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Area of Science:

  • Quantum Information Theory
  • Tensor Networks
  • Tropical Algebra

Background:

  • Bell inequalities are crucial for understanding quantum mechanics.
  • Calculating classical bounds for Bell inequalities can be computationally intensive.
  • Existing methods may not scale well for complex multipartite systems.

Purpose of the Study:

  • To develop a novel framework for calculating classical bounds of Bell inequalities.
  • To leverage tensor network contractions within tropical algebra for this purpose.
  • To explore the applicability of this method in various quantum scenarios.

Main Methods:

  • Framing Bell inequality bound calculations as tensor network contractions.
  • Utilizing tropical algebra (min-plus algebra) for these contractions.
  • Applying the method to multipartite and bipartite systems with multiple outcomes.

Main Results:

  • Demonstrated that finding classical bounds is equivalent to tensor network contraction in tropical algebra.
  • Illustrated the method's efficacy with paradigmatic examples.
  • Showcased extension to the thermodynamic limit for translationally invariant systems.

Conclusions:

  • The tropical algebra tensor network approach provides an efficient method for determining Bell inequality classical bounds.
  • Established a connection between tropical eigenvalues and classical bounds per particle.
  • This framework offers new insights into quantum correlations and renormalization procedures.