Higher-dimensional performance of port-based teleportation

Area of Science:

• Quantum Information Science
• Quantum Computing
• Quantum Communication

Background:

• Port-based teleportation (PBT) offers a simplified quantum teleportation protocol without final unitary corrections.
• Calculating PBT performance in higher dimensions (d>2) is computationally intensive using conventional Hilbert-space methods.
• Existing bounds for PBT success measures like entanglement fidelity become trivial in higher dimensions.

Purpose of the Study:

• To develop an efficient method for calculating higher-dimensional Port-based teleportation performance.
• To analyze the behavior of PBT for arbitrary dimensions (d) and a low number of ports (N).

Main Methods:

• Construction of a graph-theoretic algebra, a subset of the Temperley-Lieb algebra.
• Application of this algebra to explicitly compute PBT success probability and fidelity for "pretty-good measurements" in arbitrary dimensions.
• Derivation of a simple upper bound for PBT performance.

Main Results:

• The graph-theoretic algebra allows explicit computation of higher-dimensional PBT performance with negligible overhead.
• Entanglement fidelity for low N and arbitrary d asymptotically approaches N/d^2 for large d.
• This result confirms a previously known lower bound in the literature.

Conclusions:

• A computationally efficient framework for analyzing higher-dimensional PBT has been established.
• The study provides explicit formulas for PBT success probability and fidelity.
• The findings confirm theoretical predictions and offer insights into the scalability of PBT.