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Concurrence Percolation in Quantum Networks.

Xiangyi Meng1,2, Jianxi Gao3, Shlomo Havlin1,4

  • 1Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.

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We introduce concurrence percolation theory (ConPT) for quantum networks, enabling more efficient entanglement transmission. This new theory offers a lower entanglement threshold than classical methods, enhancing quantum communication capabilities.

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Area of Science:

  • Quantum Information Science
  • Statistical Physics
  • Network Theory

Background:

  • Establishing long-distance quantum entanglement is crucial for quantum communication networks (QN).
  • Classical percolation theory assumes perfect entanglement paths are necessary for entanglement transmission.
  • This assumption limits understanding and optimization of quantum communication efficiency.

Purpose of the Study:

  • To develop a new statistical theory for entanglement transmission in quantum networks.
  • To relax the condition of perfectly entangled states and focus on concurrence.
  • To investigate a 'quantum advantage' in entanglement distribution beyond classical predictions.

Main Methods:

  • Introduction of Concurrence Percolation Theory (ConPT), generalizing bond percolation.
  • Utilizing 'sponge-crossing' paths instead of clusters for connectivity analysis.
  • Applying series and parallel rules, inspired by resistance network analysis, and star-mesh transforms.

Main Results:

  • ConPT predicts a lower entanglement transmission threshold than classical percolation methods.
  • This threshold is achievable on various networks, including series-parallel networks and the Bethe lattice.
  • Observed percolation-like universal critical behavior in entanglement statistics.

Conclusions:

  • ConPT offers a more general and efficient approach to quantum communication improvement.
  • The theory provides new insights into quantum advantage under network locality constraints.
  • Findings open new perspectives for the theory of criticality in entanglement statistics.