Target space entanglement
inquantum mechanics
offermions and matrices
杉下 宗太郎（名古屋⼤）
arXiv:2105.13726 [JHEP 08 (2021) 046]
2021/12/22 セミナー@京⼤素論量⼦もつれ
• 量⼦論特有の相関<latexit sha1_base64="dev/1X3zPzmXWN5NlRHYZs4dtpc=">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</latexit>

EPR pair1
p (|0i ⌦ |0i + |1i ⌦ |1i)2

2つのqubitがもつれた状態• 量⼦情報（量⼦計算・量⼦通信）に重要• ホログラフィーにも重要
笠・⾼柳公式<latexit sha1_base64="aWR9FNQf20Yyi9sECJBZknnk/b8=">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</latexit>

場の理論における量⼦もつれ（〜境界での相関）
バルクの幾何<latexit sha1_base64="HYmmOvdAErLJ14FxJIRY9vxCFmM=">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</latexit>AĀ

今⽇の話: target spaceの量⼦もつれ<latexit sha1_base64="8Lp81jclpG0NfuWo4Q6c4ytIM3s=">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</latexit>(~x)

n Target space（標的空間）＝ 場が動く空間

target space

cf. base space(底空間) = 場が定義されている空間~x<latexit sha1_base64="Ccg9zv01Y+bMV29pp9Pdj8EHgjo=">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</latexit><latexit sha1_base64="+dpdkcgFdCpLQ1m8nFqAiOS0qD4=">AAANcXicnVdPb9xUEJ+WUsrShRQOqKpULY0iWpGuvCGC9hCppQHlACSlSRO1W1W283bXWv+T7U2zsfbYT8IJAfd+BL4ABz4C4tgrB34z7znZbHa9DrZsvzczv5l582bGthP7XppZ1l8XLr5z6d3L7115v/bB1fqHHy1c+/hpGg0SV+24kR8le46dKt8L1U7mZb7aixNlB46vdp3+I+bvHqgk9aJwOxvG6kVgd0Ov47l2BtLLhU/bcc+73T44vNP2wkY7sLOe4+Q/jV4uLFpNS47G2UHLDBYf3Hzz+J/XN99sRdcuf0Zt2qeIXBpQQIpCyjD2yaYU53Nq0QrFoL2gHLQEI0/4ikZUoyWgB5BTkLFB7+PexYxlV+kVZPeN5HS554YaYs7WU7Hjwh8fVwJkg5asP61frLfWH9av1t/WvzN1sc0B/OuRA3S/xGoOmSFoChYS3DulHmbwJKY1xKGFcQIpBV8DWoadCBTmB8JfmeD7ojsT3uoEL0FsuvBjGpdjwLYjiQlzhqWrSUUqNfQi3onEVWEXXNEUgBtiP3LwHNlfBQ89kUnFipK97wGfY61NXCPIhrITjPYh59ER5Fi/tuqLla7EnTXHkiUpvPMwZk2rkj+juRhPvNMZqD1YGUPO2vEAdPaNdS2beYp4BVjj8jGHPergKiQckVmWPM+g6dBgCn4Haw4lpgWFtQSlvsSSVanURzqnOjqyFy7ke1hzciydYK7A07uUmqj7qIJN2qG7tEHf0jae9xHVVUHNztsnJgpcS5xRA0h0ZZeVqY6axH5fVsuVE8t9DZFH1eH6Tna+YWS+h+ZtYPdKYsD6bYkER+FwThTG63y2ziJ7i8woq2ol6yu36oiPfcnE8s6UYdX3JHacmzo6Svat3EJq+if7s1/qsdaXzo1BkcfcayKpw3IPuEv3UamnpQoqV72OAneWXKrOFR9skYnEp6Zo1XnPPL2rXLfVbN9F9BT0h6bzFKiCf5qr/St2W1teM12oSZbJ16WKZ4N+RKXs4vkIlfMDzoegrEteVztr0vmmd8/E7Cu/HTk7mHaSy/kxf1E66KhUF7+rBpKzs7SdSFTRF0qkc9O3Q3mrO1IXbZzl2AOpWD3ijMhlPh8Tn0F9XgE3nEANK2EmbQ0r2TqaQB1VwkzaOqpkqz+B6s/FuMhOjSnq3JW+nwt9HnZzBnazAnZjBnajAvbZDOwzg+VaX5cY+NJpFKpQS26aby9b+lkiWjLpgLl51s6FTdF5dNYXo/PiY4N/Ip1nuoYtPD1T2+vm2ynAlZnq4i8vTyLQxr2YjUzHOJkvSd/UnbQhPil5x4530caUjn9+jzrSQ4pV+mPzwqtxyv/2C38drcl/jLODpyvN1lfNLx/j9+Mb0scVukG36Da62tf0ADm3hW8cfrf+TL/R71ff1q/XG/VbWvTiBYP5hE4d9S/+A5rFqAM=</latexit>• 実スカラー場•(~x) 2 R

base space

場の理論でよく考えられている量⼦もつれは
base spaceの量⼦もつれ<latexit sha1_base64="aWR9FNQf20Yyi9sECJBZknnk/b8=">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</latexit><latexit sha1_base64="HYmmOvdAErLJ14FxJIRY9vxCFmM=">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</latexit>A

target spaceはあまり考えられていないĀ

[Mazenc, Ranard (2019)], [Hampapura, Harper, Lawrence (2020)],[Das, Kaushal, Mandal, Trivedi (2020)], [Das, Kaushal, Liu, Mandal, Trivedi (2020)], [Frenkel, Hartnoll (2021)]•

弦理論: base spaceではなくtarget spaceが私達の住む空間 X µ ( )<latexit sha1_base64="Tv6ZE40PErDedEYpfH1yfytEI5k=">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</latexit>(world-sheet)⾏列模型の量⼦もつれ• ⾏列量⼦⼒学 X µ (t, ~x) (1+0)次元の場の理論（＝量⼦⼒学）<latexit sha1_base64="LG0VBFsdDCrt08/UuojySsu8LEE=">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</latexit>

例: BFSS模型＝

base spaceなし

M理論

target spaceの量⼦もつれが時空の幾何と関係していると思うのが⾃然。
[Das, Kaushal, Mandal, Trivedi (2020)], [Das, Kaushal, Liu, Mandal, Trivedi (2020)]

1
n ⼿始めに、⾏列1個の⼀番簡単な⾏列量⼦⼒学を考えた L = tr Ẋ 2
2<latexit sha1_base64="0DAHE2zX7dtgCgFT+MKeLM8/Z3o=">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</latexit>• 同種粒⼦(フェルミオン)の量⼦⼒学

tr V (X)target space EEの定義？
l 普通のbase space EE
密度⾏列 ⇢<latexit sha1_base64="CtdWZNjTldmoh3sGsxu0QwTYJTA=">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</latexit><latexit sha1_base64="XAhCl/6fBDSpIGrCk+U4uHNksYM=">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</latexit>

H = HA ⌦ HĀ ,⇢A = trĀ ⇢(HA = ⌦x2A Hx ,SA =<latexit sha1_base64="JV3Bs5QxEqaA1d7Lrzx8VDwOehg=">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</latexit><latexit sha1_base64="1hC0ZeAPdOPorlsf4wMsXsVvKko=">AAANcnicnVdPb9xUEJ+2UMrShRQuCC5boggO25UTVi0cIjVqQDkACWrSRO1Wke283Vjrf/Lzlm6s5dNwQQg+B1+AAx+BMxw58Jt5z8lms+t1sGX7vZn5zcybNzO2vTQMdO44f964eeuNN2+/deftxjt3m+++t3Lv/Wc6GWW+OvCTMMmOPFerMIjVQR7koTpKM+VGXqgOveET5h++UpkOkng/H6fqZeQO4qAf+G4O0vHKh73sNDne2uzl2XHR89ys2JpMhLay6nQcOVpXB+t2sEr22Evu3b5PPTqhhHwaUUSKYsoxDskljfMFrZNDKWgvqQAtwygQvqIJNWgN6BHkFGRc0Ie4DzBj2S79ANkTKzlf7oWlxpizdS12fPgT4sqAbNGa84fzs/O387vzi/OX8+9CXWxzBP9OyQN6WGG1gMwYNAULGe79Sg9zeJLSJm0gFjnkR6BGONuwk4DC/Ej4GzP8UHTnwuvO8DLEZgA/5nE5Bmw7kZgwZ1y5Gi1S2tLLeGcSV4Vd8EVTBG6M/SjA82R/FTwMREaLFSV7fwp8gbV2cE0gG8tOMDqEXEBnkGP9xmooVgYSd9acSpZoeBdgzJq6kj+TpZhAvDMZaDzYmEIu2vEIdPaNdbXtXCNeEdbYPuewR31cpYQnMm3J8xyaXltMye9jzbHEtKSwlqjSl1SySkt96CXV0Ze98CF/ijVn59IZ5go8s0vaRj1EFezSAT2gHfqK9vH8ElHtCmpx3j61UeBa4owaQWIgu6xsdTQk9ieyWq6cVO6biDyqDtfXsvMtK/MNNO8De1QRA9bvSiQ4Cq+XRGG6zhfrLLO3zIyqqlayvmqrnvg4lEys7kw5Vv2FxI5z00RHyb5VW9C2f7I/J5UeG316aQzKPOZek0gdVnvAXXqISr0sVVK56k0UuLMUUnW++OCKTCI+dUSryXvmmV3luq1n+wGip6A/tp2nRJX8y1zjX7nbxvKm7UIdvINMvq7VPFv0HSrlEM8nqJxvcW6Bsi15Xe9sSOeb3z0zu6/8duTsYNpFLhfn/FXpoJNKXfyuGknOLtJ2IVFHXyyRLmzfjuWt7kld9HBWY19JxZoRZ0Qh8+WY9Arq0xq48QxqXAsza2tcy9bZDOqsFmbW1lktW8MZ1HApxkd2GkxZ5770/ULoy7C7C7C7NbA7C7A7NbDPF2CfWyzX+rbEIJROo1CFRnLXfnu50s8y0ZJLByzss3EtrEbnMVlfjq6LTy3+qXSe+Rr28AxsbW/bb6cIV26ri7+8AolAD/dyNrEd42K+Jn3TdNKW+KTkHTvdRVtzOv71PepLDylXGU7NS6+mKf/bL/x1rM/+Y1wdPNvorD/sfP59d/XxQ/v/cYc+pk/oM3S1R/QYObeHbxyffqSf6Ff67e4/zY+a95v2Z+XmDYv5gC4dzfZ/oi6lQQ==</latexit>

HĀ = ⌦x2Ā Hx )trA ⇢A log ⇢A<latexit sha1_base64="aWR9FNQf20Yyi9sECJBZknnk/b8=">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</latexit>Ā<latexit sha1_base64="HYmmOvdAErLJ14FxJIRY9vxCFmM=">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</latexit>

AØ 問題点
ヒルベルト空間はtarget spaceに関してテンソル積の構造でない H 6= ⌦ 2R H
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部分トレースどう計算？
l reduced density matrixの意味を考え直すと、もっと⼀般の場合に使える定義が可能

target space~x<latexit sha1_base64="Ccg9zv01Y+bMV29pp9Pdj8EHgjo=">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</latexit>

EEの⼀般化として、これ⾃体⾯⽩いbase spaceOutlinen Target space EEの定義
EEの定義を拡張する

n 同種粒⼦の量⼦⼒学の場合
特にフェルミオンn 具体例
⼀次元⾃由フェルミガス

エントロピー＝不確かさ
l エントロピーは不確かさの度合いを表す指標.
限られた情報しか知り得ない⼈にとっての全体の情報のわからなさ.

<latexit sha1_base64="xOSTLAghiVKN37/4kBA0PFXToDQ=">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</latexit>• エンタングルメントエントロピー

H = HB ⌦ HB̄
<latexit sha1_base64="iEm7hDquVWqCPTBYrDtkIzBUyzQ=">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</latexit>B̄

部分系のことしか調べられない⼈にとっての全系のわからなさB<latexit sha1_base64="y3iEliuMUAON34T21jQURsC7ezc=">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</latexit>

A = L(HB ) ⌦ 1B̄ ⇢ L(H) しか使えない⼈<latexit sha1_base64="NuH/gbUPLC7zWEPLY6kZZHxUQQo=">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</latexit>

部分代数• ほかの部分代数に対しても、付随するエントロピーを定義できる（代数的アプローチ）.
Ohya-Petzの教科書 (1993)
格⼦ゲージ理論への応⽤ [Casini-Huerta-Rosabal (2013)]

部分代数とエントロピー
L(H) : ヒルベルト空間に作⽤する演算⼦全体の集合<latexit sha1_base64="QVZlqjJh6EiAPNHkjuM8EOk+HYo=">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</latexit>

⾜し算、積などで閉じている.

O1 , O2 2 L(H) ! c1 O1 + c2 O2 , O1 O2 2 L(H)<latexit sha1_base64="gRdMYJpfU3Qgo+OgpZ0VS53NezM=">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</latexit>

代数(環)になっている.

O1† 2 L(H)<latexit sha1_base64="ZjVczjbf4TqfM3bEhVX+Bqa9tTw=">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</latexit>

A ⇢ L(H) : 部分代数（部分集合でそれ⾃⾝で閉じてるもの）<latexit sha1_base64="mfgcCBerOtgEmGy82f7/BEeu6U4=">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</latexit>

限られた演算⼦しか使えない``粗視化’’

全体がわからないことによる不確かさ
エントロピー

部分代数とreduced density matrix
l reduced density matrix ⇢B = trB̄ ⇢<latexit sha1_base64="iBDCBZ4DLBYk9v9q1WtXw6iMrRA=">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</latexit><latexit sha1_base64="iEm7hDquVWqCPTBYrDtkIzBUyzQ=">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</latexit>

B̄

A = L(HB ) ⌦ 1B̄ ⇢ L(H)<latexit sha1_base64="NuH/gbUPLC7zWEPLY6kZZHxUQQo=">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</latexit>•!にだけ作⽤する演算⼦の集合<latexit sha1_base64="2gaIxYg2V18gBMEouimXFWHfzt4=">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</latexit>

部分代数

1B̄
⇢A = ⇢B ⌦dimHB̄
<latexit sha1_base64="c+pDLms31rxiQpt6DQxHkioNPIQ=">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</latexit>⇢A 2 As.t.

tr(⇢A O) = tr(⇢O)

8B<latexit sha1_base64="y3iEliuMUAON34T21jQURsC7ezc=">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</latexit>

O2A

l もっと⼀般の部分代数 A でも同じ式で特徴づける.
<latexit sha1_base64="UPQhaSGGdvHGRpUiwBTTiUYYMcU=">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</latexit><latexit sha1_base64="c+pDLms31rxiQpt6DQxHkioNPIQ=">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</latexit>⇢A 2 As.t.

tr(⇢A O) = tr(⇢O)

8

O2A

部分代数ごとに``reduced density matrix’’が定義できる!

⇢, A<latexit sha1_base64="u6+bo+QxWvU+yTjcPghlEsz63N0=">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</latexit>!

⇢A

SA (⇢) 部分代数に付随したエントロピー<latexit sha1_base64="y0lH+Pc8Vw8+ydXM89G4ZpTTWlc=">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</latexit>

ヒルベルト空間の分解部分代数 A ⇢ L(H)<latexit sha1_base64="kpB+nLhDKnWLi9Myv1loARHzEFc=">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</latexit>

定理：ヒルベルト空間は次の形にブロック分解可能<latexit sha1_base64="PZbnVuE957c0BjFIq57FC0sh674=">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</latexit>

H=

M
k

<latexit sha1_base64="UaEtyBlnCwhyJLwKR/s/S7SVIN4=">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</latexit>

HAk ⌦ HĀk

s.t.

A=

M
k

L(HAk ) ⌦ 1Āk

⼀般にはテンソル積そのものにはならないが、テンソル積の直和には分解できる!
<latexit sha1_base64="c+pDLms31rxiQpt6DQxHkioNPIQ=">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</latexit>l ⇢A の構成法<latexit sha1_base64="UoUN0nW3yEsq5wtd8cWZq01Hx68=">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</latexit>⇢A 2 As.t.

tr(⇢A O) = tr(⇢O)<latexit sha1_base64="/82UTiKq1rrt8ai5yUaOY+yzu/g=">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</latexit>

各ブロックへの射影 ⇧k<latexit sha1_base64="76EajaOIiHmBiwEYv8DJvpK6w88=">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</latexit><latexit sha1_base64="sCGU+/blvhwLK8ezNqHbP5rUPuw=">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</latexit>

⇢A =

M
k

pk = tr(⇧k ⇢⇧k ),1Āk
pk ⇢k,A ⌦dim(HĀk )

8

O2A

1
⇢k =
⇧k ⇢⇧kpk⇢k,A = trĀk ⇢k<latexit sha1_base64="uZA2oUrgcsks+SaXKgpnknIEezU=">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</latexit>シン・エンタングルメントエントロピーの定義<latexit sha1_base64="kBJmekSVtSRl5ShdJ+9Q0gKjPNI=">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</latexit>

⇢A =

M

1Āk
pk ⇢k,A ⌦dim(HĀk )k<latexit sha1_base64="ZmQXm2ZmMpaQMuSlCTEhHB2FVxQ=">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</latexit>⇢A =縮約密度⾏列<latexit sha1_base64="PZbnVuE957c0BjFIq57FC0sh674=">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</latexit>on

M

SA (⇢) =HAk ⌦ HĀkk

pk ⇢k,A

on

HA =

q
cl
trA ⇢A log ⇢A = SA(⇢) + SA(⇢)

X

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cl
SA
(⇢) =
q
SA
(⇢) =
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H=

M

X
k

pk log pkkpk S(⇢k,A )M

pk = tr(⇧k ⇢⇧k ),⇢k =1⇧k ⇢⇧kpk

H Ak

k

通常のEEの⼀般化！

古典確率分布 {pk } のShannonエントロピー<latexit sha1_base64="CxXK6HiLsScwtEVnbYnhlfhp7ps=">AAANX3icnVfNbttGEJ6kaZKqUeK0p6IXtYbRHhyBdoS0PRhIEafwIa1dxI6NREFA0iuZEP/ApdLIhB6i1+QJgrxIX6CHHHPMudce+s3s0pZliaJLguTuzHwzs7MzQ9JLw0DnjvP+0uVPrnx69dr1zxqf32jevLV0+4snOhlmvtrzkzDJDjxXqzCI1V4e5KE6SDPlRl6o9r3BA+bvv1SZDpJ4Nx+l6nnk9uOgF/huDtJ+t0hfDLrjF0vLTtuRo3V+sGYHy2SPneT21W+oS4eUkE9DikhRTDnGIbmkcT6jNXIoBe05FaBlGAXCVzSmBq0APYScgowL+gD3PmYs26E/IHtoJWfLPbPUGHO2rsWOD39CXBmQLVpx/nbeOv84fznvnI/Ov3N1sc0h/DsiD+hBhdUCMiPQFCxkuPcqPczhSUobtI5Y5JAfghrhXIWdBBTmR8Jfn+KHojsXXmeKlyE2ffgxi8sxYNuJxIQ5o8rVaJHSll7GO5O4KuyCL5oicGPsRwGeJ/ur4GEgMlqsKNn7I+ALrLWNawzZWHaC0SHkAjqGHOs3VkOx0pe4s+ZUskTDuwBj1tSR/BkvxATinclA48H6BHLejkegs2+sa9XONeIVYY2rJxz2qIerlPBEZlXyPIemVxZT8ntYcywxLSmsJar0JZWs0lIfekF19GQvfMgfYc3ZiXSGuQLP7JK2UQ9RBdu0R3doix7SLp4/IaodQc3P28c2ClxLnFFDSPRll5WtjobE/lBWy5WTyn0DkUfV4fpFdr5lZR5B8y6wBxUxYP2uRIKj8GpBFCbrfL7OMnvLzKiqaiXrq7bqiY8DycTqzpRj1T9K7Dg3TXSU7Fu1BW37J/tzWOmx0acXxqDMY+41idRhtQfcpQeo1LNSJZWr3kSBO0shVeeLD67IJOJTW7SavGee2VWu23q27yB6Cvpj23lKVMk/yzX+lbttLG/YLtTGO8jk60rNs0W/oVL28XyAyvkV58+gbEpe1zsb0vlmd8/M7iu/HTk7mHaay8UJf1k66LhSF7+rhpKz87SdStTRF0ukC9u3Y3mre1IXXZzV2JdSsWbEGVHIfDEmPYf6rgZuNIUa1cJM2xrVsnU8hTquhZm2dVzL1mAKNViI8ZGdBlPWuS99vxD6Iuz2HOx2DezWHOxWDezTOdinFsu1vikxCKXTKFShkdy2316u9LNMtOTSAQv7bFwIq9F5TNaXo4viU4t/LJ1ntoYdPANb25v22ynCldvq4i+vQCLQxb2cjW3HOJ2vSN80nbQlPil5x0520daMjn9xj3rSQ8pVhhPz0qtJyv/2C38da9P/GOcHT9bba/fad3/vLN/v2P+P6/Q1fUvfo6v9QPeRczv4xmFbf9JrenPjQ/Na82ZzyYhevmQxX9KZo/nVf1AJncQ=</latexit>

各セクターのEEを平均化したもの
cf. symmetry resolved EE

具体例：Qubit✓✓i
純粋状態 | i = cos |0i + e sin |1i
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n 1個のQubit H = span{|0i , |1i}<latexit 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何でも測れる⼈ A = span{1, x , y , z }<latexit 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L(H)<latexit 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特に純粋状態だと SA ( ) = 0<latexit sha1_base64="ZOLp7mlTtn06Vkok63k6n26wqPA=">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</latexit>

SA (⇢) = S(⇢)

通常のvon Neumann entropy(この⼈にとっては)純粋状態は曖昧さのない状態
実際、任意精度で何でも測定を⾏えるならば ✓,<latexit sha1_base64="OTNwzWRVKltjWqHx0468VyFaXRQ=">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</latexit>（正確には密度⾏列が決定できる）

決定可能.

具体例：Qubit✓✓i
純粋状態 | i = cos |0i + e sin |1i
22<latexit sha1_base64="cLlIsToHGG0tIx/z8bBWw5leDrs=">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</latexit>

n 1個のQubit H = span{|0i , |1i}<latexit sha1_base64="itqvHJBDynVVxzQ7DKtISdsJ+jo=">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</latexit>n<latexit sha1_base64="w1a2FiZObJjxvTJGIvcY33kfiBU=">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</latexit>n !⽅向のスピンしか測れない⼈

A = span{1,z } = c0

H = span{|0i}<latexit sha1_base64="obeOYF8rh7Y5n8PNGkk2vPuIDxo=">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</latexit>✓

10span{|1i}

◆o
0
0

n

c1

✓

◆o
0
1

0
0

✓
<latexit sha1_base64="AGEgZ/qlW8akMKzwKONN7g8BjZ8=">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</latexit><latexit sha1_base64="uH6muYz3MkNGtX0EQxm7OIEzKZ4=">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</latexit>

SA ( ) =<latexit sha1_base64="epMu+H4hEVK2ay+ZoKFuUgvBwbU=">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</latexit>

この⼈はどう頑張っても | i と ⇢ =<latexit sha1_base64="gIbqGNb2B2ntxUm0gsQaXe6VI5A=">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</latexit>

✓

p0
0

0
p1

◆

p0 log p0

p1 log p1の区別つかない.

✓p0 = cos2 ,2✓
p1 = sin2
2

エントロピー＝不確定度

代数的アプローチなら、1個のQubitに対しても``EE’’が定義できる！

◆

Observational Entropy
物性・熱⼒学の分野でも同様の概念が提唱されている.

Safranek, Deutsch, Aguirre (2017 - )• General framework to encompass classical and quantum equilibriumand non-equilibrium coarse-grained entropy
ほぼ代数的アプローチと同じ定義.
演算⼦を制限することによる粗視化のエントロピー.

ここまでのまとめl 使える演算⼦が制限されている観測者に対して、全体がわからないことによる不確定さの度合いとしてエントロピーが定義できる。
<latexit sha1_base64="iEm7hDquVWqCPTBYrDtkIzBUyzQ=">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</latexit>

B̄B"内のことしかわからない⼈にとってのエントロピー<latexit sha1_base64="y3iEliuMUAON34T21jQURsC7ezc=">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</latexit>＝ 通常のbase space EE

Ø 演算⼦の制限⽅法（部分代数のとり⽅）は⾊々. Hilbert 空間がテンソル積になっている必要はない.

• ⼀般的なエンタングルメントエントロピーqclSA (⇢) = SA(⇢) + SA(⇢)<latexit sha1_base64="gwa85yThal0AzRr0N0Bb/SBpj48=">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</latexit>

X<latexit sha1_base64="+MMb5kEuBY9hEwrPPzVTaCYhayw=">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</latexit>

cl
SA
(⇢) =

pk log pk ,k<latexit sha1_base64="SOThhImkW4oNGRcF8wC+ZKBR+c0=">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</latexit>•

⼀般的なRenyiエントロピー(n)SA (⇢) =log trA ⇢nA
1

q
SA
(⇢) =

n

log
=

⇣P

X
k

n
n
k pk trAk ⇢k,A

1

n

⌘

pk S(⇢k,A )次の話<latexit sha1_base64="Zd+in4F69rCekuZ223KM+cFqshE=">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</latexit>

Ø (多)粒⼦の量⼦⼒学に対してH=

target space EEを考える.

i=1

x<latexit sha1_base64="it39/bxsEx+mLeSBA6KYT1fTxY0=">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</latexit>

!

✓
N
X

p2i
2m

+ V (xi )◆Outlinen Target space EEの定義
EEの定義を拡張する

n 同種粒⼦の量⼦⼒学の場合
特にフェルミオンn 具体例
⼀次元⾃由フェルミガス

⼀粒⼦の量⼦⼒学
n 空間&を動く粒⼦の量⼦⼒学Z| i=dx (x) |xi#(!) 波動関数<latexit sha1_base64="ngDWiA9H3+zcfpN3dljjck+g/1k=">AAANgXicnVfNbttGEJ4kbZqoVeu0x16UGkYSQBFoVUhbFAYSxC18aGoXsWMjUWCQ1EomxD9wqUQyoUfIgxQ99tre+wI99BF67rWHfjNc2rIsUXRJkNydmW9mdnZmSDqx7+nUsv66dv3Ge+/f/ODW7dqHH9U//mTtzqcvdDRKXHXgRn6UHDm2Vr4XqoPUS311FCfKDhxfHTrDp8w/fKMS7UXhfjqJ1evAHoRe33PtFKTjtXvdoUqzbqy96VbXC9PjZ927jd640W0y7f74gfDH0+O1datlydG4PNg0g3Uyx1505+Zd6lKPInJpRAEpCinF2CebNM5XtEkWxaC9pgy0BCNP+IqmVKMNoEeQU5CxQR/iPsCMZTv0FrI9I7lY7pWhhpizdS12XPjj40qAbNCG9af1s/WP9Yf1i/W39e9SXWxzBP9OyAF6WGI1g8wENAULCe79Ug9TeBLTFrURixTyI1ADnE3YiUBhfiD89hzfF92p8DpzvASxGcCPRVyOAduOJCbMmZSuRouUNvQi3onEVWEXXNEUgBtiPzLwHNlfBQ89kdFiRcnenwCfYa0tXFPIhrITjPYh59Ep5Fh/btUXKwOJO2uOJUs0vPMwZk0dyZ/pSown3uUZmHvQnkEu2/EAdPaNdTXNXCNeAdbYPOOwR31chYQjMk3J8xSaxgZT8PtYcygxLSisJSj1JZas0lIfekV19GUvXMifYM3JmXSCuQIv3yVtou6jCnbpgB7SDn1H+3h+g6h2BLU8b5+bKHAtcUaNIDGQXVamOmoS+56slisnlvsWIo+qw/W97HzDyPwAzfvAHpXEgPXbEgmOwnhFFGbrfLnOInuLzCiraiXrK7fqiI9DycTyzpRi1V9L7Dg38+go2bdyC9r0T/anV+pxrk+vjEGRx9xrIqnDcg+4Sw9RqRelCipXfR4F7iyZVJ0rPtgiE4lPLdGa5z3z8l3luq1m+yGip6A/NJ2nQBX8i9zcv2K3c8tbpgu18A7K83Wj4tmgH1Eph3g+ReU8w/kElG3J62pnTTrf4u6ZmH3ltyNnB9POczk7469LB52W6uJ31Uhydpm2c4kq+kKJdGb6dihvdUfqoouzHPtGKjYfcUZkMl+NiS+h7lXATeZQk0qYeVuTSrZO51CnlTDztk4r2RrOoYYrMS6yM8cUde5K38+Evgq7uwS7WwG7swS7UwH7cgn2pcFyrW9LDHzpNApVmEvumm8vW/pZIlpS6YCZedauhNXoPHnWF6Or4mODfy6dZ7GGPTw9U9vb5tspwJWa6uIvL08i0MW9mE1Nxzifb0jfzDtpQ3xS8o6d7aKNBR3/6h71pYcUq/Rn5oVXs5T/7Rf+Ojbn/zEuD160W5uPWl/+1Fl//Mj8f9yiz+kLuo+u9hU9Rs7t4RvHpXf0K/1Gv9dv1B/UrXo7F71+zWA+owtH/dv/AJWeqcA=</latexit>

M#についてテンソル積になっていない"
l 部分領域 ! ⊂ # にだけ作⽤できる⼈にとってのEEを考える
Z
dxdx0 O(x, x0 ) |xihx0 | だけできる⼈
こういう演算<latexit sha1_base64="CamHnr375Z44ZFEFoSn9x0tJ0S4=">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</latexit>A!

⼀粒⼦の量⼦⼒学のEE<latexit sha1_base64="ZmQXm2ZmMpaQMuSlCTEhHB2FVxQ=">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</latexit>• ``縮約密度⾏列’’

⇢A =

M

<latexit sha1_base64="ZRy8500JC3MEeHO24isUpzcuR1M=">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</latexit>pk ⇢k,ASA (⇢) =k

⼀粒⼦だと、H = H1
<latexit sha1_base64="o5wmpGXvTQ1vGsIrDUiF32sHPUI=">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</latexit><latexit sha1_base64="a53Rk73PNQp2QxW5nz+C5U3rGog=">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</latexit>• 純粋状態 | i =ZA<latexit sha1_base64="La5cvIleEJz7p6bf7rX1fsBjVoY=">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</latexit>

p1 =

Z

̅
粒⼦が"にいる or いない("にいる).

H0dx (x) |xi +qcltrA ⇢A log ⇢A = SA(⇢) + SA
(⇢)

Z

q
cl
SA ( ) = SA( ) + SA( )<latexit sha1_base64="zTNUyprt2lIyW/CF4YZP1EKRPHs=">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</latexit>Ādx (x) |xi

dx| (x)|2 ,

=

p0 =

A

Z

dx| (x)|2 = 1

p0 log p0

p1

Ā

EE = 古典確率分布(Bernoulli分布) {p1 , 1<latexit sha1_base64="1Z4M8iAgjfrSLxbiKhKdbiBPMw8=">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</latexit>

p1 log p1p1 } のShannonエントロピー

同種粒⼦の多体系の量⼦⼒学
n ボソン or フェルミオンの(粒⼦系(x (1) , · · · , x (N ) ) = (±)sgn<latexit sha1_base64="Acy+qC6bZUdd3Xwc16OeBRRzpQs=">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</latexit>̅• !に$個, !に&− $個いる状態への射影 ⇧k (A)<latexit sha1_base64="ARlNeN2nyGBP9b9ihiaY2UH+jxU=">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</latexit><latexit sha1_base64="ycYprTuAYNLjFw0vxhKf+6oNN10=">AAANi3icnVfdcttUEN62UIrBkJZLbgyZDGUm9cip+R08U6YpkwtIwjRpMq3bjKQcOxr9jo5c6mj8HDwDwzNwC7wAFzwC19xywbero8RxbFmpNJLO2d1vd8+e3ZXkJIGnM8v6+9r1G2+8efOtW2833nm3+d77K7fvPNHxKHXVvhsHcXro2FoFXqT2My8L1GGSKjt0AnXg+A+Zf/BSpdqLo71snKjnoT2MvIHn2hlIRyudfmhnJ64d5FuTF/nd7U8nvb7jDeMkGOmj3O9ZkxfbrSmZI/9oZdVqW3K0Lg86ZrBK5tiNb9/8iPp0TDG5NKKQFEWUYRyQTRrnM+qQRQlozykHLcXIE76iCTVoDegR5BRkbNB93IeYsWyXfoLssZGcL/fMUCPM2boWOy78CXClQLZozfrL+sX61/rT+tX6x/pvoS62OYJ/J+QA7VdYzSEzBk3BQor7oNLDDJ4k1KMNxCKD/AjUEOc67MSgMD8U/sYMPxDdmfC6M7wUsRnCj3lcjgHbjiUmzBlXrkaLlDb0Mt6pxFVhF1zRFIIbYT9y8BzZXwUPPZHRYkXJ3p8An2OtbVwTyEayE4wOIOfRKeRYf2E1ECtDiTtrTiRLNLzzMGZNXcmfyVKMJ94VGVh4sDGFXLTjIejsG+taN3ONeIVY4/oZhz0a4ColHJFZlzzPoOmVwZT8AdYcSUxLCmsJK31JJKu01IdeUh0D2QsX8idYc3omnWKuwCt2SZuoB6iCHdqne7RFj2gPz68Q1a6gFuftYxMFriXOqBEkhrLLylRHQ2J/LKvlyknk3kPkUXW4vpOdbxmZ76F5D9jDihiwflsiwVF4tSQK03W+WGeZvWVmVFW1kvVVW3XER18ysbozZVj1lxI7zs0iOkr2rdqCNv2T/Tmu9LjQp5fGoMxj7jWx1GG1B9ylfVTqRamSylVfRIE7Sy5V54oPtsjE4lNbtBZ5z7xiV7lu69m+h+gp6I9M5ylRJf8it/Cv3O3Ccs90oTbeQUW+rtU8W7SNSjnA8yEq5wec34KyKXld72xI55vfPVOzr/x25Oxg2nku52f8Vemgk0pd/K4aSc4u0nYuUUdfJJHOTd+O5K3uSF30cVZjX0rFFiPOiFzmyzHJJdQnNXDjGdS4FmbW1riWrdMZ1GktzKyt01q2/BmUvxTjIjsLTFnnrvT9XOjLsDsLsDs1sFsLsFs1sE8XYJ8aLNf6psQgkE6jUIWF5I759rKln6WiJZMOmJtn40pYjc5TZH05uio+MfjH0nnma9jF0zO1vWm+nUJcmaku/vLyJAJ93MvZxHSM8/ma9M2ik7bEJyXv2Oku2prT8a/u0UB6SLnKYGpeejVNeW2/8NfRmf3HuDx4stHufN6+/2N39cFn5v/jFn1IH9NddLUv6AFybhffOC79TL/R7/RHs9m83/y6+U0hev2awXxAF47mo/8BhnyuVQ==</latexit>

H

(N )

=

N
M
k=0

• 各セクターの確率<latexit sha1_base64="mz7VDs1yT0RdkzX77En7cEnJxDc=">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</latexit>

Hk

Hk = ⇧k (A)H(N )<latexit sha1_base64="XgFBXxbh11/zC1KUFFkiUgZ8Jj0=">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</latexit>

pk = tr[⇧k (A)⇢⇧k (A)]<latexit sha1_base64="OYzDyi41QjDIp4JH/rf9OYcLaJc=">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</latexit>

✓ ◆Z
Z
N
pk =
dk y
dN
k
A
Ā

k

z | (~y , ~z )|2(x1 , · · · , xN )

同種粒⼦の多体系の量⼦⼒学のEE<latexit sha1_base64="ycYprTuAYNLjFw0vxhKf+6oNN10=">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</latexit>

H(N ) =

N
M
k=0

Hk
1
⇢k =
⇧k (A)⇢⇧k (A)pk<latexit sha1_base64="8XqpgGo6WQlPoLrdlNyFoiAaZkg=">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</latexit>• 各セクターの密度⾏列<latexit sha1_base64="VRVw3gHn6GbAFSpgdA2nI0A7XVY=">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</latexit>• 各セクターの縮約密度⾏列 ⇢k,A = trĀ ⇢k<latexit sha1_base64="Vc3JutTAoDM/Fs+7AmMEFA5kWqs=">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</latexit>• Target space EE⇢k,A =

N
k

pk

Z

k

k 0

d yd y
A

Z

d

N

k

z ⇢(~y , ~z , ~y , ~z ) ~y

Ā

q
cl
SA (⇢) = SA(⇢) + SA(⇢)<latexit sha1_base64="5QGg44mF05CVpkRThioxXEx8EwU=">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</latexit><latexit sha1_base64="b6dWhtGnpyMcL4tS1qz9XtdGu8s=">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</latexit>

cl
SA
(⇢) =

N
X

pk log pk ,k=0

Shannon entropy

q
SA
(⇢) =

N
X

0

pk trA ⇢k,A log ⇢k,A

k=0

各セクターのEEの平均

ED

y~0

フェルミオンの場合（⾏列量⼦⼒学の場合）
1(x1 , . . . , xN ) = p det ( i (xj ))N!

<latexit sha1_base64="XhdQNNF3Oiqf2HXfPQ6kCtc2BJw=">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</latexit>• Slater determinantZ<latexit sha1_base64="NTKRwm5Nq/6ES/GJfNiynnMxdg8=">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</latexit><latexit sha1_base64="hsZHwMqoY04fsPhnNHOv1Xib7fU=">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</latexit>• overlap matrix

Xij (A) =

Z

dx
A

dx
M

⇤
i (x) j (x) =⇤i (x) j (x)ij

⼀般に対⾓的でない

Ø 固有値を)! とする (* ≤ )! ≤ ,)<latexit sha1_base64="C+BUaZP5LB3V766KUSNvtGo5Jgc=">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</latexit>

cl
SA
(⇢) =

N
X

k=0

pk log pk ,

q
SA
(⇢) =

N
X

k=0

pk trA ⇢k,A log ⇢k,A は (! で書ける.

<latexit sha1_base64="VW5EB3lGwHOf4NIazzqOseHeyE0=">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</latexit>

フェルミオンのEEの古典部分

cl
SA
(⇢) =

N
X

pk log pk

k=0

l Poisson⼆項分布のShannonエントロピーと同じ.
• N種類のコイン（それぞれ表の確率(! , 裏の確率1 − (! ）• 表が$個の確率 pk<latexit sha1_base64="8hQYlXUbrUCZ5s3ayLJTmPVi7Us=">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</latexit>

1 X
l 表が出る確率の平均
N i<latexit sha1_base64="GXIp3hspy2+uQwH9Eooebb8MC/w=">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</latexit>i ⌘1 = ··· =N =S cl ( 1 , · · · ,clN )  S [B(N, )] =<latexit sha1_base64="gcRFyEgC3e9Uw2U7g8BDL+sNbms=">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</latexit>を固定したとき、エントロピーが最⼤になるのは（普通の⼆項分布）.

<latexit sha1_base64="NdH1chKhV83vFLpwe01h/Brp6AU=">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</latexit>1log[2⇡N (12
中⼼極限定理clSA(⇢) . O(log N )<latexit sha1_base64="qRHfIdh3qACJ/UaM6NGmhN0T8vg=">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</latexit>)] +1+ O(1/N )2

フェルミオンのEE
l 古典+量⼦は簡単化
qclSA (⇢) = SA(⇢) + SA(⇢) =<latexit sha1_base64="LZvlMXKoe4WOFbtXlFclqsuEnxI=">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</latexit>X

H( i )<latexit sha1_base64="q6iFbyf6sjJbkCUXhCzsRSoTExo=">AAANfHicnVdPb+NUEJ9dYFnCBrpw5BK2VCzaJnKiaIFDpUVbUA+wLdp2G21TVbb7klrxP9nOsqmVO18FIXGFj8AX4MBH4MwVIX4z77lN08RxsWX7vZn5zcybNzO2ndj30syy/rx1+40337rz9t13au/eq7/3/tr9D16k0Thx1YEb+VHSc+xU+V6oDjIv81UvTpQdOL46dEZPmX/4SiWpF4X72SRWx4E9DL2B59oZSCdrD7aa/SxpHPX6fjRs9B49bJ88a/Y+45kZHp+srVstS47G9UHbDNbJHHvR/TsfU59OKSKXxhSQopAyjH2yKcV5RG2yKAbtmHLQEow84SuaUo02gB5DTkHGBn2E+xAzlu3SD5A9NZKL5Y4MNcScradix4U/Pq4EyAZtWH9YP1l/W79bP1t/Wf8s1cU2x/DvjBygRyVWc8hMQFOwkOA+KPUwgycxbVEHscggPwY1wLkJOxEozA+E35nj+6I7E153jpcgNkP4sYjLMWDbkcSEOZPS1aQilRp6Ee9E4qqwC65oCsANsR85eI7sr4KHnsikYkXJ3p8Bn2OtLVxTyIayE4z2IefROeRYv7bqi5WhxJ01x5IlKbzzMGZNXcmf6UqMJ97pDNQedGaQy3Y8AJ19Y12bZp4iXgHWuHnBYY8GuAoJR2Q2Jc8zaHptMAV/gDWHEtOCwlqCUl9iyapU6iNdUR0D2QsX8mdYc3IhnWCuwNO7lJqo+6iCXTqgJu3Q17SP55eIaldQy/P2uYkC1xJn1BgSQ9llZaqjJrE/ldVy5cRy30LkUXW4vpGdbxiZb6F5H9heSQxYvy2R4Ci8XhGF2TpfrrPI3iIzyqpayfrKrTri40gysbwzZVj1FxI7zk0dHSX7Vm4hNf2T/Tkt9VjrS1fGoMhj7jWR1GG5B9ylR6jUq1IFlateR4E7Sy5V54oPtshE4lNLtOq8Z57eVa7barabiJ6C/tB0ngJV8K9ytX/FbmvLW6YLtfAO0vm6UfFs0DNUyiGeT1E53+H8CpRtyetqZ0063+LumZh95bcjZwfTLnM5v+CvSwedlurid9VYcnaZtkuJKvpCiXRu+nYob3VH6qKPsxz7SipWjzgjcpmvxsTXUJ9WwE3mUJNKmHlbk0q2zudQ55Uw87bOK9kazaFGKzEuslNjijp3pe/nQl+F3V2C3a2A3VmC3amAfbkE+9Jguda3JQa+dBqFKtSSu+bby5Z+loiWTDpgbp61G2FTdB6d9cXopvjY4J9L51msYQ9Pz9T2tvl2CnBlprr4y8uTCPRxL2ZT0zEu5xvSN3UnbYhPSt6xs120saDj39yjgfSQYpX+zLzwapbyv/3CX0d7/h/j+uBFp9V+3Op+311/0jH/H3fpI3pAD9HVPqcnyLk9fOO49CP9Qr/Sb/f+rX9Sf1RvatHbtwzmQ7py1B//B4d6pjs=</latexit>=

tr[X log X + (1NX) log(1NX)]

i<latexit sha1_base64="h9MfftPbphG6/kjksQAD5Gejvao=">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</latexit>

H( ) =log(1) log(1) [Bernoulli分布のShannonエントロピー]

l 独⽴な(個のBernoulli分布のShannonエントロピーと同じ
H( )  log 2 よりEEの最⼤値は N log 2<latexit sha1_base64="GJZI0fLljMTdF9aj1cc0E4tR51A=">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</latexit><latexit sha1_base64="ZQYc8FKyMn9zmET0tzid/aWUliI=">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</latexit>l Renyiエントロピーも同様<latexit sha1_base64="Uj1KrHodzweC7DwpY3PX7Wzl6Ws=">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</latexit>(n)

SA (⇢)  N log 2フェルミオンのEEの上限
SA (⇢)  N log 2<latexit sha1_base64="dPj73+dMHUweUb81riX+HIM9c60=">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</latexit>

l 粒⼦数(が有限ならば、エントロピーは有限.
注：ヒルベルト空間の次元は無限場の理論だと⼀般に紫外発散.
⾏列模型のEEは有限.

cl(⇢) . O(log N ) より⼤きい. (注: ⼀粒⼦のときは古典部分しかなかった)
l 古典部分 SA<latexit sha1_base64="qRHfIdh3qACJ/UaM6NGmhN0T8vg=">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</latexit>l 最⼤エントロピー N log 2（⽰量的, 体積則）

<latexit sha1_base64="as2i/HYD5YBkmjjU62vAxfXEgro=">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</latexit>

ü これは⼀般的な上限. 基底状態等のEEはもっと⼩さい（準⽰量的, ⾯積則）1
⼀次元⾃由フェルミガス SA (⇢) ⇠ log N
3<latexit sha1_base64="mmDa9cpk1s7RmMyNqqlIvGki9N8=">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</latexit>（あとで）Outlinen Target space EEの定義
EEの定義を拡張する

n 同種粒⼦の量⼦⼒学の場合
特にフェルミオンn 具体例
⼀次元⾃由フェルミガス

円周上のフェルミガス
<latexit sha1_base64="rcvguHK5/0EJOALp+5qyFL0qgzM=">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</latexit>• ⼀粒⼦固有関数

1 2⇡i ni x
p
(x)
=
e L
i
L

<latexit sha1_base64="RGCTJeOSv0NB0BCH8ql2AXYfIhg=">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</latexit>

L/2  x  L/2…

n1 = 0, n2 =<latexit sha1_base64="lA4H/zLERqoG323wWB6PVtgqNA0=">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</latexit><latexit sha1_base64="XhdQNNF3Oiqf2HXfPQ6kCtc2BJw=">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</latexit>• 基底状態

1, n3 = 1, n4 =2, n5 = 2, · · ·1(x1 , . . . , xN ) = p det ( i (xj ))N!

($ = 奇数 とする)

EE for a single intervall ⻑さ -. の区間のEE （円周との⽐が " ）<latexit sha1_base64="S1SwvZk5Iliz2+FoLuZLVMzYXOA=">AAANiHicnVdPc9tUEN8WKMVgSOHIRZDJkM64HiX1tPSQmYYGJgcgYZo0mdatR5afHdX6N3pyiaPxt+BLMHwDrnDgC3DgI3DmyoHfrp4Sx7FlBWkkvbe7v919+3ZXUjf2PZ3a9l83br719ju33r39Xu39D+offrRy5+NnOholrjp0Iz9KjruOVr4XqsPUS311HCfKCbq+OuoOnzD/6I1KtBeFB+k4Vi8DZxB6fc91UpA6K83jTua9nqxv391qe2Ha2bZ6p1a7YbXdE6/jrZ/elcHrV21Hp5h1Vlbtpi2HdXWwYQarZI796M6tz6hNPYrIpREFpCikFGOfHNI4X9AG2RSD9pIy0BKMPOErmlCN1oAeQU5BxgF9iPsAM5Zt0Y+Q7RnJ+XIvDDXEnK1rsePCHx9XAqRFa/af9s/2P/Yf9i/23/a/C3WxzRH8O6Eu0MMSqxlkxqApWEhw75d6mMKTmLZoE7FIIT8CNcDZgJ0IFOYHwt+c4fuiOxVea4aXIDYD+DGPyzFg25HEhDnj0tVokdKGXsQ7kbgq7IIrmgJwQ+xHBl5X9lfBQ09ktFhRsvcnwGdYaxPXBLKh7ASjfch5dAY51p9b9cXKQOLOmmPJEg3vPIxZU0vyZ7IU44l3eQbmHmxOIRfteAA6+8a6GmauEa8Aa2ycc9ijPq5CoisyDcnzFJpODabg97HmUGJaUFhLUOpLLFmlpT70kuroy164kD/BmpNz6QRzBV6+S9pE3UcV7NEh3aNd+poO8HyEqLYEtThvn5oocC1xRo0gMZBdVqY6ahL7nqyWKyeW+xYij6rD9Y3svGVkvoXmA2CPS2LA+h2JBEfhdEkUput8sc4ie4vMKKtqJesrt9oVH4eSieWdKcWqv5TYcW7m0VGyb+UWtOmf7E+v1ONcn14agyKPuddEUoflHnCXHqJSL0sVVK76PArcWTKpOld8cEQmEp+aojXPe+blu8p1W832PURPQX9oOk+BKviXubl/xW7nlrdMF2riHZTn61rF06LvUSlHeD5B5XyHcxuUHcnramdNOt/87pmYfeW3I2cH0y5yOTvnr0oHnZTq4nfVSHJ2kbYLiSr6Qol0Zvp2KG/1rtRFG2c59o1UbD7ijMhkvhwTX0F9UQE3nkGNK2FmbY0r2TqbQZ1VwszaOqtkaziDGi7FuMjOHFPUuSt9PxP6MuzeAuxeBezuAuxuBezzBdjnBsu1viMx8KXTKFRhLrlnvr0c6WeJaEmlA2bmWbsWVqPz5FlfjK6Ljw3+qXSe+Rr28fRMbe+Yb6cAV2qqi7+8PIlAG/diNjEd42K+Jn0z76SW+KTkHTvdRa05Hf/6HvWlhxSr9KfmhVfTlP/tF/46Nmb/Ma4Onm02Nx407//QWn3cMv8ft+lT+pzW0dUe0mPk3D6+cVz6iX6l3+j3eq1u1x/WH+WiN28YzCd06ah/9R+KW6sz</latexit>

overlap matrix

Xij (A) =

Z

dx
A

"

⇤
i (x) j (x)rL<latexit sha1_base64="EdqhFSZ3NBfu9X1e0aUuu9ZarnI=">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</latexit><latexit sha1_base64="A6LOhTHlErl9FMnMg5ETDT7zmEE=">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</latexit>

S(A) =

tr[X log X + (1NX) log(1N

X)]

2.0

1.5

Not linear in !

<latexit sha1_base64="vDrecQfAV5yMMxHf5ebkDgrYAHk=">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</latexit>r = 1/2
1.0

0.5

N<latexit sha1_base64="8SR7WpVnzYjWdI4Vxqcm69TDSFo=">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</latexit>

0.0

0

20

40

60

80

100

Large !
l (が⼤きいときの漸近形は解析的に計算可能 (XX模型と同じ計算に帰着)"[Jin, Korepin (2004), Calabrese, Essler (2010)]

1
S ⇠ log[2N sin(⇡r)] + ⌥1
3<latexit sha1_base64="a94a56y+hnfsxXmkjgrKlcbxSG8=">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</latexit><latexit sha1_base64="x/QZgU6eKJkrMHDsmE+EyGiqlcc=">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</latexit>⌥1 = i

Z 1

⇡w
dw
log
2
cosh
(⇡w)
1

1
2 + iw
1
iw
2

rL<latexit sha1_base64="EdqhFSZ3NBfu9X1e0aUuu9ZarnI=">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</latexit>⇠ 0.495

⾯積則(準⽰量的)！
2.0

1.5<latexit sha1_base64="vDrecQfAV5yMMxHf5ebkDgrYAHk=">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</latexit>r = 1/2
1.0

⼩さい&でも割と良い近似
0.5N<latexit sha1_base64="8SR7WpVnzYjWdI4Vxqcm69TDSFo=">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</latexit>

0.0

0

20

40

60

80

100

場の理論との⽐較<latexit sha1_base64="+W8z850evMM077FqW4Mi+Qi7JUA=">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</latexit>• (粒⼦系

S⇠

1
log[N sin(⇡r)] +3✓

1
log 2 + ⌥1
3

◆

"

rL
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S=

1
L
log
sin(⇡r) + c̃3': UV cutoff, *:̃ 正則化に依存する定数

注: XX模型の連続極限は# = 1 free fermion<latexit sha1_base64="RVWQZGKwY9AVSEFSq8s2+pFelPo=">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</latexit>

N⇠L

粒⼦数~カットオフ

場の理論的にnon universalな定数#も̃
量⼦⼒学的には意味ある?

相互情報量2#l 2つの区間の相互情報量(mutual information)<latexit sha1_base64="wtwSEu1EG/jpbIgFlHoUGv/+DA8=">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</latexit>

I(I1 ; I2 ) = S(I1 ) + S(I2 )S(I1 [ I2 ) （領域間の相関）

rL<latexit sha1_base64="f/SXvsNw+uBMia6VogI+UdBzc9Y=">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</latexit>

large ' (Fisher-Hartwig予想)
1
sin[⇡(d + r)] sin[⇡(d2 log[2N sin(⇡r)] + log
3
sin2 (⇡d)

2 0.010dL<latexit sha1_base64="F7gnruivg+2CAOJB99h/ve0X2t0=">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</latexit><latexit sha1_base64="B/qGgvIUHsr1QyDdKKHz8aO+iNQ=">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</latexit>

0.008

0.006

0.004

N = 101, r = 0.01
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0.002

0.000
0.0

2"

0.2

0.4

0.6

0.8

1.0

3

r)]

+ 2⌥1

相互情報量2#l 2つの区間の相互情報量(mutual information)<latexit sha1_base64="wtwSEu1EG/jpbIgFlHoUGv/+DA8=">AAANhHicnVdPb+NUEJ9doCyBQBeOXAxVxRbSyMmGBYSKFm1BrQS0qO222u2qit2X1Ir/yXaWTa18B74G4s4VjnwBDnwEzlw58Jt5z22aJo67tmy/NzO/mXnzZsa2E/temtn237duv/Lqa0uv33mj9uZb9bffWb777uM0GiauOnAjP0qOnG6qfC9UB5mX+eooTlQ3cHx16AweMf/wuUpSLwr3s1GsngXdfuj1PLebgXSy/LG1fW/7pPXl9kl7bcOy9niy9gk/2mvrMjt2h7HF05PlFbtpy2FdH7TMYIXMsRvdXfqAjumUInJpSAEpCinD2KcupTifUotsikF7RjloCUae8BWNqUarQA8hpyDTBX2Aex8zlu3QT5A9NZKz5Z4aaog5W0/Fjgt/fFwJkBat2n/Zv9j/2n/av9r/2P/N1cU2h/DvjBygByVWc8iMQFOwkODeK/UwgycxbVAbscggPwQ1wNmAnQgU5gfCb0/xfdGdCa8zxUsQmz78mMXlGLDtSGLCnFHpalKRSg29iHcicVXYBVc0BeCG2I8cPEf2V8FDT2RSsaJk78+Az7HWJq4xZEPZCUb7kPPoHHKsX1v1xUpf4s6aY8mSFN55GLOmjuTPeCHGE+90BmoP2hPIeTsegM6+sa6GmaeIV4A1Ni447FEPVyHhiExD8jyDphcGU/B7WHMoMS0orCUo9SWWrEqlPtIF1dGTvXAhf4Y1JxfSCeYKPL1LqYm6jyrYoQNapy36hvbx/AJR7Qhqft7umShwLXFGDSHRl11WpjpqEvtTWS1XTiz3DUQeVYfrW9l5y8h8B837wB6VxID1dyUSHIUXC6IwWefzdRbZW2RGWVUrWV+5VUd8HEgmlnemDKv+XGLHuamjo2Tfyi2kpn+yP6elHmt96cIYFHnMvSaSOiz3gLv0AJV6VaqgctXrKHBnyaXqXPGhKzKR+NQUrTrvmad3leu2mu11RE9Bf2g6T4Eq+Fe52r9it7XlDdOFmngH6XxdrXha9AMq5RDPR6ic73F+Dcqm5HW1syadb3b3TMy+8tuRs4Npl7mcX/BXpIOOS3Xxu2ooOTtP26VEFX2hRDo3fTuUt7ojdXGMsxz7XCpWjzgjcpkvxsTXUB9VwI2mUKNKmGlbo0q2zqdQ55Uw07bOK9kaTKEGCzEuslNjijp3pe/nQl+E3ZmD3amA3ZqD3aqAfTIH+8RgudY3JQa+dBqFKtSSO+bbqyv9LBEtmXTA3DxrN8Km6Dw664vRTfGxwe9J55mtYRdPz9T2pvl2CnBlprr4y8uTCBzjXszGpmNczlelb+pOaolPSt6xk13UmtHxb+5RT3pIsUp/Yl54NUl5ab/w19Ga/se4PnjcbrYeNO//2Fl5+MD8f9yh9+lDuoeu9hk9RM7t4hvHpZ/pN/qd/qgv1Rv1+/VPtejtWwbzHl056l/9D7YLpf8=</latexit>

I(I1 ; I2 ) = S(I1 ) + S(I2 )S(I1 [ I2 ) （領域間の相関）

2 0.0102"rL<latexit sha1_base64="f/SXvsNw+uBMia6VogI+UdBzc9Y=">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</latexit>dL<latexit sha1_base64="F7gnruivg+2CAOJB99h/ve0X2t0=">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</latexit>

解析形（large "）

0.008

1
sin2 (⇡d)
I(I1 ; I2 ) ⇠ log
3sin[⇡(d + r)] sin[⇡(d<latexit sha1_base64="RkWduotfiKIj5bUoNyalTZ7UQ7c=">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</latexit>

0.006

r)]

0.004

N = 101, r = 0.01
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0.002

0.000
0.0

0.2

0.4

0.6

0.8

1.0

3

& → ∞ でも有限！
場の理論でも⼀般に紫外有限.
CFT (free compact boson at self-dual radius)の結果と⼀致（なぜ？） [Calabrese, Cardy (2004)]

ま と めTarget spaceの量⼦もつれ
l 量⼦もつれの⼀般的定義•

演算⼦の部分代数ごとにエントロピーが定義できる

l 同種粒⼦の量⼦⼒学のtarget space EE•

EEの上限と有限性

l ⼀次元⾃由フェルミガス
•数値計算とラージ(での解析計算

まだ基本的なことも全然調べられていない(はず)⾊々応⽤がありそう展望
l Multi-matrix QM
今回は⾏列1個の場合(⾃由フェルミオン), 複数の場合をやりたい
BFSS, fermionic, …
量⼦⼒学ですらない場合？(IKKT), 経路積分による計算法

l 場の理論のtarget space EE (全然調べられていない)l ホログラフィーとの関係