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Combining contextuality and causality: a game semantics approach

Samson Abramsky, Rui Soares Barbosa, Amy Searle

Abstract

We develop an approach to combining contextuality with causality, which is general enough to cover causal background structure, adaptive measurement-based quantum computation, and causal networks. The key idea is to view contextuality as arising from a game played between Experimenter and Nature, allowing for causal dependencies in the actions of both the Experimenter (choice of measurements) and Nature (choice of outcomes).

Combining contextuality and causality: a game semantics approach

Abstract

We develop an approach to combining contextuality with causality, which is general enough to cover causal background structure, adaptive measurement-based quantum computation, and causal networks. The key idea is to view contextuality as arising from a game played between Experimenter and Nature, allowing for causal dependencies in the actions of both the Experimenter (choice of measurements) and Nature (choice of outcomes).
Paper Structure (19 sections, 7 theorems, 17 equations)

This paper contains 19 sections, 7 theorems, 17 equations.

Table of Contents

  1. Introduction
  2. Previous work
  3. Examples
  4. Example I: causal background à la GP
  5. Example II: Anders--Browne
  6. Game semantics of causality
  7. Measurement scenarios
  8. Causal measurement scenarios
  9. Strategies
  10. The presheaf of strategies
  11. Historical note
  12. Causal contextuality
  13. Special cases
  14. Flat scenarios
  15. GP scenarios
  16. ...and 4 more sections

Key Result

Proposition 4.1

If $s, t \in \sigma$, $s \subseteq t$, and $s \rhd x$, then

Theorems & Definitions (12)

  • Proposition 4.1: Monotonicity
  • proof
  • Proposition 4.2: Maximality
  • Proposition 4.3
  • Proposition 4.4
  • proof
  • Proposition 4.5
  • Proposition 7.1
  • proof
  • Example 7.2
  • ...and 2 more