Comment on 'Product states and Schmidt rank of mutually unbiased bases in dimension six'

Daniel McNulty; Stefan Weigert

doi:10.1088/1751-8121/adcb07

Comment on 'Product states and Schmidt rank of mutually unbiased bases in dimension six'

Daniel McNulty^*, Stefan Weigert

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A lemma by Chen et al. [J. Phys. A: Math. Theor. 50, 475304 (2017)] provides a necessary condition on the structure of any complex Hadamard matrix in a set of four mutually unbiased bases in C^6. The proof of the lemma is shown to contain a mistake, ultimately invalidating three theorems derived in later publications.

Original language	English
Article number	168001
Number of pages	4
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	58
Issue number	16
DOIs	https://doi.org/10.1088/1751-8121/adcb07
Publication status	Published - 17 Apr 2025

Bibliographical note

Access to Document

10.1088/1751-8121/adcb07

McNulty_Weigert_LemmaByChenYu
© 2025 IOP Publishing Ltd. This is an author-produced version of the published paper. Uploaded in accordance with the University’s Research Publications and Open Access policy.
Accepted author manuscript, 110 KBLicence: CC BY

Cite this

@article{6505a942645a419ba4164908fd3aa446,

title = "Comment on 'Product states and Schmidt rank of mutually unbiased bases in dimension six'",

abstract = "A lemma by Chen et al. [J. Phys. A: Math. Theor. 50, 475304 (2017)] provides a necessary condition on the structure of any complex Hadamard matrix in a set of four mutually unbiased bases in C^6. The proof of the lemma is shown to contain a mistake, ultimately invalidating three theorems derived in later publications.",

author = "Daniel McNulty and Stefan Weigert",

note = "{\textcopyright} 2025 IOP Publishing Ltd. This is an author-produced version of the published paper. Uploaded in accordance with the University{\textquoteright}s Research Publications and Open Access policy. ",

year = "2025",

month = apr,

day = "17",

doi = "10.1088/1751-8121/adcb07",

language = "English",

volume = "58",

journal = "Journal of Physics A: Mathematical and Theoretical",

issn = "1751-8113",

publisher = "IOP Publishing",

number = "16",

}

TY - JOUR

T1 - Comment on 'Product states and Schmidt rank of mutually unbiased bases in dimension six'

AU - McNulty, Daniel

AU - Weigert, Stefan

PY - 2025/4/17

Y1 - 2025/4/17

N2 - A lemma by Chen et al. [J. Phys. A: Math. Theor. 50, 475304 (2017)] provides a necessary condition on the structure of any complex Hadamard matrix in a set of four mutually unbiased bases in C^6. The proof of the lemma is shown to contain a mistake, ultimately invalidating three theorems derived in later publications.

AB - A lemma by Chen et al. [J. Phys. A: Math. Theor. 50, 475304 (2017)] provides a necessary condition on the structure of any complex Hadamard matrix in a set of four mutually unbiased bases in C^6. The proof of the lemma is shown to contain a mistake, ultimately invalidating three theorems derived in later publications.

U2 - 10.1088/1751-8121/adcb07

DO - 10.1088/1751-8121/adcb07

M3 - Article

SN - 1751-8113

VL - 58

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 16

M1 - 168001

ER -