Performance comparison of the two reconstruction methods for stabilizer-based quantum secret sharing

TL;DR

This paper compares two reconstruction methods for stabilizer-based quantum secret sharing, revealing that the unitary method has advantages in circuit depth and gate count for specific codes.

Contribution

It demonstrates that the unitary reconstruction method outperforms the erasure correcting procedure in circuit depth and gate complexity for the $[[5, 1, 3]]$ stabilizer code.

Findings

Unitary procedure has smaller circuit depth.

Unitary procedure uses fewer circuit gates.

Results are specific to $[[5, 1, 3]]$ stabilizer codes.

Abstract

Stabilizer-based quantum secret sharing has two methods to reconstruct a quantum secret: The erasure correcting procedure and the unitary procedure. It is known that the unitary procedure has a smaller circuit width. On the other hand, it is unknown which method has smaller depth and fewer circuit gates. In this paper, it is shown that the unitary procedure has smaller depth and fewer circuit gates when the circuits are designed for quantum secret sharing using $[[5, 1, 3]]$ binary stabilizer codes.