{"id":1377,"date":"2026-10-25T18:00:00","date_gmt":"2026-10-25T09:00:00","guid":{"rendered":"https:\/\/quantumsea.net\/?p=1377"},"modified":"2026-10-23T06:12:44","modified_gmt":"2026-10-22T21:12:44","slug":"qs-holevo-ensemble-label-information-20261023","status":"publish","type":"post","link":"https:\/\/quantumsea.net\/?p=1377","title":{"rendered":"Holevo\u91cf\u3001\u5e73\u5747\u72b6\u614b\u304c\u540c\u3058\u3067\u3082\u53d6\u308a\u51fa\u305b\u308b\u60c5\u5831\u306e\u4e0a\u9650\u304c\u9055\u3046\u7406\u7531"},"content":{"rendered":"<p>\u540c\u3058\u5bc6\u5ea6\u884c\u5217\u3092\u6301\u3064\u91cf\u5b50\u30d3\u30c3\u30c8\u3092\u53d7\u3051\u53d6\u3063\u3066\u3082\u3001\u9001\u308a\u624b\u304c\u9078\u3093\u3060\u30e1\u30c3\u30bb\u30fc\u30b8\u306b\u3064\u3044\u3066\u5f97\u3089\u308c\u308b\u60c5\u5831\u304c\u540c\u3058\u3068\u306f\u9650\u308a\u307e\u305b\u3093\u3002\u9055\u3044\u306f\u3001\u5e73\u5747\u3057\u305f\u72b6\u614b\u306e\u5965\u306b\u3001\u3069\u306e\u30e1\u30c3\u30bb\u30fc\u30b8\u3068\u3069\u306e\u72b6\u614b\u3092\u7d50\u3073\u4ed8\u3051\u305f\u304b\u3068\u3044\u3046\u6e96\u5099\u306e\u898f\u5247\u304c\u3042\u308b\u3053\u3068\u3067\u3059\u3002Holevo\u91cf\uff08\u30db\u30ec\u30dc\u91cf\uff09\u306f\u3001\u305d\u306e\u898f\u5247\u3068\u6e2c\u5b9a\u304b\u3089\u5f97\u3089\u308c\u308b\u60c5\u5831\u306e\u95a2\u4fc2\u3092\u6574\u7406\u3057\u307e\u3059\u3002<\/p>\n<section 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bit\u306b\u5206\u304b\u308c\u307e\u3059\u3002<\/li>\n<li>\u03c7\u306f\u6e2c\u5b9a\u3067\u5f97\u3089\u308c\u308b\u53e4\u5178\u7684\u306a\u76f8\u4e92\u60c5\u5831\u91cf\u306e\u4e0a\u9650\u3067\u3059\u3002\u3044\u3064\u3082\u4e00\u5ea6\u306e\u6e2c\u5b9a\u3067\u305d\u306e\u5024\u307e\u3067\u8aad\u307f\u53d6\u308c\u308b\u3068\u3044\u3046\u4fdd\u8a3c\u3067\u306f\u306a\u304f\u3001\u5171\u6709\u6e08\u307f\u306e\u3082\u3064\u308c\u306a\u3069\u306e\u6761\u4ef6\u3082\u5206\u3051\u3066\u6271\u3044\u307e\u3059\u3002<\/li>\n<\/ul>\n<\/section>\n<h2>\u72b6\u614b\u3092\u5e73\u5747\u3059\u308b\u524d\u306b\u3001\u30e1\u30c3\u30bb\u30fc\u30b8\u3068\u306e\u5bfe\u5fdc\u3092\u6b8b\u3059<\/h2>\n<p>\u9001\u308a\u624b\u304c\u53e4\u5178\u7684\u306a\u30e9\u30d9\u30ebX\u3092\u78ba\u7387p(x)\u3067\u9078\u3073\u3001\u305d\u306e\u30e9\u30d9\u30eb\u306b\u5bfe\u5fdc\u3059\u308b\u91cf\u5b50\u72b6\u614b\u03c1<sub>x<\/sub>\u3092\u6e96\u5099\u3059\u308b\u3068\u3057\u307e\u3059\u3002\u53d7\u3051\u624b\u306f\u6e96\u5099\u898f\u5247\u3092\u77e5\u3063\u3066\u3044\u307e\u3059\u304c\u3001\u4eca\u56de\u3069\u306ex\u304c\u9078\u3070\u308c\u305f\u304b\u306f\u77e5\u308a\u307e\u305b\u3093\u3002\u78ba\u7387\u3068\u72b6\u614b\u3092\u7d44\u306b\u3057\u305f\u96c6\u5408\u3092\u3001\u3053\u3053\u3067\u306f\u30a2\u30f3\u30b5\u30f3\u30d6\u30eb\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\n<p>\u30e9\u30d9\u30eb\u3092\u77e5\u3089\u305a\u306b\u72b6\u614b\u3060\u3051\u3092\u898b\u308b\u3068\u3001\u5e73\u5747\u306e\u5bc6\u5ea6\u884c\u5217\u306f\u03c1\u0304=\u03a3<sub>x<\/sub>p(x)\u03c1<sub>x<\/sub>\u3067\u3059\u3002\u53d7\u3051\u624b\u304c\u884c\u3046\u6e2c\u5b9a\u306e\u7d50\u679c\u3092Y\u3068\u3059\u308b\u3068\u3001\u6e2c\u5b9a\u306e\u8981\u7d20E<sub>y<\/sub>\u3092\u4f7f\u3063\u3066\u3001\u30e9\u30d9\u30ebx\u306e\u3068\u304d\u306b\u7d50\u679cy\u304c\u51fa\u308b\u78ba\u7387\u306fp(y|x)=tr(E<sub>y<\/sub>\u03c1<sub>x<\/sub>)\u3068\u66f8\u3051\u307e\u3059\u3002E<sub>y<\/sub>\u306f\u6b63\u3067\u3001\u3059\u3079\u3066\u306e\u7d50\u679c\u306b\u3064\u3044\u3066\u8db3\u3059\u3068\u5358\u4f4d\u884c\u5217\u306b\u306a\u308b\u3001\u4e00\u822c\u5316\u3055\u308c\u305f\u6e2c\u5b9a\u306e\u8868\u3057\u65b9\u3067\u3059\u3002[1\u3001\u00a710.6.1]<\/p>\n<p>\u6e2c\u5b9a\u7d50\u679c\u306e\u3070\u3089\u3064\u304dH(Y)\u305d\u306e\u3082\u306e\u304c\u3001\u30e1\u30c3\u30bb\u30fc\u30b8\u3092\u77e5\u3063\u305f\u91cf\u306b\u306a\u308b\u308f\u3051\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u30e9\u30d9\u30eb\u3068\u7121\u95a2\u4fc2\u306a\u4e71\u6570\u304c\u305f\u304f\u3055\u3093\u51fa\u3066\u3082\u3001X\u3092\u63a8\u6e2c\u3059\u308b\u52a9\u3051\u306b\u306f\u306a\u3089\u306a\u3044\u304b\u3089\u3067\u3059\u3002\u4e21\u8005\u306e\u7d50\u3073\u4ed8\u304d\u3092\u8868\u3059<strong>\u76f8\u4e92\u60c5\u5831\u91cfI(X;Y)<\/strong>\u3092\u4f7f\u3044\u307e\u3059\u3002\u53e4\u5178\u7684\u306a\u96e2\u6563\u5909\u6570\u3067\u306fH(X)\u2212H(X|Y)\u3068\u66f8\u3051\u3001\u7d50\u679cY\u3092\u77e5\u308b\u3053\u3068\u3067X\u306e\u4e0d\u78ba\u304b\u3055\u304c\u3069\u308c\u3060\u3051\u6e1b\u308b\u304b\u3092\u8868\u3057\u307e\u3059\u3002<\/p>\n<h2>\u5e73\u5747\u306e\u4e0d\u78ba\u304b\u3055\u304b\u3089\u3001\u5404\u4fe1\u53f7\u306e\u5185\u5074\u306e\u4e0d\u78ba\u304b\u3055\u3092\u5f15\u304f<\/h2>\n<p>\u6709\u9650\u6b21\u5143\u306e\u72b6\u614b\u03c1\u306b\u5bfe\u3057\u3001\u30d5\u30a9\u30f3\u30fb\u30ce\u30a4\u30de\u30f3\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u306fS(\u03c1)=\u2212\u03a3\u03bb log\u2082\u03bb\u3067\u3059\u3002\u03bb\u306f\u5bc6\u5ea6\u884c\u5217\u306e\u56fa\u6709\u5024\u3067\u30010 log\u20820\u306f0\u3068\u3057\u307e\u3059\u3002\u5e95\u30922\u306b\u305d\u308d\u3048\u308b\u306e\u3067\u5358\u4f4d\u306fbit\u3067\u3059\u3002\u672c\u7a3f\u306eS\u306f\u539f\u8cc7\u6599\u304cH\u3068\u66f8\u3044\u3066\u3044\u308b\u91cf\u5b50\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002<\/p>\n<p>Holevo\u91cf\u306f<strong>\u03c7=S(\u03c1\u0304)\u2212\u03a3<sub>x<\/sub>p(x)S(\u03c1<sub>x<\/sub>)<\/strong>\u3068\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002[1\u3001\u5f0f10.214] 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information\u3001\u53d6\u308a\u51fa\u305b\u308b\u60c5\u5831\u3068\u547c\u3076\u3068\u3001\u305d\u306e\u5024\u3082\u03c7\u4ee5\u4e0b\u3067\u3059\u3002[1\u3001\u5f0f10.205\u300110.211] 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bit\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u3053\u306e\u5834\u5408\u30010\u30681\u3092\u533a\u5225\u3059\u308bZ\u57fa\u5e95\u306e\u6e2c\u5b9a\u3092\u9078\u3079\u3070\u3001\u30e9\u30d9\u30eb\u3068\u7d50\u679c\u306f\u5fc5\u305a\u4e00\u81f4\u3057\u307e\u3059\u3002H(X)=1\u3001\u7d50\u679c\u3092\u77e5\u3063\u305f\u5f8c\u306eH(X|Y)=0\u306a\u306e\u3067\u3001I(X;Y)=1 bit\u3067\u3059\u3002\u3053\u306e\u5177\u4f53\u4f8b\u3067\u306f\u4e0a\u9650\u3092\u9054\u6210\u3067\u304d\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u6e2c\u5b9a\u3059\u308b\u524d\u306bX\u57fa\u5e95\u3078\u8aad\u307f\u65b9\u3092\u5909\u3048\u308b\u3068\u3001\u3069\u3061\u3089\u306e\u30e9\u30d9\u30eb\u3067\u3082+\u3068\u2212\u304c\u534a\u3005\u306b\u51fa\u307e\u3059\u3002\u305d\u306e\u6e2c\u5b9a\u306eI(X;Y)\u306f0\u3067\u3059\u3002\u03c7\u304c1\u3067\u3082\u3001\u4efb\u610f\u306e\u6e2c\u308a\u65b9\u304c1 bit\u3092\u53d6\u308a\u51fa\u305b\u308b\u308f\u3051\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<p>\u6b21\u306e\u6e96\u5099B\u3067\u306f\u3001\u30e9\u30d9\u30eb\u304c0\u3067\u30821\u3067\u3082\u3001\u307e\u3063\u305f\u304f\u540c\u3058I\/2\u3092\u9001\u308a\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u30e9\u30d9\u30eb\u3068\u306f\u72ec\u7acb\u306a\u5225\u306e\u4e71\u6570\u3067|0\u27e9\u304b|1\u27e9\u3092\u534a\u3005\u306b\u7528\u610f\u3057\u3001\u305d\u306e\u4e71\u6570\u306e\u8a18\u9332\u3082\u53d7\u3051\u624b\u3078\u6e21\u3055\u306a\u3044\u6e96\u5099\u3067\u3059\u3002\u5e73\u5747\u72b6\u614b\u306f\u3084\u306f\u308aI\/2\u3067\u3059\u304c\u3001\u5404\u30e9\u30d9\u30eb\u306e\u72b6\u614b\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u30821\u306a\u306e\u3067\u3001\u03c7=1\u22121=0 bit\u3067\u3059\u3002<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/quantumsea.net\/wp-content\/uploads\/2026\/10\/qs-holevo-ensemble-label-information-20261023-figure-dbdb33ec5755.png\" alt=\"\u3069\u3061\u3089\u306e\u5e73\u5747\u72b6\u614b\u3082I\/2\u3002\u6e96\u5099A\u306f\u30e9\u30d9\u30eb\u3054\u3068\u306b\u76f4\u4ea4\u3059\u308b\u7d14\u7c8b\u72b6\u614b\u3067\u5404\u4fe1\u53f7\u306e\u5e73\u5747\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc0\u3001Holevo\u91cf1 bit\u3002\u6e96\u5099B\u306f\u30e9\u30d9\u30eb\u306b\u3088\u3089\u305aI\/2\u3067\u5404\u4fe1\u53f7\u306e\u5e73\u5747\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc1\u3001Holevo\u91cf0 bit\u3002\" 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6a\u306e\u3067\u3001\u672c\u7a3f\u306e\u5358\u72ec\u4fe1\u53f7\u306e\u6bd4\u8f03\u3068\u6df7\u540c\u3057\u307e\u305b\u3093\u3002<\/p>\n<p>\u307e\u305f\u3001\u9577\u3044\u7b26\u53f7\u5217\u3092\u307e\u3068\u3081\u3066\u9001\u3063\u3066\u6e2c\u308b\u901a\u4fe1\u306e\u5230\u9054\u7387\u3084\u3001\u96d1\u97f3\u3092\u542b\u3080\u5b9f\u88c5\u306e\u901f\u5ea6\u306f\u3001\u3053\u3053\u3067\u306e\u4e8c\u3064\u306e\u7406\u60f3\u884c\u5217\u304b\u3089\u306f\u6c7a\u307e\u308a\u307e\u305b\u3093\u3002Holevo\u91cf\u306f\u6e2c\u5b9a\u306e\u53ef\u80fd\u6027\u3092\u8003\u3048\u308b\u5927\u5207\u306a\u4e0a\u9650\u3067\u3059\u304c\u3001\u88c5\u7f6e\u306e\u6e2c\u5b9a\u7cbe\u5ea6\u3001\u7b26\u53f7\u5316\u3001\u5fc5\u8981\u306a\u8a66\u6599\u6570\u3084\u6642\u9593\u3092\u7701\u3044\u3066\u6027\u80fd\u4fdd\u8a3c\u3078\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002<\/p>\n<h2>\u51fa\u5178<\/h2>\n<ol>\n<li>John Preskill, <a href=\"https:\/\/www.preskill.caltech.edu\/ph219\/chap10_6A_2025.pdf\">Quantum Information, Chapter 10: Quantum Shannon Theory<\/a>\uff082025\u5e746\u6708\u6539\u8a02\u306e\u8b1b\u7fa9\u8349\u7a3f\uff09\u3002\u00a710.6.1\u201310.6.2\u3001\u672c\u658740\u201342\u9801\u3001\u5f0f10.204\u201310.205\u300110.211\u201310.214\u30022026\u5e7410\u670823\u65e5\u306b\u516c\u5f0f\u63b2\u8f09\u7248\u3092\u78ba\u8a8d\u3002\u4e8c\u3064\u306e\u30a2\u30f3\u30b5\u30f3\u30d6\u30eb\u3001\u6e2c\u5b9a\u306e\u6bd4\u8f03\u3001\u6570\u5024\u7167\u5408\u3068\u56f3\u8868\u306f\u72ec\u81ea\u4f5c\u6210\u3002<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u540c\u3058\u5bc6\u5ea6\u884c\u5217\u3092\u6301\u3064\u91cf\u5b50\u30d3\u30c3\u30c8\u3092\u53d7\u3051\u53d6\u3063\u3066\u3082\u3001\u9001\u308a\u624b\u304c\u9078\u3093\u3060\u30e1\u30c3\u30bb\u30fc\u30b8\u306b\u3064\u3044\u3066\u5f97\u3089\u308c\u308b\u60c5\u5831\u304c\u540c\u3058\u3068\u306f\u9650\u308a\u307e\u305b\u3093\u3002\u9055\u3044\u306f\u3001\u5e73\u5747\u3057\u305f\u72b6\u614b\u306e\u5965\u306b\u3001\u3069\u306e\u30e1\u30c3\u30bb\u30fc\u30b8\u3068\u3069\u306e\u72b6\u614b\u3092\u7d50\u3073\u4ed8\u3051\u305f\u304b\u3068\u3044\u3046\u6e96\u5099\u306e\u898f\u5247\u304c\u3042\u308b\u3053\u3068\u3067\u3059\u3002Holevo [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":1375,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":true,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":false,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[30],"tags":[184],"class_list":["post-1377","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-computing","tag-quantum-computers"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/quantumsea.net\/wp-content\/uploads\/2026\/10\/qs-holevo-ensemble-label-information-20261023-featured-a8c219a0df71.png","_links":{"self":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts\/1377","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1377"}],"version-history":[{"count":1,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts\/1377\/revisions"}],"predecessor-version":[{"id":1378,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts\/1377\/revisions\/1378"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/media\/1375"}],"wp:attachment":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1377"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1377"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1377"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}