Skip to main content

Causal Polytopes

  • Chapter
  • First Online:
Rethinking Causality in Quantum Mechanics

Part of the book series: Springer Theses ((Springer Theses))

  • 530 Accesses

Abstract

We characterise the set of correlations between quantum labs that respect causality and prove that they form a convex polytope. We show the technique of polytope characterisation—how to obtain the vertices, which are input to a software to obtain the facets—for a bipartite scenario and apply it in the simplest tripartite case.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Oreshkov O, Costa F, Brukner ÄŚ (2012) Quantum correlations with no causal order. Nat Commun 3:1092

    Article  ADS  Google Scholar 

  2. Oreshkov O, Giarmatzi C (2016) Causal and causally separable processes. New J Phys 18:093020

    Article  Google Scholar 

  3. Abbott AA, Giarmatzi C, Costa F, Branciard C (2016) Multipartite causal correlations: polytopes and inequalities. Phys Rev A 94:032131

    Article  ADS  Google Scholar 

  4. Bell JS (1964) On the Einstein-Poldolsky-Rosen paradox. Physics 1:195–200

    Article  Google Scholar 

  5. Branciard C, Rosset D, Gisin N, Pironio S (2012) Bilocal versus nonbilocal correlations in entanglement-swapping experiments. Phys Rev A 85:032119

    Article  ADS  Google Scholar 

  6. Fritz T (2012) Beyond bell’s theorem: correlation scenarios. New J Phys 14:103001

    Article  MathSciNet  Google Scholar 

  7. Chaves R, Luft L, Gross D (2014) Causal structures from entropic information: geometry and novel scenarios. New J Phys 16:043001

    Article  MathSciNet  Google Scholar 

  8. Fritz T (2015) Beyond bell’s theorem ii: scenarios with arbitrary causal structure. Commun Math Phys 341:391–434

    Article  ADS  MathSciNet  Google Scholar 

  9. Henson J, Lal R, Pusey MF (2014) Theory-independent limits on correlations from generalized bayesian networks. New J Phys 16:113043

    Article  Google Scholar 

  10. Pienaar J (2016) Which causal scenarios are interesting? https://arxiv.org/abs/1606.07798

  11. AraĂşjo M et al (2015) Witnessing causal nonseparability. New J Phys 17:102001

    Article  Google Scholar 

  12. Branciard C, AraĂşjo M, Feix A, Costa F, Brukner ÄŚ (2016) The simplest causal inequalities and their violation. New J Phys 18:013008

    Article  MathSciNet  Google Scholar 

  13. Fine A (1982) Hidden variables, joint probability, and the bell inequalities. Phys Rev Lett 48:291

    Article  ADS  MathSciNet  Google Scholar 

  14. Pironio S (2005) Lifting bell inequalities. J Math Phys 46:062112

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Christina Giarmatzi .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Giarmatzi, C. (2019). Causal Polytopes. In: Rethinking Causality in Quantum Mechanics. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-31930-4_4

Download citation

Publish with us

Policies and ethics