Source-linked AI summary
Optimal Entanglement Formulas for Entanglement-Assisted Quantum Coding
Mark M. Wilde, Todd A. Brun
TL;DR
The paper addresses how to determine the optimal ebit consumption of entanglement-assisted quantum codes. It generalizes an existing CSS formula to arbitrary block codes and derives or conjectures formulas across binary, quaternary, continuous-variable, and convolutional constructions.
Problem
Determining the entanglement resource required by general entanglement-assisted quantum codes remains an optimization problem beyond the previously treated CSS setting.
Method
The paper develops a general block-code formula, derives special cases for binary, quaternary, and continuous-variable constructions, and conjectures formulas for quantum convolutional codes.
Results
The resulting formulas determine optimal ebit requirements for arbitrary block codes and several imported-code constructions, while the convolutional formulas are conjectured and illustrated by an example requiring two ebits.
Takeaways & Limitations
The framework extends optimal-ebit calculations beyond CSS codes to multiple entanglement-assisted quantum coding settings.
Abstract
from arXiv · showhide
We provide several formulas that determine the optimal number of entangled bits (ebits) that a general entanglement-assisted quantum code requires. Our first theorem gives a formula that applies to an arbitrary entanglement-assisted block code. Corollaries of this theorem give formulas that apply to a code imported from two classical binary block codes, to a code imported from a classical quaternary block code, and to a continuous-variable entanglement-assisted quantum block code. Finally, we conjecture two formulas that apply to entanglement-assisted quantum convolutional codes.