2000 character limit reached
Quantum non-classicality in the simplest causal network (2404.12790v1)
Published 19 Apr 2024 in quant-ph
Abstract: Bell's theorem prompts us with a fundamental inquiry: what is the simplest scenario leading to the incompatibility between quantum correlations and the classical theory of causality? Here we demonstrate that quantum non-classicality is possible in a network consisting of only three dichotomic variables, without the need of the locality assumption neither external measurement choices. We also show that the use of interventions, a central tool in the field of causal inference, significantly improves the noise robustness of this new kind of non-classical behaviour, making it feasible for experimental tests with current technology.
- J. S. Bell, On the einstein podolsky rosen paradox, Physics Physique Fizika 1, 195 (1964).
- J. Pearl, Causality (Cambridge university press, 2009).
- C. J. Wood and R. W. Spekkens, The lesson of causal discovery algorithms for quantum correlations: causal explanations of bell-inequality violations require fine-tuning, New Journal of Physics 17, 033002 (2015).
- E. Wolfe, R. W. Spekkens, and T. Fritz, The inflation technique for causal inference with latent variables, Journal of Causal Inference 7, 20170020 (2019).
- T. Fritz, Beyond bell’s theorem: correlation scenarios, New Journal of Physics 14, 103001 (2012).
- I. Šupić, J.-D. Bancal, and N. Brunner, Quantum nonlocality in networks can be demonstrated with an arbitrarily small level of independence between the sources, Physical Review Letters 125, 240403 (2020).
- J. B. Brask and R. Chaves, Bell scenarios with communication, Journal of Physics A: Mathematical and Theoretical 50, 094001 (2017).
- X. Coiteux-Roy, E. Wolfe, and M.-O. Renou, No bipartite-nonlocal causal theory can explain nature’s correlations, Physical review letters 127, 200401 (2021).
- A. Pozas-Kerstjens, N. Gisin, and A. Tavakoli, Full network nonlocality, Physical review letters 128, 010403 (2022).
- M. Gachechiladze, N. Miklin, and R. Chaves, Quantifying causal influences in the presence of a quantum common cause, Physical Review Letters 125, 230401 (2020).
- R. J. Evans, Graphs for margins of bayesian networks, Scandinavian Journal of Statistics 43, 625 (2016).
- J. Pearl, On the testability of causal models with latent and instrumental variables, in Proceedings of the Eleventh conference on Uncertainty in artificial intelligence (1995) pp. 435–443.
- A. Balke and J. Pearl, Bounds on treatment effects from studies with imperfect compliance, Journal of the American statistical Association 92, 1171 (1997).
- L. D. Garcia, M. Stillman, and B. Sturmfels, Algebraic geometry of bayesian networks, Journal of Symbolic Computation 39, 331 (2005).
- R. Chaves, Polynomial bell inequalities, Physical review letters 116, 010402 (2016).
- J. Nocedal and S. J. Wright, Quadratic programming, Numerical optimization , 448 (2006).
- C. Branciard, N. Gisin, and S. Pironio, Characterizing the nonlocal correlations created via entanglement swapping, Physical review letters 104, 170401 (2010).
- S. P. Boyd and L. Vandenberghe, Convex optimization (Cambridge university press, 2004).
- Gurobi Optimization, LLC, Gurobi Optimizer Reference Manual (2022).
- We obtain this classical upper bound using QP with a precision of 10−9superscript10910^{-9}10 start_POSTSUPERSCRIPT - 9 end_POSTSUPERSCRIPT.
- J. Henson, R. Lal, and M. F. Pusey, Theory-independent limits on correlations from generalized bayesian networks, New Journal of Physics 16, 113043 (2014).
- P. Sekatski, S. Boreiri, and N. Brunner, Partial self-testing and randomness certification in the triangle network, Physical Review Letters 131, 100201 (2023).
- C. M. Lee and M. J. Hoban, Towards device-independent information processing on general quantum networks, Physical review letters 120, 020504 (2018).