On safe post-selection for Bell tests with ideal detectors: Causal diagram approach

Pawel Blasiak; Ewa Borsuk; Marcin Markiewicz

doi:10.22331/q-2021-11-11-575

On safe post-selection for Bell tests with ideal detectors: Causal diagram approach

Pawel Blasiak¹, Ewa Borsuk¹, and Marcin Markiewicz²

¹Institute of Nuclear Physics Polish Academy of Sciences, PL-31342 Kraków, Poland
²International Centre for Theory of Quantum Technologies, University of Gdańsk, PL-80308 Gdańsk, Poland

Published:	2021-11-11, volume 5, page 575
Eprint:	arXiv:2012.07285v3
Doi:	https://doi.org/10.22331/q-2021-11-11-575
Citation:	Quantum 5, 575 (2021).

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Abstract

Reasoning about Bell nonlocality from the correlations observed in post-selected data is always a matter of concern. This is because conditioning on the outcomes is a source of non-causal correlations, known as a $\textit{selection bias}$, rising doubts whether the conclusion concerns the actual causal process or maybe it is just an effect of processing the data. Yet, even in the idealised case without detection inefficiencies, post-selection is an integral part of experimental designs, not least because it is a part of the entanglement generation process itself. In this paper we discuss a broad class of scenarios with post-selection on multiple spatially distributed outcomes. A simple criterion is worked out, called the $\textit{all-but-one}$ principle, showing when the conclusions about nonlocality from breaking Bell inequalities with post-selected data remain in force. Generality of this result, attained by adopting the high-level diagrammatic tools of causal inference, provides safe grounds for systematic reasoning based on the standard form of multipartite Bell inequalities in a wide array of entanglement generation schemes, without worrying about the dangers of selection bias. In particular, it can be applied to post-selection defined by single-particle events in each detection chanel when the number of particles in the system is conserved.

Featured image: Where post-selection is made, additional correlations may appear undermining causal conclusions drawn from an experiment. It is called a selection bias. Modern tools of causal inference provide a signpost for when this can lead to a foul-up and how this can be rectified.

► BibTeX data

@article{Blasiak2021safepostselection,
  doi = {10.22331/q-2021-11-11-575},
  url = {https://doi.org/10.22331/q-2021-11-11-575},
  title = {On safe post-selection for {B}ell tests with ideal detectors: {C}ausal diagram approach},
  author = {Blasiak, Pawel and Borsuk, Ewa and Markiewicz, Marcin},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {575},
  month = nov,
  year = {2021}
}

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[3] Huw Price and Ken Wharton, "Entanglement Swapping and Action at a Distance", Foundations of Physics 51 6, 105 (2021).

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[10] Valentin Gebhart, Luca Pezzè, and Augusto Smerzi, "Genuine Multipartite Nonlocality with Causal-Diagram Postselection", Physical Review Letters 127 14, 140401 (2021).

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