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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 letter, it is shown that the unitary procedure has smaller depth and fewer circuit gates than the erasure correcting procedure which follows a standard framework performing measurements and unitary operators according to the measurements outcomes, when the circuits are designed for quantum secret sharing using the [[5, 1, 3]] binary stabilizer code. The evaluation can be reversed if one discovers a better circuit for the erasure correcting procedure which does not follow the standard framework.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E107-A No.3 pp.526-529

- Publication Date
- 2024/03/01

- Publicized
- 2023/09/20

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.2023TAL0001

- Type of Manuscript
- Special Section LETTER (Special Section on Information Theory and Its Applications)

- Category
- Quantum Information Theory

Shogo CHIWAKI

Tokyo Institute of Technology

Ryutaroh MATSUMOTO

Tokyo Institute of Technology,Aalborg University

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Shogo CHIWAKI, Ryutaroh MATSUMOTO, "Performance Comparison of the Two Reconstruction Methods for Stabilizer-Based Quantum Secret Sharing" in IEICE TRANSACTIONS on Fundamentals,
vol. E107-A, no. 3, pp. 526-529, March 2024, doi: 10.1587/transfun.2023TAL0001.

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 letter, it is shown that the unitary procedure has smaller depth and fewer circuit gates than the erasure correcting procedure which follows a standard framework performing measurements and unitary operators according to the measurements outcomes, when the circuits are designed for quantum secret sharing using the [[5, 1, 3]] binary stabilizer code. The evaluation can be reversed if one discovers a better circuit for the erasure correcting procedure which does not follow the standard framework.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2023TAL0001/_p

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@ARTICLE{e107-a_3_526,

author={Shogo CHIWAKI, Ryutaroh MATSUMOTO, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Performance Comparison of the Two Reconstruction Methods for Stabilizer-Based Quantum Secret Sharing},

year={2024},

volume={E107-A},

number={3},

pages={526-529},

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 letter, it is shown that the unitary procedure has smaller depth and fewer circuit gates than the erasure correcting procedure which follows a standard framework performing measurements and unitary operators according to the measurements outcomes, when the circuits are designed for quantum secret sharing using the [[5, 1, 3]] binary stabilizer code. The evaluation can be reversed if one discovers a better circuit for the erasure correcting procedure which does not follow the standard framework.},

keywords={},

doi={10.1587/transfun.2023TAL0001},

ISSN={1745-1337},

month={March},}

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TY - JOUR

TI - Performance Comparison of the Two Reconstruction Methods for Stabilizer-Based Quantum Secret Sharing

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 526

EP - 529

AU - Shogo CHIWAKI

AU - Ryutaroh MATSUMOTO

PY - 2024

DO - 10.1587/transfun.2023TAL0001

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E107-A

IS - 3

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - March 2024

AB - 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 letter, it is shown that the unitary procedure has smaller depth and fewer circuit gates than the erasure correcting procedure which follows a standard framework performing measurements and unitary operators according to the measurements outcomes, when the circuits are designed for quantum secret sharing using the [[5, 1, 3]] binary stabilizer code. The evaluation can be reversed if one discovers a better circuit for the erasure correcting procedure which does not follow the standard framework.

ER -