum nonlocality.

Quantum non-locality—it ainʼt necessarily so...

- Philosophy
- 2014

Bellʼs theorem is 50 years old. There still remains a controversy about its implications. Much of this controversy has its roots in confusion regarding the premises from which the theorem can be…

Demonstration of Quantum Nonlocality in the Presence of Measurement Dependence.

- PhysicsPhysical review letters
- 2015

It is shown that the measurement independence assumption can be widely relaxed while still demonstrating quantum nonlocality, excluding a much larger range of measurement dependent local models than would be possible with an adapted Clauser-Horne-Shimony-Holt (CHSH) inequality.

Bell tests with min-entropy sources

- Computer Science
- 2013

Lower bounds on the min-entropy of the source used to choose the inputs required to deduce any quantum or nonlocal behavior from a Bell inequality violation are found.

Farkas's Lemma and the nature of reality: Statistical implications of quantum correlations

- Physics
- 1984

A general algorithm is given for determining whether or not a given set of pair distributions allows for the construction of all the members of a specified set of higher-order distributions which…

Limited measurement dependence in multiple runs of a Bell test

- Computer Science
- 2013

It is proved that there remain Bell violations for a sufficiently high, yet non-maximal degree of free will which cannot be simulated by a classical attack, regardless of how many runs of the experiment those choices are correlated over.

Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres

- PhysicsNature
- 2015

The data imply statistically significant rejection of the local-realist null hypothesis and could be used for testing less-conventional theories, and for implementing device-independent quantum-secure communication and randomness certification.