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Asymptotic Performance of Port-Based Teleportation.

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Port-based teleportation (PBT) error scales inversely with the square of the number of ports (N). This fundamental limit is crucial for quantum information processing and cryptography applications.

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Area of Science:

  • Quantum Information Science
  • Quantum Shannon Theory
  • Quantum Cryptography

Background:

  • Quantum teleportation is a cornerstone of quantum Shannon theory.
  • Port-based teleportation (PBT) offers advanced applications beyond standard teleportation, including quantum computation and cryptography.
  • Understanding the performance limits of PBT is essential for its practical implementation.

Purpose of the Study:

  • To determine the fundamental performance limit of port-based teleportation (PBT).
  • To analyze the error scaling with the number of ports (N) in PBT protocols.
  • To investigate PBT variants utilizing maximally entangled resource states.

Main Methods:

  • Derivation of an achievability bound by connecting PBT optimization to Dirichlet eigenvalue problems.
  • Development of an improved converse bound with matching order in the number of ports.
  • Application of representation theory and random matrix theory to analyze PBT performance and related distributions.

Main Results:

  • The optimal PBT error is found to be proportional to 1/N^2 for a large number of ports (N).
  • Leading-order asymptotics for PBT variants using maximally entangled states are determined.
  • A refinement of a convergence result for Schur-Weyl distribution fluctuations is presented.

Conclusions:

  • The study establishes the fundamental error limit for port-based teleportation.
  • The findings provide critical insights for designing efficient quantum processors and secure quantum communication systems.
  • The mathematical techniques employed offer new tools for analyzing quantum information protocols.