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Causality in a Quantum World

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Exploring Quantum Foundations with Single Photons

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Abstract

This chapter focuses on using the theory of causal modeling to study relaxations of Bell’s assumptions, in particular relaxations of the local causality assumption

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Notes

  1. 1.

    Strictly speaking, Eq. (5.2) is the Markov condition, and the causal interpretation requires the implicit assumption that interventions on the various variables are possible.

  2. 2.

    Although one has to be careful when modeling quantum systems with classical causal models, properties such as faithfulness still apply [31].

  3. 3.

    The sets of probability distributions compatible with both models is in the intersection of the sets that are compatible with either model. In the case of parameter independence these models are mutually exclusive, because one contains a link \(A\rightarrow B\) and the other a link \(B\rightarrow A\).

  4. 4.

    Relativity merely implies that there can be no superluminal information transfer (i.e. signal locality), but not that causal influences cannot travel faster than the speed of light. For example, both phase- an group- velocity of a wavepacket can be superluminal, but the signal velocity (identified with the velocity of an edge) is always bounded by the speed of light in vacuum [51]. In other words, causal influences can conceivably travel faster than light, as long as they do not permit superluminal signaling.

  5. 5.

    One motivation for this might be that parameter independence, when suitably generalized holds in orthodox quantum mechanics [6].

  6. 6.

    Different tests could be designed using the equivalent conditions \(P(A\vert X,Y) = P(A\vert X)\) or \(P(A,Y \vert X)=P(A\vert X)P(Y\vert X)\), but these are only reliable in the case where marginal independence of the settings holds exactly.

  7. 7.

    The term “average” is used because the marginal distributions over the observed variables are defined as an average over the unobserved ones.

  8. 8.

    Strictly speaking, any modification of the “natural” causal mechanism is an intervention, even if it only partially breaks the causal links [31, 62], but for the present purpose the strong definition is most appropriate.

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Acknowledgements

This chapter is based on work that was first published in Ref. [49], and, where appropriate, I have incorporated text of that paper. The experiments were performed with Christina Giarmatzi and the theory was largely developed by Rafael Chaves.

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  1. School of Mathematics and Physics, The University of Queensland, Queensland, QLD, Australia

    Martin Ringbauer

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Ringbauer, M. (2017). Causality in a Quantum World. In: Exploring Quantum Foundations with Single Photons. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-64988-7_5

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