A triality between weak mutually unbiased bases, zeros of their analytic representations, and finite geometries View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2017

AUTHORS

T. Olupitan , C. Lei , A. Vourdas

ABSTRACT

Quantum systems with variables in Z(d) are considered, and three different structures are studied. We show that there is a correspondence (triality) between (1) weak mutually unbiased bases; (2) their analytic representation in the complex plane based on Theta functions, and their zeros; (3) finite geometries in the Z(d) X Z(d) phase space More... »

PAGES

361-366

Book

TITLE

Physical and Mathematical Aspects of Symmetries

ISBN

978-3-319-69163-3
978-3-319-69164-0

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-319-69164-0_54

DOI

http://dx.doi.org/10.1007/978-3-319-69164-0_54

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1100290085


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Department of Computing, University of Bradford, BD7 1DP, Bradford, UK", 
          "id": "http://www.grid.ac/institutes/grid.6268.a", 
          "name": [
            "Department of Computing, University of Bradford, BD7 1DP, Bradford, UK"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Olupitan", 
        "givenName": "T.", 
        "id": "sg:person.016620740074.91", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016620740074.91"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Computing, University of Bradford, BD7 1DP, Bradford, UK", 
          "id": "http://www.grid.ac/institutes/grid.6268.a", 
          "name": [
            "Department of Computing, University of Bradford, BD7 1DP, Bradford, UK"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Lei", 
        "givenName": "C.", 
        "id": "sg:person.015150124647.46", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015150124647.46"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Computing, University of Bradford, BD7 1DP, Bradford, UK", 
          "id": "http://www.grid.ac/institutes/grid.6268.a", 
          "name": [
            "Department of Computing, University of Bradford, BD7 1DP, Bradford, UK"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Vourdas", 
        "givenName": "A.", 
        "id": "sg:person.012726447121.07", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012726447121.07"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "2017", 
    "datePublishedReg": "2017-01-01", 
    "description": "Quantum systems with variables in Z(d) are considered, and three different structures are studied. We show that there is a correspondence (triality) between (1) weak mutually unbiased bases; (2) their analytic representation in the complex plane based on Theta functions, and their zeros; (3) finite geometries in the Z(d) X Z(d) phase space", 
    "editor": [
      {
        "familyName": "Duarte", 
        "givenName": "Sergio", 
        "type": "Person"
      }, 
      {
        "familyName": "Gazeau", 
        "givenName": "Jean-Pierre", 
        "type": "Person"
      }, 
      {
        "familyName": "Faci", 
        "givenName": "Sofiane", 
        "type": "Person"
      }, 
      {
        "familyName": "Micklitz", 
        "givenName": "Tobias", 
        "type": "Person"
      }, 
      {
        "familyName": "Scherer", 
        "givenName": "Ricardo", 
        "type": "Person"
      }, 
      {
        "familyName": "Toppan", 
        "givenName": "Francesco", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-3-319-69164-0_54", 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-3-319-69163-3", 
        "978-3-319-69164-0"
      ], 
      "name": "Physical and Mathematical Aspects of Symmetries", 
      "type": "Book"
    }, 
    "keywords": [
      "finite geometry", 
      "analytic representation", 
      "quantum systems", 
      "phase space", 
      "unbiased bases", 
      "complex plane", 
      "theta functions", 
      "zeros", 
      "geometry", 
      "triality", 
      "representation", 
      "different structures", 
      "space", 
      "correspondence", 
      "plane", 
      "variables", 
      "function", 
      "system", 
      "structure", 
      "basis"
    ], 
    "name": "A triality between weak mutually unbiased bases, zeros of their analytic representations, and finite geometries", 
    "pagination": "361-366", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1100290085"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-319-69164-0_54"
        ]
      }
    ], 
    "publisher": {
      "name": "Springer Nature", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-319-69164-0_54", 
      "https://app.dimensions.ai/details/publication/pub.1100290085"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2022-10-01T07:00", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20221001/entities/gbq_results/chapter/chapter_53.jsonl", 
    "type": "Chapter", 
    "url": "https://doi.org/10.1007/978-3-319-69164-0_54"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-69164-0_54'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-69164-0_54'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-69164-0_54'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-69164-0_54'


 

This table displays all metadata directly associated to this object as RDF triples.

118 TRIPLES      22 PREDICATES      45 URIs      38 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-319-69164-0_54 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author Nfa8c7a3c1893488ea8802df8ecc66904
4 schema:datePublished 2017
5 schema:datePublishedReg 2017-01-01
6 schema:description Quantum systems with variables in Z(d) are considered, and three different structures are studied. We show that there is a correspondence (triality) between (1) weak mutually unbiased bases; (2) their analytic representation in the complex plane based on Theta functions, and their zeros; (3) finite geometries in the Z(d) X Z(d) phase space
7 schema:editor N82e336dade52467483a5b25f35a7945c
8 schema:genre chapter
9 schema:isAccessibleForFree false
10 schema:isPartOf Nf01ef0326af64feab71fd2b7661eb6e1
11 schema:keywords analytic representation
12 basis
13 complex plane
14 correspondence
15 different structures
16 finite geometry
17 function
18 geometry
19 phase space
20 plane
21 quantum systems
22 representation
23 space
24 structure
25 system
26 theta functions
27 triality
28 unbiased bases
29 variables
30 zeros
31 schema:name A triality between weak mutually unbiased bases, zeros of their analytic representations, and finite geometries
32 schema:pagination 361-366
33 schema:productId N9c8d27b8440e4950ba72f845bd9b20f6
34 Nc0067a90090144cba058bf232d0ebfac
35 schema:publisher N1199f2978c3841cfa4859e3d9f38c082
36 schema:sameAs https://app.dimensions.ai/details/publication/pub.1100290085
37 https://doi.org/10.1007/978-3-319-69164-0_54
38 schema:sdDatePublished 2022-10-01T07:00
39 schema:sdLicense https://scigraph.springernature.com/explorer/license/
40 schema:sdPublisher Nb5a4d7e5f94e40ef9d375a3e90ed1702
41 schema:url https://doi.org/10.1007/978-3-319-69164-0_54
42 sgo:license sg:explorer/license/
43 sgo:sdDataset chapters
44 rdf:type schema:Chapter
45 N1199f2978c3841cfa4859e3d9f38c082 schema:name Springer Nature
46 rdf:type schema:Organisation
47 N323a05353d384bc388e990ad12099946 rdf:first N8b0239db5a1a4e2ca21a9ee19efeb06b
48 rdf:rest Ndf7c7970e39740dcadfb40ded738772d
49 N3e92819a9dd444559c4200b5bef9ce35 schema:familyName Gazeau
50 schema:givenName Jean-Pierre
51 rdf:type schema:Person
52 N3f986ffff97f4c199a6f253e4f7c79ec rdf:first N3e92819a9dd444559c4200b5bef9ce35
53 rdf:rest N425af1852a9c4819b89bfb3bc4129c58
54 N425af1852a9c4819b89bfb3bc4129c58 rdf:first N9294a89bcccf439b921bd531773a6bf1
55 rdf:rest Nfef0a220f3784ad49d6ca4bc61612614
56 N545058fca51a4ca293cf34d2e3f520a8 rdf:first sg:person.012726447121.07
57 rdf:rest rdf:nil
58 N82e336dade52467483a5b25f35a7945c rdf:first Ne57981ef36d9468ca1b1a948e277f792
59 rdf:rest N3f986ffff97f4c199a6f253e4f7c79ec
60 N8b0239db5a1a4e2ca21a9ee19efeb06b schema:familyName Scherer
61 schema:givenName Ricardo
62 rdf:type schema:Person
63 N8fa54352dc5244159b06dab317828bf2 schema:familyName Toppan
64 schema:givenName Francesco
65 rdf:type schema:Person
66 N9294a89bcccf439b921bd531773a6bf1 schema:familyName Faci
67 schema:givenName Sofiane
68 rdf:type schema:Person
69 N969c42bf098e43449aa281a4fe77830d rdf:first sg:person.015150124647.46
70 rdf:rest N545058fca51a4ca293cf34d2e3f520a8
71 N9c8d27b8440e4950ba72f845bd9b20f6 schema:name dimensions_id
72 schema:value pub.1100290085
73 rdf:type schema:PropertyValue
74 Nb5a4d7e5f94e40ef9d375a3e90ed1702 schema:name Springer Nature - SN SciGraph project
75 rdf:type schema:Organization
76 Nc0067a90090144cba058bf232d0ebfac schema:name doi
77 schema:value 10.1007/978-3-319-69164-0_54
78 rdf:type schema:PropertyValue
79 Nd676e0c819a7468c858d6d7f298676dc schema:familyName Micklitz
80 schema:givenName Tobias
81 rdf:type schema:Person
82 Ndf7c7970e39740dcadfb40ded738772d rdf:first N8fa54352dc5244159b06dab317828bf2
83 rdf:rest rdf:nil
84 Ne57981ef36d9468ca1b1a948e277f792 schema:familyName Duarte
85 schema:givenName Sergio
86 rdf:type schema:Person
87 Nf01ef0326af64feab71fd2b7661eb6e1 schema:isbn 978-3-319-69163-3
88 978-3-319-69164-0
89 schema:name Physical and Mathematical Aspects of Symmetries
90 rdf:type schema:Book
91 Nfa8c7a3c1893488ea8802df8ecc66904 rdf:first sg:person.016620740074.91
92 rdf:rest N969c42bf098e43449aa281a4fe77830d
93 Nfef0a220f3784ad49d6ca4bc61612614 rdf:first Nd676e0c819a7468c858d6d7f298676dc
94 rdf:rest N323a05353d384bc388e990ad12099946
95 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
96 schema:name Mathematical Sciences
97 rdf:type schema:DefinedTerm
98 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
99 schema:name Pure Mathematics
100 rdf:type schema:DefinedTerm
101 sg:person.012726447121.07 schema:affiliation grid-institutes:grid.6268.a
102 schema:familyName Vourdas
103 schema:givenName A.
104 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012726447121.07
105 rdf:type schema:Person
106 sg:person.015150124647.46 schema:affiliation grid-institutes:grid.6268.a
107 schema:familyName Lei
108 schema:givenName C.
109 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015150124647.46
110 rdf:type schema:Person
111 sg:person.016620740074.91 schema:affiliation grid-institutes:grid.6268.a
112 schema:familyName Olupitan
113 schema:givenName T.
114 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016620740074.91
115 rdf:type schema:Person
116 grid-institutes:grid.6268.a schema:alternateName Department of Computing, University of Bradford, BD7 1DP, Bradford, UK
117 schema:name Department of Computing, University of Bradford, BD7 1DP, Bradford, UK
118 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...