Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The Quantum Advantage in Binary Teams and the Coordination Dilemma: Supplementary

Shashank A. Deshpande, Ankur A. Kulkarni

TL;DR

The supplementary material proves that quantum advantage in binary coordination problems arises if and only if the problem class lies in the orbit of CAC or 1/2-CAC, and it rules out all other classes through centralisation arguments and no-signalling bounds. It employs Jordan’s lemma and an embedding construction to show that all strategies can be reduced to 2-qubit representations, enabling a complete characterization and tight bounds. The work also derives the optimal deterministic policy for the 1/2-CAC instance and provides parametric constructions for quantum strategies, along with detailed analyses of cost bounds and equivalence transformations. Overall, the paper delineates the precise structural conditions under which quantum resources yield an advantage in coordinated binary-activity settings, with implications for how such advantages scale with problem complexity and resource constraints.

Abstract

This document contains supporting material for our paper ``The Quantum Advantage in Binary Teams and the Coordination Dilemma''

The Quantum Advantage in Binary Teams and the Coordination Dilemma: Supplementary

TL;DR

The supplementary material proves that quantum advantage in binary coordination problems arises if and only if the problem class lies in the orbit of CAC or 1/2-CAC, and it rules out all other classes through centralisation arguments and no-signalling bounds. It employs Jordan’s lemma and an embedding construction to show that all strategies can be reduced to 2-qubit representations, enabling a complete characterization and tight bounds. The work also derives the optimal deterministic policy for the 1/2-CAC instance and provides parametric constructions for quantum strategies, along with detailed analyses of cost bounds and equivalence transformations. Overall, the paper delineates the precise structural conditions under which quantum resources yield an advantage in coordinated binary-activity settings, with implications for how such advantages scale with problem complexity and resource constraints.

Abstract

This document contains supporting material for our paper ``The Quantum Advantage in Binary Teams and the Coordination Dilemma''
Paper Structure (19 sections, 12 theorems, 89 equations, 1 table)

This paper contains 19 sections, 12 theorems, 89 equations, 1 table.

Table of Contents

  1. Introduction
  2. Proof of Results in Section \ref{['sec:equivalences']}
  3. Proof of Proposition \ref{['prop:transpose']}
  4. Proof of Proposition \ref{['prop:permute']}
  5. Proof of Proposition \ref{['prop:exchange']}
  6. Supporting Results for Proof of Theorem \ref{['thm:main']}
  7. Problem classes with no centralisation advantage
  8. Elimination of other problem classes
  9. Elimination of 1-1 problem class ${\cal C}_{11}$
  10. Elimination of 1-3 and 3-1 problem classes ${\cal C}_{13}$ and ${\cal C}_{31}$
  11. ${\cal C}_{12}$, ${\cal C}_{21}$ and the ${{1\over 2}}$-CAC problem class
  12. ${\cal C}_{22}$ and the CAC problem class
  13. Optimal deterministic policy for the ${{1\over 2}}$-CAC instance in Section \ref{['sec:1/2cacpoc']}
  14. Proof of Theorem \ref{['thm:qubitsenough']}
  15. Proof of Proposition \ref{['prop:alphaprob']}
  16. ...and 4 more sections

Key Result

Proposition S.III.1

If ${\cal C}(M,N)\in{\cal C}^o$, then ${\cal C}(M,N)$ does not admit a centralisation, and hence a quantum advantage.

Theorems & Definitions (23)

  • Definition S.III.1
  • Definition S.III.2
  • Proposition S.III.1
  • proof
  • Corollary S.III.2
  • proof
  • Corollary S.III.3
  • proof
  • Definition S.III.3
  • Lemma S.III.4
  • ...and 13 more