Finite-Function-Encoding Quantum States

J 2022

Finite-Function-Encoding Quantum States

APPEL, Paul, Alexander J. HEILMAN, Ezekiel W. WERTZ, David W. LYONS, Marcus HUBER et. al.

Základní údaje

Originální název

Finite-Function-Encoding Quantum States

Autoři

APPEL, Paul (276 Německo), Alexander J. HEILMAN, Ezekiel W. WERTZ, David W. LYONS, Marcus HUBER, Matej PIVOLUSKA (703 Slovensko, garant, domácí) a Giuseppe VITAGLIANO

Vydání

QUANTUM, WIEN, VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF, 2022, 2521-327X

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10306 Optics

Stát vydavatele

Rakousko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 6.400

Kód RIV

RIV/00216224:14610/22:00125965

Organizační jednotka

Ústav výpočetní techniky

DOI

http://dx.doi.org/10.22331/q-2022-05-09-708

UT WoS

000799374500001

Klíčová slova anglicky

non-locality; entanglement; high-dimensional quantum states

Štítky

J-D1, J-Q1, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 15. 3. 2023 18:14, Mgr. Alena Mokrá

Anotace

V originále

We introduce finite-function-encoding (FFE) states which encode arbitrary d-valued logic functions, i.e., multivariate functions over the ring of integers modulo d, and investigate some of their structural properties. We also point out some differences between polynomial and non-polynomial function encoding states: The former can be associated to graphical objects, that we dub tensor-edge hypergraphs (TEH), which are a generalization of hypergraphs with a tensor attached to each hyperedge encoding the coefficients of the different monomials. To complete the framework, we also introduce a notion of finite-function-encoding Pauli (FP) operators, which correspond to elements of what is known as the generalized symmetric group in mathematics. First, using this machinery, we study the stabilizer group associated to FFE states and observe how qudit hypergraph states introduced in Ref. [1] admit stabilizers of a particularly simpler form. Afterwards, we investigate the classification of FFE states under local unitaries (LU), and, after showing the complexity of this problem, we focus on the case of bipartite states and especially on the classification under local FP operations (LFP). We find all LU and LFP classes for two qutrits and two ququarts and study several other special classes, pointing out the relation between maximally entangled FFE states and complex Butson-type Hadamard matrices. Our investigation showcases also the relation between the properties of FFE states, especially their LU classification, and the theory of finite rings over the integers.

Návaznosti

MUNI/G/1596/2019, interní kód MU

Název: Development of algorithms for application of quantum computers in electronic-structure calculations in solid-state physics and chemistry (Akronym: Qubits4PhysChem)

Investor: Masarykova univerzita, Development of algorithms for application of quantum computers in electronic-structure calculations in solid-state physics and chemistry, INTERDISCIPLINARY - Mezioborové výzkumné projekty

Citovat

APPEL, Paul, Alexander J. HEILMAN, Ezekiel W. WERTZ, David W. LYONS, Marcus HUBER, Matej PIVOLUSKA a Giuseppe VITAGLIANO. Finite-Function-Encoding Quantum States. QUANTUM. WIEN: VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF, 2022, roč. 6, č. 708, s. 1-34. ISSN 2521-327X. Dostupné z: https://dx.doi.org/10.22331/q-2022-05-09-708.

@article{1859041,
   author = {Appel, Paul and Heilman, Alexander J. and Wertz, Ezekiel W. and Lyons, David W. and Huber, Marcus and Pivoluska, Matej and Vitagliano, Giuseppe},
   article_location = {WIEN},
   article_number = {708},
   doi = {http://dx.doi.org/10.22331/q-2022-05-09-708},
   keywords = {non-locality; entanglement; high-dimensional quantum states},
   language = {eng},
   issn = {2521-327X},
   journal = {QUANTUM},
   title = {Finite-Function-Encoding Quantum States},
   url = {https://quantum-journal.org/papers/q-2022-05-09-708/},
   volume = {6},
   year = {2022}
}

TY  - JOUR
ID  - 1859041
AU  - Appel, Paul - Heilman, Alexander J. - Wertz, Ezekiel W. - Lyons, David W. - Huber, Marcus - Pivoluska, Matej - Vitagliano, Giuseppe
PY  - 2022
TI  - Finite-Function-Encoding Quantum States
JF  - QUANTUM
VL  - 6
IS  - 708
SP  - 1-34
EP  - 1-34
PB  - VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF
SN  - 2521327X
KW  - non-locality
KW  - entanglement
KW  - high-dimensional quantum states
UR  - https://quantum-journal.org/papers/q-2022-05-09-708/
N2  - We introduce finite-function-encoding (FFE) states which encode arbitrary d-valued logic functions, i.e., multivariate functions over the ring of integers modulo d, and investigate some of their structural properties. We also point out some differences between polynomial and non-polynomial function encoding states: The former can be associated to graphical objects, that we dub tensor-edge hypergraphs (TEH), which are a generalization of hypergraphs with a tensor attached to each hyperedge encoding the coefficients of the different monomials. To complete the framework, we also introduce a notion of finite-function-encoding Pauli (FP) operators, which correspond to elements of what is known as the generalized symmetric group in mathematics. First, using this machinery, we study the stabilizer group associated to FFE states and observe how qudit hypergraph states introduced in Ref. [1] admit stabilizers of a particularly simpler form. Afterwards, we investigate the classification of FFE states under local unitaries (LU), and, after showing the complexity of this problem, we focus on the case of bipartite states and especially on the classification under local FP operations (LFP). We find all LU and LFP classes for two qutrits and two ququarts and study several other special classes, pointing out the relation between maximally entangled FFE states and complex Butson-type Hadamard matrices. Our investigation showcases also the relation between the properties of FFE states, especially their LU classification, and the theory of finite rings over the integers.
ER  -

APPEL, Paul, Alexander J. HEILMAN, Ezekiel W. WERTZ, David W. LYONS, Marcus HUBER, Matej PIVOLUSKA a Giuseppe VITAGLIANO. Finite-Function-Encoding Quantum States. \textit{QUANTUM}. WIEN: VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF, 2022, roč.~6, č.~708, s.~1-34. ISSN~2521-327X. Dostupné z: https://dx.doi.org/10.22331/q-2022-05-09-708.

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