{"id":1305,"date":"2026-10-25T00:00:00","date_gmt":"2026-10-24T15:00:00","guid":{"rendered":"https:\/\/quantumsea.net\/?p=1305"},"modified":"2026-10-23T02:33:58","modified_gmt":"2026-10-22T17:33:58","slug":"qs-schmidt-coefficients-basis-invariant-20261023","status":"publish","type":"post","link":"https:\/\/quantumsea.net\/?p=1305","title":{"rendered":"Schmidt\u5206\u89e3\u3001\u5f0f\u306e\u9805\u6570\u306b\u60d1\u308f\u3055\u308c\u305a\u91cf\u5b50\u72b6\u614b\u306e\u91cd\u307f\u3092\u8aad\u3080"},"content":{"rendered":"<p>\u4e8c\u3064\u306e\u91cf\u5b50\u7cfb\u3092\u5408\u308f\u305b\u305f\u72b6\u614b\u3092\u66f8\u304d\u4e0b\u3059\u3068\u3001\u3044\u304f\u3064\u3082\u306e\u9805\u304c\u73fe\u308c\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u5f0f\u306b\u9805\u304c\u591a\u3044\u3053\u3068\u3068\u3001\u4e8c\u3064\u306e\u7cfb\u306e\u9593\u306b\u3082\u3064\u308c\u304c\u3042\u308b\u3053\u3068\u306f\u540c\u3058\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u5404\u7cfb\u306e\u57fa\u5e95\u3001\u3064\u307e\u308a\u72b6\u614b\u3092\u8868\u3059\u3082\u306e\u3055\u3057\u3092\u9078\u3073\u76f4\u3059\u3060\u3051\u3067\u3001\u898b\u304b\u3051\u306e\u9805\u6570\u306f\u5909\u308f\u308a\u307e\u3059\u3002<\/p>\n<p><strong>Schmidt\u5206\u89e3\uff08\u30b7\u30e5\u30df\u30c3\u30c8\u5206\u89e3\uff09<\/strong>\u306f\u3001\u4e8c\u4f53\u7cfb\u306e\u7d14\u7c8b\u72b6\u614b\u3092\u3001\u5bfe\u5fdc\u3059\u308b\u57fa\u5e95\u306e\u7d44\u3068\u975e\u8ca0\u306e\u4fc2\u6570\u3067\u6574\u7406\u3059\u308b\u65b9\u6cd5\u3067\u3059\u3002\u4fc2\u6570\u3092\u4e8c\u4e57\u3057\u305f\u91cd\u307f\u3092\u898b\u308b\u3068\u3001\u57fa\u5e95\u306e\u898b\u304b\u3051\u306b\u5de6\u53f3\u3055\u308c\u305a\u306b\u6bd4\u8f03\u3067\u304d\u308b\u60c5\u5831\u304c\u6b8b\u308a\u307e\u3059\u3002\u3053\u3053\u3067\u306f\u4e8c\u3064\u306e\u91cf\u5b50\u30d3\u30c3\u30c8A\u3001B\u3092\u4f8b\u306b\u3001\u4fc2\u6570\u884c\u5217\u3092\u4f5c\u308b\u3068\u3053\u308d\u304b\u3089\u3001\u4fc2\u6570\u30fb\u91cd\u307f\u30fb\u30e9\u30f3\u30af\u306e\u9055\u3044\u307e\u3067\u3092\u8ffd\u3044\u307e\u3059\u3002<\/p>\n<section class=\"influvetor-quick-summary\">\n<p><strong>\u7c21\u5358\u306b\u307e\u3068\u3081\u308b\u3068\uff1f<\/strong><\/p>\n<ul>\n<li>Schmidt\u5206\u89e3\u3067\u306f\u3001\u4e8c\u4f53\u7cfb\u306e\u7d14\u7c8b\u72b6\u614b\u3092\u3001A\u5074\u3068B\u5074\u306e\u76f4\u4ea4\u3059\u308b\u57fa\u5e95\u306e\u7d44\u3078\u6574\u7406\u3057\u307e\u3059\u3002\u5143\u306e\u5f0f\u306b\u3042\u308b\u9805\u306e\u6570\u3092\u6570\u3048\u308b\u65b9\u6cd5\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/li>\n<li>\u975e\u8ca0\u306eSchmidt\u4fc2\u6570\u3092\u4e8c\u4e57\u3057\u305f\u5024\u304c\u3001\u7247\u65b9\u3060\u3051\u306e\u72b6\u614b\u306e\u56fa\u6709\u5024\u306b\u306a\u308a\u307e\u3059\u3002\u4fc2\u6570\u305d\u306e\u3082\u306e\u3092\u78ba\u7387\u3068\u3057\u3066\u8db3\u3059\u306e\u306f\u8aa4\u308a\u3067\u3059\u3002<\/li>\n<li>\u975e\u30bc\u30ed\u4fc2\u6570\u306e\u6570\u304cSchmidt\u30e9\u30f3\u30af\u3067\u3059\u3002\u7d14\u7c8b\u72b6\u614b\u306a\u3089\u30e9\u30f3\u30af1\u306f\u7a4d\u72b6\u614b\u30012\u4ee5\u4e0a\u306f\u3082\u3064\u308c\u305f\u72b6\u614b\u3067\u3059\u304c\u3001\u540c\u3058\u30e9\u30f3\u30af\u3067\u3082\u91cd\u307f\u306e\u504f\u308a\u306f\u7570\u306a\u308a\u307e\u3059\u3002<\/li>\n<\/ul>\n<\/section>\n<h2>\u56db\u3064\u306e\u632f\u5e45\u3092\u30012\u884c2\u5217\u3078\u4e26\u3079\u308b<\/h2>\n<p>\u4e8c\u3064\u306e\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u7d14\u7c8b\u72b6\u614b\u3092\u3001A\u3001B\u306e\u9806\u3067 <code>|\u03c8\u3009\uff1dc00|00\u3009\uff0bc01|01\u3009\uff0bc10|10\u3009\uff0bc11|11\u3009<\/code> \u3068\u8868\u3057\u307e\u3059\u3002\u5404c\u306f\u632f\u5e45\u3067\u3001\u4e00\u822c\u306b\u306f\u8907\u7d20\u6570\u3067\u3059\u3002\u72b6\u614b\u3092\u898f\u683c\u5316\u3057\u3066\u3044\u308b\u306a\u3089\u3001\u56db\u3064\u306e\u632f\u5e45\u306e\u7d76\u5bfe\u5024\u306e\u4e8c\u4e57\u3092\u8db3\u3059\u30681\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u3053\u306e\u56db\u3064\u3092\u3001A\u306e\u5024\u3092\u884c\u3001B\u306e\u5024\u3092\u5217\u3068\u3057\u3066\u4e26\u3079\u305f\u3082\u306e\u304c\u4fc2\u6570\u884c\u5217C\u3067\u3059\u3002\u6700\u521d\u306e\u884c\u306bc00\u3068c01\u3001\u6b21\u306e\u884c\u306bc10\u3068c11\u3092\u7f6e\u304d\u307e\u3059\u3002\u3053\u308c\u306f\u5168\u4f53\u306e\u5bc6\u5ea6\u884c\u5217\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u4e8c\u91cf\u5b50\u30d3\u30c3\u30c8\u5168\u4f53\u306e\u5bc6\u5ea6\u884c\u5217\u306f4\u884c4\u5217\u3067\u3059\u304c\u3001\u3053\u3053\u3067\u4f7f\u3046\u8868\u306f\u72b6\u614b\u30d9\u30af\u30c8\u30eb\u306e\u56db\u3064\u306e\u6210\u5206\u3092\u4e26\u3079\u76f4\u3057\u305f2\u884c2\u5217\u3067\u3059\u3002<\/p>\n<p>C\u306b\u7279\u7570\u5024\u5206\u89e3\u3001\u7565\u3057\u3066SVD\u3092\u884c\u3046\u3068\u3001\u975e\u8ca0\u306e\u7279\u7570\u5024s\u3068\u3001\u5de6\u53f3\u306e\u57fa\u5e95\u3092\u53d6\u308a\u51fa\u305b\u307e\u3059\u3002\u3053\u306es\u304cSchmidt\u4fc2\u6570\u3067\u3059\u3002\u5bfe\u5fdc\u3059\u308bA\u306e\u57fa\u5e95\u3092a\u3001B\u306e\u57fa\u5e95\u3092b\u3068\u3059\u308b\u3068\u3001\u72b6\u614b\u306f <code>|\u03c8\u3009\uff1d\u03a3 s_k |a_k\u3009\u2297|b_k\u3009<\/code> \u3068\u3044\u3046\u5f62\u306b\u306a\u308a\u307e\u3059\u3002A\u5074\u3082B\u5074\u3082\u3001\u540c\u3058\u5074\u306e\u57fa\u5e95\u540c\u58eb\u306f\u76f4\u4ea4\u3057\u3001\u9577\u3055\u306f1\u3067\u3059\u3002<\/p>\n<p>\u8907\u7d20\u6570\u3092\u6271\u3046\u5b9f\u88c5\u3067\u306f\u3001\u53f3\u5074\u306e\u30d9\u30af\u30c8\u30eb\u306e\u5171\u5f79\u306b\u3082\u6ce8\u610f\u3057\u307e\u3059\u3002\u901a\u5e38\u306eSVD\u3092C\uff1dU\u03a3V\u2020\u3068\u66f8\u304f\u7d04\u675f\u306a\u3089\u3001\u3053\u306e\u4fc2\u6570\u306e\u4e26\u3079\u65b9\u3067B\u5074\u306b\u4f7f\u3046\u306e\u306fV\u306e\u5217\u3092\u8907\u7d20\u5171\u5f79\u3057\u305f\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2\u304c\u8fd4\u3059\u3082\u306e\u304cV\u306a\u306e\u304bV\u2020\u306a\u306e\u304b\u3082\u78ba\u8a8d\u3057\u307e\u3059\u3002\u5b9f\u6570\u3060\u3051\u306e\u4f8b\u3067\u554f\u984c\u304c\u898b\u3048\u306a\u304f\u3066\u3082\u3001\u8907\u7d20\u6570\u306e\u72b6\u614b\u3078\u305d\u306e\u307e\u307e\u6301\u3061\u8fbc\u3081\u308b\u3068\u306f\u9650\u308a\u307e\u305b\u3093\u3002<\/p>\n<h2>\u5f0f\u306e\u9805\u6570\u3068\u3001Schmidt\u30e9\u30f3\u30af\u306f\u9055\u3046<\/h2>\n<p>\u307e\u305a <code>|+\u3009\u2297|+\u3009<\/code> \u3092\u8003\u3048\u307e\u3059\u3002|+\u3009\u306f(|0\u3009\uff0b|1\u3009)\/\u221a2\u3067\u3059\u304b\u3089\u3001\u5c55\u958b\u3059\u308b\u306800\u300101\u300110\u300111\u306e\u56db\u9805\u304c\u5168\u3066\u73fe\u308c\u3001\u632f\u5e45\u306f\u5168\u30661\/2\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u308c\u3067\u3082\u3001\u6700\u521d\u304b\u3089A\u306e\u72b6\u614b\u3068B\u306e\u72b6\u614b\u306e\u7a4d\u306b\u306a\u3063\u3066\u304a\u308a\u3001\u3082\u3064\u308c\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<p>\u4fc2\u6570\u884c\u5217\u306f\u3001\u5168\u6210\u5206\u304c1\/2\u306e\u8868\u3067\u3059\u3002SVD\u3067\u5f97\u3089\u308c\u308b\u975e\u30bc\u30ed\u306e\u7279\u7570\u5024\u306f1\u3060\u3051\u3067\u3001\u3082\u3046\u4e00\u3064\u306f0\u3067\u3059\u3002\u975e\u30bc\u30ed\u306eSchmidt\u4fc2\u6570\u306e\u6570\u3092Schmidt\u30e9\u30f3\u30af\u3068\u547c\u3076\u306e\u3067\u3001\u3053\u306e\u72b6\u614b\u306e\u30e9\u30f3\u30af\u306f1\u3067\u3059\u3002\u300c\u56db\u9805\u3042\u308b\u304b\u3089\u3082\u3064\u308c\u3066\u3044\u308b\u300d\u3068\u3044\u3046\u5224\u65ad\u304c\u3067\u304d\u306a\u3044\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002<\/p>\n<p>\u6b21\u306b <code>\u221a0.8|00\u3009\uff0b\u221a0.2|11\u3009<\/code> \u3092\u8003\u3048\u307e\u3059\u3002\u4fc2\u6570\u884c\u5217\u306f\u5bfe\u89d2\u6210\u5206\u304c\u221a0.8\u3001\u221a0.2\u3067\u3001\u975e\u5bfe\u89d2\u6210\u5206\u306f0\u3067\u3059\u3002\u4e8c\u3064\u306eSchmidt\u4fc2\u6570\u304c\u3069\u3061\u3089\u3082\u975e\u30bc\u30ed\u306a\u306e\u3067\u3001\u30e9\u30f3\u30af\u306f2\u3067\u3059\u3002\u3053\u306e\u7d14\u7c8b\u72b6\u614b\u306f\u3001\u4e00\u3064\u306eA\u306e\u72b6\u614b\u3068\u4e00\u3064\u306eB\u306e\u72b6\u614b\u306e\u7a4d\u306b\u306f\u307e\u3068\u3081\u3089\u308c\u307e\u305b\u3093\u3002<\/p>\n<h2>\u4fc2\u6570\u3092\u4e8c\u4e57\u3057\u3066\u3001\u6bd4\u8f03\u3059\u308b\u91cd\u307f\u3078<\/h2>\n<p>\u898f\u683c\u5316\u3055\u308c\u305f\u72b6\u614b\u3067\u306f\u3001Schmidt\u4fc2\u6570\u306e\u4e8c\u4e57\u3092\u5168\u3066\u8db3\u3059\u30681\u3067\u3059\u3002\u5148\u307b\u3069\u306e\u4f8b\u306a\u3089\u4fc2\u6570\u306f\u7d040.8944\u30680.4472\u3067\u3059\u304c\u3001\u91cd\u307f\u306f0.8\u30680.2\u306b\u306a\u308a\u307e\u3059\u3002\u4fc2\u6570\u306e\u548c\u306f1\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u8a08\u7b97\u7d50\u679c\u3092\u78ba\u7387\u3068\u3057\u3066\u8aad\u3080\u3068\u304d\u306f\u3001\u3069\u3061\u3089\u3092\u8868\u793a\u3057\u3066\u3044\u308b\u306e\u304b\u3092\u533a\u5225\u3057\u307e\u3059\u3002<\/p>\n<p>A\u3060\u3051\u306e\u72b6\u614b\u3092\u4f5c\u308b\u305f\u3081\u306bB\u3092\u90e8\u5206\u30c8\u30ec\u30fc\u30b9\u3059\u308b\u3068\u3001B\u5074\u306e\u57fa\u5e95\u304c\u76f4\u4ea4\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u7570\u306a\u308b\u756a\u53f7\u3092\u7d50\u3076\u9805\u304c\u6d88\u3048\u307e\u3059\u3002\u6b8b\u308b\u306e\u306f\u3001A\u5074\u306e\u5404\u57fa\u5e95\u306e\u72b6\u614b\u3078s_k\u00b2\u306e\u91cd\u307f\u3092\u4ed8\u3051\u305f\u548c\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001A\u3060\u3051\u306e\u5bc6\u5ea6\u884c\u5217\u306e\u975e\u30bc\u30ed\u56fa\u6709\u5024\u306fs_k\u00b2\u306b\u306a\u308a\u307e\u3059\u3002B\u3060\u3051\u3092\u6b8b\u3057\u305f\u5834\u5408\u306b\u3082\u540c\u3058\u975e\u30bc\u30ed\u56fa\u6709\u5024\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u4e8c\u3064\u306e\u7cfb\u306e\u6b21\u5143\u304c\u7570\u306a\u308b\u5834\u5408\u3001\u4f59\u5206\u306a\u30bc\u30ed\u56fa\u6709\u5024\u306e\u6570\u307e\u3067\u540c\u3058\u3068\u306f\u9650\u308a\u307e\u305b\u3093\u3002<\/p>\n<figure><a href=\"https:\/\/quantumsea.net\/wp-content\/uploads\/2026\/10\/qs-schmidt-coefficients-basis-invariant-20261023-figure-db21cfec163a.png\"><img decoding=\"async\" src=\"https:\/\/quantumsea.net\/wp-content\/uploads\/2026\/10\/qs-schmidt-coefficients-basis-invariant-20261023-figure-db21cfec163a.png\" alt=\"\u56db\u9805\u306e\u7a4d\u72b6\u614b\u306fSchmidt\u30e9\u30f3\u30af1\u3001\u504f\u3063\u305f\u91cd\u307f0.8\u30680.2\u306e\u7d14\u7c8b\u72b6\u614b\u3068\u5747\u7b49\u306a0.5\u30680.5\u306e\u7d14\u7c8b\u72b6\u614b\u306f\u3068\u3082\u306b\u30e9\u30f3\u30af2\u3068\u306a\u308b\u6bd4\u8f03\u3002\u4fc2\u6570\u3068\u4e8c\u4e57\u3057\u305f\u91cd\u307f\u3092\u533a\u5225\u3059\u308b\u3002\" style=\"display:block;width:100%;max-width:720px;height:auto;margin-inline:auto\"><\/a><figcaption>\u72ec\u81ea\u306e\u4e8c\u91cf\u5b50\u30d3\u30c3\u30c8\u4f8b\u3002\u6a2a\u68d2\u306fSchmidt\u4fc2\u6570\u306e\u4e8c\u4e57\u3067\u3001\u5408\u8a081\u306e\u91cd\u307f\u3092\u8868\u3059\u3002SVD\u3068\u7e2e\u7d04\u72b6\u614b\u306e\u56fa\u6709\u5024\u3092\u8a08\u7b97\u3067\u7167\u5408\u3057\u305f\u3082\u306e\u3067\u3001\u91cf\u5b50\u88c5\u7f6e\u306e\u6e2c\u5b9a\u7d50\u679c\u3067\u306f\u306a\u3044\u3002<\/figcaption><\/figure>\n<p>\u5747\u7b49\u306a\u4f8b <code>(|00\u3009\uff0b|11\u3009)\/\u221a2<\/code> \u306e\u91cd\u307f\u306f0.5\u30010.5\u3067\u3059\u3002\u3053\u3061\u3089\u3082\u30e9\u30f3\u30af\u306f2\u3067\u3059\u304c\u30010.8\u30010.2\u306e\u4f8b\u3068\u540c\u3058\u5206\u5e03\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u30e9\u30f3\u30af\u306f\u3001\u975e\u30bc\u30ed\u306e\u7d44\u304c\u3044\u304f\u3064\u5fc5\u8981\u304b\u3092\u793a\u3057\u307e\u3059\u3002\u91cd\u307f\u304c\u3069\u308c\u307b\u3069\u5747\u7b49\u304b\u307e\u3067\u3001\u4e00\u3064\u306e\u6574\u6570\u3067\u8868\u3057\u3066\u3044\u308b\u308f\u3051\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<h2>\u57fa\u5e95\u3092\u5909\u3048\u3066\u3082\u3001\u4fc2\u6570\u306f\u5909\u308f\u3089\u306a\u3044<\/h2>\n<p>A\u3060\u3051\u3001\u307e\u305f\u306fB\u3060\u3051\u306b\u30e6\u30cb\u30bf\u30ea\u5909\u63db\u3092\u65bd\u3059\u3068\u3001\u5c40\u6240\u306e\u57fa\u5e95\u304c\u56de\u8ee2\u3057\u307e\u3059\u3002\u4fc2\u6570\u884c\u5217\u306e\u5404\u6210\u5206\u306f\u5909\u308f\u3063\u3066\u3082\u3001\u7279\u7570\u5024\u306f\u5909\u308f\u308a\u307e\u305b\u3093\u3002\u3053\u308c\u306f\u3001\u540c\u3058\u4e8c\u4f53\u7cfb\u306e\u5206\u3051\u65b9\u3092\u4fdd\u3063\u305f\u307e\u307e\u884c\u3046\u5c40\u6240\u306e\u5909\u63db\u306b\u3064\u3044\u3066\u306e\u6027\u8cea\u3067\u3059\u3002A\u3068B\u3092\u7d50\u3073\u3064\u3051\u308b\u4e00\u822c\u306e\u4e8c\u4f53\u7cfb\u306e\u64cd\u4f5c\u306b\u307e\u3067\u5e83\u3052\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002<\/p>\n<p>\u72ec\u81ea\u8a08\u7b97\u3067\u306f\u3001\u91cd\u307f0.8\u30010.2\u306e\u4f8b\u306eA\u5074\u3078Hadamard\u5909\u63db\u3092\u65bd\u3057\u3001\u3055\u3089\u306bB\u5074\u3078\u4f4d\u76f8\u3092\u52a0\u3048\u307e\u3057\u305f\u3002\u5143\u306e\u4fc2\u6570\u884c\u5217\u306f\u5bfe\u89d2\u306e\u4e8c\u6210\u5206\u3060\u3051\u3067\u3057\u305f\u304c\u3001\u5909\u63db\u5f8c\u306f\u56db\u6210\u5206\u304c\u975e\u30bc\u30ed\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u308c\u3067\u3082\u4e8c\u3064\u306eSchmidt\u4fc2\u6570\u3068\u3001\u305d\u306e\u4e8c\u4e57\u306e0.8\u30010.2\u306f\u4e00\u81f4\u3057\u307e\u3059\u3002\u632f\u5e45\u306e\u898b\u305f\u76ee\u3092\u6bd4\u3079\u308b\u3088\u308a\u3001\u57fa\u5e95\u306b\u4f9d\u5b58\u3057\u306a\u3044\u60c5\u5831\u3092\u53d6\u308a\u51fa\u3057\u3066\u6bd4\u3079\u308b\u5229\u70b9\u304c\u3053\u3053\u306b\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u4e00\u65b9\u3001Schmidt\u4fc2\u6570\u304c\u540c\u3058\u5024\u306b\u91cd\u306a\u3063\u3066\u3044\u308b\u5834\u5408\u306a\u3069\u306b\u306f\u3001\u5bfe\u5fdc\u3059\u308b\u57fa\u5e95\u306e\u9078\u3073\u65b9\u304c\u4e00\u610f\u3068\u306f\u9650\u308a\u307e\u305b\u3093\u3002\u4e8c\u3064\u306e\u8a08\u7b97\u304c\u7570\u306a\u308b\u57fa\u5e95\u30d9\u30af\u30c8\u30eb\u3092\u8fd4\u3057\u305f\u3068\u3044\u3046\u3060\u3051\u3067\u3001\u7247\u65b9\u304c\u8aa4\u308a\u3068\u306f\u8a00\u3048\u307e\u305b\u3093\u3002\u5143\u306e\u72b6\u614b\u3092\u518d\u69cb\u6210\u3067\u304d\u308b\u304b\u3001\u4fc2\u6570\u304c\u4e00\u81f4\u3059\u308b\u304b\u3001\u76f4\u4ea4\u6027\u304c\u4fdd\u305f\u308c\u308b\u304b\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/p>\n<h2>\u9069\u7528\u3059\u308b\u72b6\u614b\u3068\u3001\u6570\u5024\u306e\u5c0f\u3055\u3055\u3092\u78ba\u8a8d\u3059\u308b<\/h2>\n<p>\u3053\u3053\u307e\u3067\u306e\u8b70\u8ad6\u306f\u3001\u5168\u4f53\u304c\u4e00\u3064\u306e\u72b6\u614b\u30d9\u30af\u30c8\u30eb\u3067\u8868\u305b\u308b\u7d14\u7c8b\u72b6\u614b\u3067\u3042\u308b\u3053\u3068\u3092\u524d\u63d0\u306b\u3057\u3066\u3044\u307e\u3059\u3002\u6df7\u5408\u72b6\u614b\u306e4\u884c4\u5217\u306e\u5bc6\u5ea6\u884c\u5217\u3092\u3001\u8aac\u660e\u306a\u304f2\u884c2\u5217\u3078\u8aad\u307f\u66ff\u3048\u3066\u540c\u3058\u5224\u5b9a\u3078\u5165\u308c\u3066\u306f\u3044\u3051\u307e\u305b\u3093\u3002\u6df7\u5408\u72b6\u614b\u306e\u3082\u3064\u308c\u306e\u5224\u5b9a\u306f\u5225\u306e\u554f\u984c\u3067\u3059\u3002<\/p>\n<p>\u305f\u3068\u3048\u307000\u309280%\u300111\u309220%\u306e\u78ba\u7387\u3067\u6e96\u5099\u3057\u305f\u6df7\u5408\u72b6\u614b\u306f\u3001\u7a4d\u72b6\u614b\u3092\u78ba\u7387\u7684\u306b\u9078\u3093\u3060\u3060\u3051\u3067\u3059\u3002A\u3060\u3051\u306e\u56fa\u6709\u5024\u306f0.8\u30010.2\u3068\u306a\u308a\u3001\u5148\u306e\u3082\u3064\u308c\u305f\u7d14\u7c8b\u72b6\u614b\u3068\u4e00\u81f4\u3057\u307e\u3059\u3002\u305d\u308c\u3067\u3082\u5168\u4f53\u306f\u540c\u3058\u72b6\u614b\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u300c\u7247\u65b9\u306e\u91cd\u307f\u304c\u540c\u3058\u300d\u3060\u3051\u304b\u3089\u3001\u5168\u4f53\u306e\u3082\u3064\u308c\u3092\u65ad\u5b9a\u3057\u306a\u3044\u3053\u3068\u304c\u5927\u5207\u3067\u3059\u3002<\/p>\n<p>\u6570\u5024\u8a08\u7b97\u3067\u306f\u3001\u672c\u6765\u30bc\u30ed\u306e\u7279\u7570\u5024\u304c\u4e38\u3081\u8aa4\u5dee\u3067\u3054\u304f\u5c0f\u3055\u304f\u6b8b\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u30e9\u30f3\u30af\u3092\u8868\u793a\u3059\u308b\u3068\u304d\u306f\u3001\u4f55\u4ee5\u4e0b\u3092\u30bc\u30ed\u3068\u307f\u306a\u3059\u304b\u3068\u3044\u3046\u8a31\u5bb9\u5024\u3082\u8a18\u9332\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u8a08\u7b97\u4e0a\u306e\u5224\u65ad\u57fa\u6e96\u3067\u3042\u308a\u3001\u5c0f\u3055\u306a\u5024\u3092\u6d88\u3057\u305f\u3060\u3051\u3067\u5b9f\u969b\u306e\u72b6\u614b\u306e\u6027\u8cea\u304c\u78ba\u5b9a\u3059\u308b\u308f\u3051\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<p>Schmidt\u5206\u89e3\u3092\u4f7f\u3046\u3068\u304d\u306f\u3001\u307e\u305a\u4e8c\u4f53\u7cfb\u3078\u306e\u5206\u3051\u65b9\u3068\u57fa\u5e95\u306e\u4e26\u3073\u3092\u5b9a\u3081\u3001\u7d14\u7c8b\u72b6\u614b\u3067\u3042\u308b\u3053\u3068\u3068\u898f\u683c\u5316\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002\u305d\u306e\u3046\u3048\u3067\u3001\u4fc2\u6570\u3001\u4e8c\u4e57\u3057\u305f\u91cd\u307f\u3001\u975e\u30bc\u30ed\u306e\u500b\u6570\u3092\u5206\u3051\u3066\u8aad\u3080\u3002\u5f0f\u306e\u9805\u6570\u3084\u898b\u305f\u76ee\u306b\u5f15\u3063\u3071\u3089\u308c\u305a\u3001\u6bd4\u8f03\u3057\u305f\u3044\u60c5\u5831\u3092\u9078\u3076\u305f\u3081\u306e\u9053\u5177\u3068\u3057\u3066\u4f7f\u3048\u307e\u3059\u3002<\/p>\n<h2>\u51fa\u5178<\/h2>\n<ol>\n<li>John Watrous, <a href=\"https:\/\/cs.uwaterloo.ca\/~watrous\/TQI\/TQI.double.1.pdf\">The Theory of Quantum Information, Chapter 1<\/a>\uff082018\uff09\u3002\u5370\u5237\u30da\u30fc\u30b831\u3001Schmidt decompositions\u3001\u5f0f1.162\u301c1.164\u3002\u4e8c\u4f53\u7cfb\u30d9\u30af\u30c8\u30eb\u3068\u7279\u7570\u5024\u5206\u89e3\u306e\u95a2\u4fc2\u3002<\/li>\n<li>\u540c\u66f8\u3001<a href=\"https:\/\/cs.uwaterloo.ca\/~watrous\/TQI\/TQI.2.pdf\">Chapter 2<\/a>\uff082018\uff09\u3002Sections 2.1.2\u306e\u91cf\u5b50\u72b6\u614b\u30fb\u6df7\u5408\u3068\u7d14\u7c8b\u72b6\u614b\uff08\u5370\u5237\u30da\u30fc\u30b862\u301c64\uff09\u3002\u6570\u5024\u3068\u56f3\u306f\u672c\u7a3f\u306e\u72ec\u81ea\u8a08\u7b97\u3002<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u4e8c\u3064\u306e\u91cf\u5b50\u7cfb\u3092\u5408\u308f\u305b\u305f\u72b6\u614b\u3092\u66f8\u304d\u4e0b\u3059\u3068\u3001\u3044\u304f\u3064\u3082\u306e\u9805\u304c\u73fe\u308c\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u5f0f\u306b\u9805\u304c\u591a\u3044\u3053\u3068\u3068\u3001\u4e8c\u3064\u306e\u7cfb\u306e\u9593\u306b\u3082\u3064\u308c\u304c\u3042\u308b\u3053\u3068\u306f\u540c\u3058\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u5404\u7cfb\u306e\u57fa\u5e95\u3001\u3064\u307e\u308a\u72b6\u614b\u3092\u8868\u3059\u3082\u306e\u3055\u3057\u3092\u9078\u3073\u76f4\u3059\u3060\u3051\u3067\u3001\u898b\u304b\u3051\u306e\u9805\u6570\u306f\u5909\u308f\u308a\u307e [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":1303,"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-1305","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-schmidt-coefficients-basis-invariant-20261023-featured-ef6197952050.png","_links":{"self":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts\/1305","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=1305"}],"version-history":[{"count":1,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts\/1305\/revisions"}],"predecessor-version":[{"id":1306,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts\/1305\/revisions\/1306"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/media\/1303"}],"wp:attachment":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1305"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1305"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1305"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}