Relaxed Bell inequalities as a trade-off relation between measurement dependence and hiddenness
arXiv:2206.06196 · doi:10.1103/PhysRevA.108.022214
Abstract
Quantum correlations that violate the Bell inequality cannot be explained by any (measurement independent) local hidden variable theory. However, the violation only implies incompatibility of the underlying assumptions of reality, locality, and measurement independence, and does not address the extent to which each assumption is violated quantitatively. In contrast, Hall (2010,2011) gave a quantification of each assumption and generalized the Bell-CHSH inequality that gives a trade-off relationship between the underlying assumptions. In this paper, we introduce a quantification of hidden variables (hiddenness) and derive a new trade-off relation between the hiddenness and the measurement dependency that holds for any local hidden variable theory.
arXiv comment10 pages
References in corpus (20)
- Significant-loophole-free test of Bell's theorem with entangled photons
- Random Numbers Certified by Bell's Theorem
- A strong loophole-free test of local realism
- Violation of Bell inequalities by photons more than 10 km apart
- No Signalling and Quantum Key Distribution
- From Bell's Theorem to Secure Quantum Key Distribution
- The Free Will Theorem
- Private Randomness Expansion With Untrusted Devices
- Local deterministic model of singlet state correlations based on relaxing measurement independence
- Relaxed Bell inequalities and Kochen-Specker theorems
- How much measurement independence is needed in order to demonstrate nonlocality?
- Arbitrarily small amount of measurement independence is sufficient to manifest quantum nonlocality
- Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis
- The effects of reduced "free will" on Bell-based randomness expansion
- Distinguishability Measures and Entropies for General Probabilistic Theories
- Relaxed Bell Inequalities with Arbitrary Measurement Dependence for Each Observer
- Complementary contributions of indeterminism and signalling to quantum correlations
- Optimal free-will on one side in reproducing the singlet correlation
- Measurement-dependence cost for Bell nonlocality: causal vs retrocausal models
- Parameter Dependence and Bell nonlocality