Causation does not explain contextuality

Sally Shrapnel and Fabio Costa

Centre for Engineered Quantum Systems, School of Mathematics and Physics, The University of Queensland, St Lucia, QLD 4072, Australia

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Realist interpretations of quantum mechanics presuppose the existence of elements of reality that are independent of the actions used to reveal them. Such a view is challenged by several no-go theorems that show quantum correlations cannot be explained by non-contextual ontological models, where physical properties are assumed to exist prior to and independently of the act of measurement. However, all such contextuality proofs assume a traditional notion of causal structure, where causal influence flows from past to future according to ordinary dynamical laws. This leaves open the question of whether the apparent contextuality of quantum mechanics is simply the signature of some exotic causal structure, where the future might affect the past or distant systems might get correlated due to non-local constraints. Here we show that quantum predictions require a deeper form of contextuality: even allowing for arbitrary causal structure, no model can explain quantum correlations from non-contextual ontological properties of the world, be they initial states, dynamical laws, or global constraints.


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[1] S. Kochen and E. Specker, ``The problem of hidden variables in quantum mechanics,'' J. Math. Mech. 17, 59-87 (1967).

[2] J. S. Bell, ``On the problem of hidden variables in quantum mechanics,'' Rev. Mod. Phys. 38, 447-452 (1966).

[3] A. Cabello, ``Experimentally testable state-independent quantum contextuality,'' Phys. Rev. Lett. 101, 210401 (2008).

[4] R. W. Spekkens, ``Contextuality for preparations, transformations, and unsharp measurements,'' Phys. Rev. A 71, 052108 (2005).

[5] Z. Chen and A. Montina, ``Measurement contextuality is implied by macroscopic realism,'' Phys. Rev. A 83, 042110 (2011).

[6] R. Kunjwal, ``Contextuality beyond the Kochen-Specker theorem,'' arXiv:1612.07250 [quant-ph].

[7] M. D. Mazurek, M. F. Pusey, R. Kunjwal, K. J. Resch, and R. W. Spekkens, ``An experimental test of noncontextuality without unphysical idealizations,'' Nat. commun. 7, 11780 (2016).

[8] D. Schmid and R. W. Spekkens, ``Contextual Advantage for State Discrimination,'' Phys. Rev. X 8, 011015 (2018).

[9] E. G. Cavalcanti, ``Classical Causal Models for Bell and Kochen-Specker Inequality Violations Require Fine-Tuning,'' Phys. Rev. X 8, 021018 (2018).

[10] A. Chailloux, I. Kerenidis, S. Kundu, and J. Sikora, ``Optimal bounds for parity-oblivious random access codes,'' New J. Phys. 18, 045003 (2016).

[11] R. W. Spekkens, D. H. Buzacott, A. J. Keehn, B. Toner, and G. J. Pryde, ``Preparation contextuality powers parity-oblivious multiplexing,'' Phys. Rev. Lett. 102, 010401 (2009).

[12] M. Howard, J. Wallman, V. Veitch, and J. Emerson, ``Contextuality supplies the `magic' for quantum computation,'' Nature 510, 351-355 (2014).

[13] H. Price, ``Does time-symmetry imply retrocausality? How the quantum world says “Maybe”?,'' Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 43, 75-83 (2012).

[14] H. Price and K. Wharton, ``Disentangling the Quantum World,'' Entropy 17, 7752-7767 (2015).

[15] P. W. Evans, H. Price, and K. B. Wharton, ``New Slant on the EPR-Bell Experiment,'' Brit. J. Philos. Sci. 64, 297-324 (2013).

[16] K. Wharton, ``Quantum States as Ordinary Information,'' Information 5, 190-208 (2014).

[17] Y. Aharonov, E. Cohen, and T. Shushi, ``Accommodating Retrocausality with Free Will,'' Quanta 5, 53-60 (2016).

[18] M. S. Leifer and M. F. Pusey, ``Is a time symmetric interpretation of quantum theory possible without retrocausality?,'' Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 473, (2017).

[19] R. I. Sutherland, ``How retrocausality helps,'' AIP Conference Proceedings 1841, 020001 (2017).

[20] A. Carati and L. Galgani, ``Nonlocality of classical electrodynamics of point particles, and violation of Bell's inequalities,'' Nuovo Cimento B 114, 489-500 (1999).

[21] S. Weinstein, ``Nonlocality Without Nonlocality,'' Found. Phys. 39, 921-936 (2009).

[22] 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 J. Phys. 17, 033002 (2015).

[23] G. Gutoski and J. Watrous, ``Toward a general theory of quantum games,'' in 2006. Proceedings of 39th ACM STOC, pp. 565-574.

[24] G. Chiribella, G. M. D'Ariano, and P. Perinotti, ``Quantum Circuit Architecture,'' Phys. Rev. Lett. 101, 060401 (2008).

[25] G. Chiribella, G. M. D'Ariano, and P. Perinotti, ``Memory Effects in Quantum Channel Discrimination,'' Phys. Rev. Lett. 101, 180501 (2008).

[26] G. Chiribella, G. M. D'Ariano, and P. Perinotti, ``Theoretical framework for quantum networks,'' Phys. Rev. A 80, 022339 (2009).

[27] A. Bisio, G. Chiribella, G. D'Ariano, and P. Perinotti, ``Quantum networks: General theory and applications,'' . Acta Physica Slovaca. Reviews and Tutorials 61, 273-390 (2011).

[28] A. Bisio, G. M. D'Ariano, P. Perinotti, and M. Sedlák, ``Optimal processing of reversible quantum channels,'' Physics Letters A 378, 1797 - 1808 (2014).

[29] O. Oreshkov, F. Costa, and Č. Brukner, ``Quantum correlations with no causal order,'' Nat. Commun. 3, 1092 (2012).

[30] K. Modi, ``Operational approach to open dynamics and quantifying initial correlations,'' Sci. Rep. 2, 581 (2012).

[31] M. S. Leifer and R. W. Spekkens, ``Towards a formulation of quantum theory as a causally neutral theory of Bayesian inference,'' Phys. Rev. A 88, 052130 (2013).

[32] M. Ringbauer, C. J. Wood, K. Modi, A. Gilchrist, A. G. White, and A. Fedrizzi, ``Characterizing Quantum Dynamics with Initial System-Environment Correlations,'' Phys. Rev. Lett. 114, 090402 (2015).

[33] F. A. Pollock, C. Rodríguez-Rosario, T. Frauenheim, M. Paternostro, and K. Modi, ``Non-Markovian quantum processes: Complete framework and efficient characterization,'' Phys. Rev. A 97, 012127 (2018).

[34] F. Costa and S. Shrapnel, ``Quantum causal modelling,'' New J. Phys. 18, 063032 (2016).

[35] J.-M. A. Allen, J. Barrett, D. C. Horsman, C. M. Lee, and R. W. Spekkens, ``Quantum Common Causes and Quantum Causal Models,'' Phys. Rev. X 7, 031021 (2017).

[36] S. Milz, F. A. Pollock, and K. Modi, ``Reconstructing open quantum system dynamics with limited control,'' arXiv:1610.02152 [quant-ph].

[37] S. Shrapnel, F. Costa, and G. Milburn, ``Updating the Born rule,'' New J. Phys. 20 , 053010 (2018).

[38] N. Harrigan and R. Spekkens, ``Einstein, Incompleteness, and the Epistemic View of Quantum States,'' Found. Phys. 40, 125-157 (2010).

[39] M. S. Leifer, ``Is the quantum state real? An extended review of $\psi$-ontology theorems,'' Quanta 2014; 3:67-155.

[40] R. W. Spekkens, ``Negativity and Contextuality are Equivalent Notions of Nonclassicality,'' Phys. Rev. Lett. 101, 020401 (2008).

[41] J. Pearl, Causality. Cambridge University Press, 2009.

[42] O. Oreshkov and C. Giarmatzi, ``Causal and causally separable processes,'' New J. Phys. 18, 093020 (2016).

[43] M. S. Morris, K. S. Thorne, and U. Yurtsever, ``Wormholes, time machines, and the weak energy condition,'' Phys. Rev. Lett. 61, 1446 (1988).

[44] S. Durand, ``An amusing analogy: modelling quantum-type behaviours with wormhole-based time travel,'' Journal of Optics B: Quantum and Semiclassical Optics 4, S351 (2002).

[45] Ä. Baumeler and S. Wolf, ``The space of logically consistent classical processes without causal order,'' New J. Phys. 18, 013036 (2016).

[46] Ä. Baumeler, F. Costa, T. C. Ralph, S. Wolf, and M. Zych, ``Reversible time travel with freedom of choice,'' arXiv:1703.00779 [quant-ph].

[47] Ä. Baumeler, A. Feix, and S. Wolf, ``Maximal incompatibility of locally classical behavior and global causal order in multi-party scenarios,'' Phys. Rev. A 90, 042106 (2014).

[48] C. Branciard, M. Araújo, A. Feix, F. Costa, and Č. Brukner, ``The simplest causal inequalities and their violation,'' New J. Phys. 18, 013008 (2016).

[49] J. Friedman, M. S. Morris, I. D. Novikov, F. Echeverria, G. Klinkhammer, K. S. Thorne, and U. Yurtsever, ``Cauchy problem in spacetimes with closed timelike curves,'' Phys. Rev. D 42, 1915-1930 (1990).

[50] F. Echeverria, G. Klinkhammer, and K. S. Thorne, ``Billiard balls in wormhole spacetimes with closed timelike curves: classical theory,'' Phys. Rev. D 44, 1077-1099 (1991).

[51] A. Lossev and I. D. Novikov, ``The Jinn of the time machine: nontrivial self-consistent solutions,'' Class. Quantum Grav. 9, 2309 (1992).

[52] I. D. Novikov, ``Time machine and self-consistent evolution in problems with self-interaction,'' Phys. Rev. D 45, 1989-1994 (1992).

[53] E. V. Mikheeva and I. D. Novikov, ``Inelastic billiard ball in a spacetime with a time machine,'' Phys. Rev. D 47, 1432-1436 (1993).

[54] M. Nielsen and I. Chuang, Quantum Computation and Quantum Information. Cambridge University Press, 2000.

[55] E. Davies and J. Lewis, ``An operational approach to quantum probability,'' Comm. Math. Phys. 17, 239-260 (1970).

[56] E. Wigner, ``On the Quantum Correction For Thermodynamic Equilibrium,'' Phys. Rev. 40, 749-759 (1932).

[57] M. Scully and M. Zubairy, Quantum Optics. Cambridge University Press, 1997.

[58] E. G. Beltrametti and S. Bugajski, ``A classical extension of quantum mechanics,'' J. Phys. A: Math. Gen. 28, 3329 (1995).

[59] M. Araújo, A. Feix, M. Navascués, and Č. Brukner, ``A purification postulate for quantum mechanics with indefinite causal order,'' Quantum 1, 10 (2017).

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