Equiangular tight frames and unistochastic matrices

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F17%3A00475710" target="_blank" >RIV/61389005:_____/17:00475710 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1088/1751-8121/aa6e16" target="_blank" >http://dx.doi.org/10.1088/1751-8121/aa6e16</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1751-8121/aa6e16" target="_blank" >10.1088/1751-8121/aa6e16</a>

Result language

angličtina

Original language name

Equiangular tight frames and unistochastic matrices

Original language description

We demonstrate that a complex equiangular tight frame composed of N vectors in dimension d, denoted ETF (d, N), exists if and only if a certain bistochastic matrix, univocally determined by N and d, belongs to a special class of unistochastic matrices. This connection allows us to find new complex ETFs in infinitely many dimensions and to derive a method to introduce non-trivial free parameters in ETFs. We present an explicit six-parametric family of complex ETF(6,16), which defines a family of symmetric POVMs. Minimal and maximal possible average entanglement of the vectors within this qubit-qutrit family are described. Furthermore, we propose an efficient numerical procedure to compute the unitary matrix underlying a unistochastic matrix, which we apply to find all existing classes of complex ETFs containing up to 20 vectors.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Project

<a href="/en/project/GA17-01706S" target="_blank" >GA17-01706S: Mathematical-Physics Models of Novel Materials</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2017

Confidentiality

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

Name of the periodical

Journal of Physics A-Mathematical and Theoretical

ISSN

1751-8113

e-ISSN

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Volume of the periodical

50

Issue of the periodical within the volume

24

Country of publishing house

GB - UNITED KINGDOM

Number of pages

13

Pages from-to

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UT code for WoS article

000402553500003

EID of the result in the Scopus database

2-s2.0-85019641448