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Extremal Tsirelson Inequalities.

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  • 1<a href="https://ror.org/03xjwb503">Université Paris Saclay</a>, <a href="https://ror.org/03n15ch10">CEA</a>, <a href="https://ror.org/02feahw73">CNRS</a>, <a href="https://ror.org/058rvd314">Institut de physique théorique</a>, 91191 Gif-sur-Yvette, France.

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Summary
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Researchers explored the boundaries of quantum statistics in Bell experiments. They identified new inequalities to precisely map the quantum set and self-test quantum correlations.

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Area of Science:

  • Quantum Information Science
  • Quantum Foundations
  • Quantum Correlations

Background:

  • Bell-type experiments test the foundations of quantum mechanics.
  • The set of observable quantum statistics is constrained by quantum theory.
  • Identifying the precise boundary of this set is a significant challenge.

Purpose of the Study:

  • To develop tools for precisely identifying the boundary of the quantum set of statistics.
  • To study the geometry of quantum correlations in Bell-type experiments.
  • To identify Bell expressions capable of self-testing specific quantum realizations.

Main Methods:

  • Dual perspective analysis of the set of quantum statistics.
  • Decomposition of the Clauser-Horne-Shimony-Holt (CHSH) expression.
  • Identification of extremal Tsirelson inequalities.

Main Results:

  • Novel insights into the geometry of the quantum set in the (2,2,2) scenario.
  • The CHSH expression is decomposed in terms of identified extremal Tsirelson inequalities.
  • Identification of all Bell expressions that can self-test the Tsirelson realization.

Conclusions:

  • The study provides a new method to precisely characterize the boundary of quantum statistics.
  • The findings offer a deeper understanding of the geometry of quantum correlations.
  • This work enables the identification of Bell expressions for self-testing quantum states and operations.