Optimal Entanglement Formulas for Entanglement-Assisted Quantum Coding

TL;DR

This paper derives formulas to determine the optimal number of entangled bits needed for various entanglement-assisted quantum codes, enhancing understanding of resource requirements in quantum coding.

Contribution

It provides a general formula for the optimal entanglement needed in entanglement-assisted quantum codes and extends to specific code types, including classical and continuous-variable codes.

Findings

Formulas for arbitrary entanglement-assisted block codes

Corollaries for codes from classical binary and quaternary codes

Conjectured formulas for quantum convolutional codes

Abstract

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.