Circulant matrices with orthogonal rows and off-diagonal entries of absolute value 1

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F21%3AA22029W9" target="_blank" >RIV/61988987:17310/21:A22029W9 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61389005:_____/21:00544707

Výsledek na webu

<a href="https://sciendo.com/article/10.2478/cm-2021-0005" target="_blank" >https://sciendo.com/article/10.2478/cm-2021-0005</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.2478/cm-2021-0005" target="_blank" >10.2478/cm-2021-0005</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Circulant matrices with orthogonal rows and off-diagonal entries of absolute value 1

Popis výsledku v původním jazyce

It is known that a real symmetric circulant matrix with diagonal entries d ≥ 0, off-diagonal entries ±1 and orthogonal rows exists only of order 2d + 2 (and trivially of order 1) [Turek and Goyeneche 2019]. In this paper we consider a complex Hermitian analogy of those matrices. That is, we study the existence and construction of Hermitian circulant matrices having orthogonal rows, diagonal entries d ≥ 0 and any complex entries of absolute value 1 off the diagonal. As a particular case, we consider matrices whose off-diagonal entries are 4th roots of unity; we prove that the order of any such matrix with d different from an odd integer is n = 2d + 2. We also discuss a similar problem for symmetric circulant matrices defined over finite rings Zm. As an application of our results, we show a close connection to mutually unbiased bases, an important open problem in quantum information theory.

Název v anglickém jazyce

Circulant matrices with orthogonal rows and off-diagonal entries of absolute value 1

Popis výsledku anglicky

It is known that a real symmetric circulant matrix with diagonal entries d ≥ 0, off-diagonal entries ±1 and orthogonal rows exists only of order 2d + 2 (and trivially of order 1) [Turek and Goyeneche 2019]. In this paper we consider a complex Hermitian analogy of those matrices. That is, we study the existence and construction of Hermitian circulant matrices having orthogonal rows, diagonal entries d ≥ 0 and any complex entries of absolute value 1 off the diagonal. As a particular case, we consider matrices whose off-diagonal entries are 4th roots of unity; we prove that the order of any such matrix with d different from an odd integer is n = 2d + 2. We also discuss a similar problem for symmetric circulant matrices defined over finite rings Zm. As an application of our results, we show a close connection to mutually unbiased bases, an important open problem in quantum information theory.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Communications in Mathematics

ISSN

1804-1388

e-ISSN

2336-1298

Svazek periodika

29

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

20

Strana od-do

15-34

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85105719712