On approximation of infinite-dimensional quantum channels View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2008-06

AUTHORS

M. E. Shirokov, A. S. Holevo

ABSTRACT

We develop an approximation approach to infinite-dimensional quantum channels based on a detailed investigation of continuity properties of entropic characteristics of quantum channels and operations (trace-nonincreasing completely positive maps) as functions of a pair “channel, input state.” Obtained results are then applied to the problems of continuity of the χ-capacity as a function of a channel, strong additivity of the χ-capacity for infinite-dimensional channels, and approximating representation for the convex closure of the output entropy of an arbitrary quantum channel. More... »

PAGES

73-90

References to SciGraph publications

  • 2001. Statistical Structure of Quantum Theory in NONE
  • 1993. Quantum Entropy and Its Use in NONE
  • 2006-02. The Holevo Capacity of Infinite Dimensional Channels and the Additivity Problem in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2004-08. On Shor’s Channel Extension and Constrained Channels in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1974-06. Expectations and entropy inequalities for finite quantum systems in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1134/s0032946008020014

    DOI

    http://dx.doi.org/10.1134/s0032946008020014

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1031865090


    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/2008/0206", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Quantum Physics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/02", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Physical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Russian Academy of Sciences", 
              "id": "https://www.grid.ac/institutes/grid.4886.2", 
              "name": [
                "Steklov Mathematical Institute, RAS, Moscow, Russia"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Shirokov", 
            "givenName": "M. E.", 
            "id": "sg:person.014741114345.19", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014741114345.19"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Russian Academy of Sciences", 
              "id": "https://www.grid.ac/institutes/grid.4886.2", 
              "name": [
                "Steklov Mathematical Institute, RAS, Moscow, Russia"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Holevo", 
            "givenName": "A. S.", 
            "id": "sg:person.012742037634.56", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012742037634.56"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf01608390", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1005287470", 
              "https://doi.org/10.1007/bf01608390"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/b978-1-4832-0022-4.50006-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016567795"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1063/1.1498000", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021978041"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physreva.54.3824", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1022782738"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physreva.54.3824", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1022782738"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1088/0305-4470/35/17/307", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1028020343"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-44998-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029169766", 
              "https://doi.org/10.1007/3-540-44998-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/3-540-44998-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029169766", 
              "https://doi.org/10.1007/3-540-44998-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0024-3795(75)90075-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032363448"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-005-1457-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036935783", 
              "https://doi.org/10.1007/s00220-005-1457-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-005-1457-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036935783", 
              "https://doi.org/10.1007/s00220-005-1457-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-004-1116-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046003655", 
              "https://doi.org/10.1007/s00220-004-1116-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physreva.60.1888", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060495416"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physreva.60.1888", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060495416"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physreva.63.022308", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060496888"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physreva.63.022308", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060496888"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/revmodphys.50.221", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060838892"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/revmodphys.50.221", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060838892"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4213/rm1411", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072369538"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4213/tvp151", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072376178"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4213/tvp160", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072376209"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4213/tvp174", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072376246"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4213/tvp289", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072376571"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1109710137", 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-642-57997-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1109710137", 
              "https://doi.org/10.1007/978-3-642-57997-4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-642-57997-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1109710137", 
              "https://doi.org/10.1007/978-3-642-57997-4"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2008-06", 
        "datePublishedReg": "2008-06-01", 
        "description": "We develop an approximation approach to infinite-dimensional quantum channels based on a detailed investigation of continuity properties of entropic characteristics of quantum channels and operations (trace-nonincreasing completely positive maps) as functions of a pair \u201cchannel, input state.\u201d Obtained results are then applied to the problems of continuity of the \u03c7-capacity as a function of a channel, strong additivity of the \u03c7-capacity for infinite-dimensional channels, and approximating representation for the convex closure of the output entropy of an arbitrary quantum channel.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1134/s0032946008020014", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1136386", 
            "issn": [
              "0032-9460", 
              "1608-3253"
            ], 
            "name": "Problems of Information Transmission", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "2", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "44"
          }
        ], 
        "name": "On approximation of infinite-dimensional quantum channels", 
        "pagination": "73-90", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "97cc72c4d1658e536371998bf9d4ab8b5b709da1e9c6b693c9cdcf624bea3fc4"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1134/s0032946008020014"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1031865090"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1134/s0032946008020014", 
          "https://app.dimensions.ai/details/publication/pub.1031865090"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T00:28", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8695_00000589.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1134/S0032946008020014"
      }
    ]
     

    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.10.1134/s0032946008020014'

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

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1134/s0032946008020014'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1134/s0032946008020014'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1134/s0032946008020014'


     

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

    129 TRIPLES      21 PREDICATES      46 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1134/s0032946008020014 schema:about anzsrc-for:02
    2 anzsrc-for:0206
    3 schema:author Ne4ed9c87416e4d539f7c5387fa88dcfe
    4 schema:citation sg:pub.10.1007/3-540-44998-1
    5 sg:pub.10.1007/978-3-642-57997-4
    6 sg:pub.10.1007/bf01608390
    7 sg:pub.10.1007/s00220-004-1116-5
    8 sg:pub.10.1007/s00220-005-1457-8
    9 https://app.dimensions.ai/details/publication/pub.1109710137
    10 https://doi.org/10.1016/0024-3795(75)90075-0
    11 https://doi.org/10.1016/b978-1-4832-0022-4.50006-5
    12 https://doi.org/10.1063/1.1498000
    13 https://doi.org/10.1088/0305-4470/35/17/307
    14 https://doi.org/10.1103/physreva.54.3824
    15 https://doi.org/10.1103/physreva.60.1888
    16 https://doi.org/10.1103/physreva.63.022308
    17 https://doi.org/10.1103/revmodphys.50.221
    18 https://doi.org/10.4213/rm1411
    19 https://doi.org/10.4213/tvp151
    20 https://doi.org/10.4213/tvp160
    21 https://doi.org/10.4213/tvp174
    22 https://doi.org/10.4213/tvp289
    23 schema:datePublished 2008-06
    24 schema:datePublishedReg 2008-06-01
    25 schema:description We develop an approximation approach to infinite-dimensional quantum channels based on a detailed investigation of continuity properties of entropic characteristics of quantum channels and operations (trace-nonincreasing completely positive maps) as functions of a pair “channel, input state.” Obtained results are then applied to the problems of continuity of the χ-capacity as a function of a channel, strong additivity of the χ-capacity for infinite-dimensional channels, and approximating representation for the convex closure of the output entropy of an arbitrary quantum channel.
    26 schema:genre research_article
    27 schema:inLanguage en
    28 schema:isAccessibleForFree false
    29 schema:isPartOf N33270925dbaa4c34a442959899147f6d
    30 N6f996bcbb98a4f8199c84fb0c83142b4
    31 sg:journal.1136386
    32 schema:name On approximation of infinite-dimensional quantum channels
    33 schema:pagination 73-90
    34 schema:productId N04223f1174234f4bb5bccb97eac5c532
    35 N3dbffa25706b457c8974cc94ce79df46
    36 N4f05aa5b4faf40d99a57baa8b2f690ae
    37 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031865090
    38 https://doi.org/10.1134/s0032946008020014
    39 schema:sdDatePublished 2019-04-11T00:28
    40 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    41 schema:sdPublisher N686c9fd6ce6145ca92591e6c20492155
    42 schema:url http://link.springer.com/10.1134/S0032946008020014
    43 sgo:license sg:explorer/license/
    44 sgo:sdDataset articles
    45 rdf:type schema:ScholarlyArticle
    46 N04223f1174234f4bb5bccb97eac5c532 schema:name dimensions_id
    47 schema:value pub.1031865090
    48 rdf:type schema:PropertyValue
    49 N0af49c611d1e459085debc356e5740a2 rdf:first sg:person.012742037634.56
    50 rdf:rest rdf:nil
    51 N33270925dbaa4c34a442959899147f6d schema:volumeNumber 44
    52 rdf:type schema:PublicationVolume
    53 N3dbffa25706b457c8974cc94ce79df46 schema:name readcube_id
    54 schema:value 97cc72c4d1658e536371998bf9d4ab8b5b709da1e9c6b693c9cdcf624bea3fc4
    55 rdf:type schema:PropertyValue
    56 N4f05aa5b4faf40d99a57baa8b2f690ae schema:name doi
    57 schema:value 10.1134/s0032946008020014
    58 rdf:type schema:PropertyValue
    59 N686c9fd6ce6145ca92591e6c20492155 schema:name Springer Nature - SN SciGraph project
    60 rdf:type schema:Organization
    61 N6f996bcbb98a4f8199c84fb0c83142b4 schema:issueNumber 2
    62 rdf:type schema:PublicationIssue
    63 Ne4ed9c87416e4d539f7c5387fa88dcfe rdf:first sg:person.014741114345.19
    64 rdf:rest N0af49c611d1e459085debc356e5740a2
    65 anzsrc-for:02 schema:inDefinedTermSet anzsrc-for:
    66 schema:name Physical Sciences
    67 rdf:type schema:DefinedTerm
    68 anzsrc-for:0206 schema:inDefinedTermSet anzsrc-for:
    69 schema:name Quantum Physics
    70 rdf:type schema:DefinedTerm
    71 sg:journal.1136386 schema:issn 0032-9460
    72 1608-3253
    73 schema:name Problems of Information Transmission
    74 rdf:type schema:Periodical
    75 sg:person.012742037634.56 schema:affiliation https://www.grid.ac/institutes/grid.4886.2
    76 schema:familyName Holevo
    77 schema:givenName A. S.
    78 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012742037634.56
    79 rdf:type schema:Person
    80 sg:person.014741114345.19 schema:affiliation https://www.grid.ac/institutes/grid.4886.2
    81 schema:familyName Shirokov
    82 schema:givenName M. E.
    83 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014741114345.19
    84 rdf:type schema:Person
    85 sg:pub.10.1007/3-540-44998-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029169766
    86 https://doi.org/10.1007/3-540-44998-1
    87 rdf:type schema:CreativeWork
    88 sg:pub.10.1007/978-3-642-57997-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1109710137
    89 https://doi.org/10.1007/978-3-642-57997-4
    90 rdf:type schema:CreativeWork
    91 sg:pub.10.1007/bf01608390 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005287470
    92 https://doi.org/10.1007/bf01608390
    93 rdf:type schema:CreativeWork
    94 sg:pub.10.1007/s00220-004-1116-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046003655
    95 https://doi.org/10.1007/s00220-004-1116-5
    96 rdf:type schema:CreativeWork
    97 sg:pub.10.1007/s00220-005-1457-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036935783
    98 https://doi.org/10.1007/s00220-005-1457-8
    99 rdf:type schema:CreativeWork
    100 https://app.dimensions.ai/details/publication/pub.1109710137 schema:CreativeWork
    101 https://doi.org/10.1016/0024-3795(75)90075-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032363448
    102 rdf:type schema:CreativeWork
    103 https://doi.org/10.1016/b978-1-4832-0022-4.50006-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016567795
    104 rdf:type schema:CreativeWork
    105 https://doi.org/10.1063/1.1498000 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021978041
    106 rdf:type schema:CreativeWork
    107 https://doi.org/10.1088/0305-4470/35/17/307 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028020343
    108 rdf:type schema:CreativeWork
    109 https://doi.org/10.1103/physreva.54.3824 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022782738
    110 rdf:type schema:CreativeWork
    111 https://doi.org/10.1103/physreva.60.1888 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060495416
    112 rdf:type schema:CreativeWork
    113 https://doi.org/10.1103/physreva.63.022308 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060496888
    114 rdf:type schema:CreativeWork
    115 https://doi.org/10.1103/revmodphys.50.221 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060838892
    116 rdf:type schema:CreativeWork
    117 https://doi.org/10.4213/rm1411 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072369538
    118 rdf:type schema:CreativeWork
    119 https://doi.org/10.4213/tvp151 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072376178
    120 rdf:type schema:CreativeWork
    121 https://doi.org/10.4213/tvp160 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072376209
    122 rdf:type schema:CreativeWork
    123 https://doi.org/10.4213/tvp174 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072376246
    124 rdf:type schema:CreativeWork
    125 https://doi.org/10.4213/tvp289 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072376571
    126 rdf:type schema:CreativeWork
    127 https://www.grid.ac/institutes/grid.4886.2 schema:alternateName Russian Academy of Sciences
    128 schema:name Steklov Mathematical Institute, RAS, Moscow, Russia
    129 rdf:type schema:Organization
     




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


    ...