Quantum Circuit Model of Black Hole Evaporation Yasusada Nambu - - PowerPoint PPT Presentation

quantum circuit model of black hole evaporation
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Quantum Circuit Model of Black Hole Evaporation Yasusada Nambu - - PowerPoint PPT Presentation

Quantum Circuit Model of Black Hole Evaporation Yasusada Nambu Nagoya University, Japan QIST@YITP , Kyoto June 12, 2019 T.Tokuzumi, A.Matsumura, Y.Nambu Quantum circuit model of black hole evaporation, CQG 35 (2018) 235013


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SLIDE 1

Quantum Circuit Model of Black Hole Evaporation

Yasusada Nambu

Nagoya University, Japan

QIST@YITP , Kyoto

June 12, 2019

T.Tokuzumi, A.Matsumura, Y.Nambu “Quantum circuit model of black hole evaporation”, CQG 35 (2018) 235013

QIST2019-talk.key - 2019612

slide-2
SLIDE 2

Black Hole Evaporation and Monogamy

2

Hawking radiation

j iH D Y

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black hole

JR BH ER

TH D 1 8⇡M

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thermal property entangled pair of particles Final state of evaporating system ? information issue ? Possible scenario, remnant ?

  • We want to know about

Early emitted Radiation Just emitted Radiation

particles are created around BH horizon

  • Gravitational energy of BH is extracted by particle creation

QIST2019-talk.key - 2019612

slide-3
SLIDE 3

3

Page’s Theorem

Smax D S.thermal/

A

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初期宇宙とブラックホールにおける量子情報

A+B: pure state A B

なら に対して は これは を意味しており は している

年 月 日月曜日

以上の性質をブラックホールの蒸発現象を理解するために用いてみる.ミクロな状態(素過程など)は一切無視し て,ブラックホール(系 )と 輻射(系 )の2体系として蒸発に伴ってブラックホールの次元が小さくな るとする.

時間 情報量

年 月 日月曜日

NA ⌧ NB

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If for a typical state, entanglement entropy

hSAi ⇡ log NA

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A and B are maximally entangled

初期宇宙とブラックホールにおける量子情報

なら に対して は これは を意味しており は している

年 月 日月曜日

以上の性質をブラックホールの蒸発現象を理解するために用いてみる.ミクロな状態(素過程など)は一切無視し て,ブラックホール(系 )と 輻射(系 )の2体系として蒸発に伴ってブラックホールの次元が小さくな るとする.

B R B R 時間 NB > NR NB < NR

S.thermal/

R

SR ⇡ S.thermal/

R

SB ⇡ S.thermal/

B

SR

=

SR D SB

情報量

IR D S.thermal/

R

SR

S.thermal/

B

D A 4G

年 月 日月曜日

information time EE

Page time SEE: max

Page Curve

Without detail of models, we can follow evolution

  • f EE during evaporation

if we adopt unitarity

⇢A / IA

QIST2019-talk.key - 2019612

slide-4
SLIDE 4

4

Firewall?

  • Emergence of field separable (product) state

初期宇宙とブラックホールにおける量子情報

Rearly Rlate

horizon

B

であるから よって をはさんで 場の相関がなくなり 近傍に が現れる

年 月 日月曜日

の紹介

■量子回路の話 古典計算:2進数による次の写像の事 任意の は万能ゲートとよばれる つのゲート によって実現できる:

古典計算における万能ゲート.

量子計算: 系に対するユニタリー変換の事(ハミルトニアンによる時間発展) .重ね合わせ状態に対し て実行する事が可能.量子計算における万能ゲートは に対するユニタリーゲートと に対する ゲートによって構成される. ユニタリーゲートは

After Page time,

NRearly NBNRlate

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Correlation of field between B and Rlate is lost and high energetic curtain emerges around the horizon

AMPS

Almheiri, Marolf, Polchinski and Sully 2013

B+Rlate are maximally entangled with Rearly

⇢BCRlate / IBCRlate

Effect of multipartite entanglement: entanglement cannot be freely distributed

  • This phenomena is related to entanglement monogamy

QIST2019-talk.key - 2019612

slide-5
SLIDE 5

Entanglement

5

A B

  • state is separable
  • state is entangled

jA; Bi D jAijBi

jA; Bi D ja1ijb1i C ja2ijb2i C

pure state

j˚Ci D 1 p 2 .j00i C j11i/

Bell state

entangled state: quantum mechanical non-locality

A B C 3 qubit system 2 qubit system

violation of Bell’s inequality

jGHZi D 1 p 2 .j111i C j000i/ jWi D 1 p 3 .j001i C j010i C j001i/

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QIST2019-talk.key - 2019612

slide-6
SLIDE 6

Multipartite Entanglement

6

3 qubit system Way of entanglement sharing is restricted depending on structure of states: entanglement monogamy

(3,3)-Torus trace out A entangled Borromean link trace out A dis-entangled

jWi D 1 p 3 .j001i C j010i C j001i/

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A B C A B C

N .B W C/ D p 5 1 6

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N .A W BC/ D p 2=3

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jGHZi D 1 p 2 .j111i C j000i/

A B C A B C

N .A W BC/ D 1=2

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N .B W C/ D 0

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X

analogy of link

QIST2019-talk.key - 2019612

slide-7
SLIDE 7

7

Entanglement Monogamy

A B C

EAB

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EAC

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EBC

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EAjBC EAB C EAC

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monogamy relation of entanglement trade off relation between and

EAB

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EAC

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  • universal relation characterizing multi-partite entanglement
  • sharing of quantum information, no-cloning theorem

E

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:entanglement measure

qubit system square of concurrence, negativity Gaussian system square of negativity

  • may provide upper bound of and

EAB

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EAC

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V.Coffman, J.Kundu, W.K.Wootters 1998 T.J.Osbone, F .Verstraete 2006 G.Adesso, F .Illuminati 2006

QIST2019-talk.key - 2019612

slide-8
SLIDE 8

8

  • Quantum circuit model of BH evaporation

In this talk:

  • Emergence of multi-partite entangled state and separable state


in Hawking radiation ( BH evaporation ) References

T.Tokuzumi, A.Matsumura, Y.Nambu “Quantum circuit model of black hole evaporation”, CQG 35 (2018) 235013

  • We investigate this issue using a simple model of evaporation
  • Does quantum state really evolve such as to develop firewall during


evaporation? (related to monogamy of entanglement)

QIST2019-talk.key - 2019612

slide-9
SLIDE 9

9

Quantum circuit model of BH evaporation

Rule 1:

the system is composed of n qubits

Rule 2:

entanglement between Hawking particles is generated by CNOT-U gate tan D exp .4⇡M!/

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Mn D M0 s 1 n 1 NBH

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Htot = HBH ⊗ HJR ⊗ HER.

T.Tokuzumi, A. Matsumura & YN, 2018

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BH JR ER

|ψ⟩ = |BH⟩ ⊗ |JR⟩ ⊗ |ER⟩,

no particle particle

Mass is evolved following formula of Bekenstein-Hawking entropy

QIST2019-talk.key - 2019612

slide-10
SLIDE 10

10

Rule 3:

created particles are moved outward via SWAP operation For initial state

Page curve

1 2 0. 0.2 0.4 0.6 0.8 1. time step SR

j0iJR

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j0iER1

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jBH2i

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j0iBH1

<latexit sha1_base64="4wAQFhpdxi4p6tduhc9LXndabcM=">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</latexit><latexit sha1_base64="JjQAl2UBrhKRNf5JU6YjTo4Wz2c=">ACuXicjVHNSsNAEB7jf/2LelDwUpSKBylTL/7gQaqHjyotVpoS0jitsamSchuizX2BXwBD5UPIj6FIJ4Fw8+gnhU8OLBSVoELYoTsjv7zXwz+1ojmlwgfjUIrW2tXd0dnWHenr7+gfkwaEtbpdnaV027TdtKZyZhoWSwlDmCztuEwtaSb1orLfny7wlxu2NamqDosV1ILlpE3dFUQpMgj2SITHtYULyvYvuB5L56oKbGaIk9gFAMLNzuxhjOxhOrqyiE+rNnyHWRhB2zQoQwlYGCBIN8EFTh9GYgBgkNYDjzCXPKMIM6gBiHilimLUYZKaJHWAp0yDdSis1+TB2ydupj0u8QMQwQf8RJf8R6v8Bk/fq3lUYUq4YJWv+s0xXcDxL8HD24R+ZXr9/d1VGnX6n2ZowcjSbf/8Er0S6o2xfvT8UC8jAXKDVIuRMg/hvodX7l4Pg1ubAR8SbxDF9I/Sk+4S3ptypv+sU62ziBEI0v9nNYzU5qJjofxXUaYxzq1gVjMA5TNKxZWIErEqaHsO13AjLUqatCvt1VOlgZnGL6ZxD8B6zGixA=</latexit><latexit sha1_base64="JjQAl2UBrhKRNf5JU6YjTo4Wz2c=">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</latexit><latexit sha1_base64="JjQAl2UBrhKRNf5JU6YjTo4Wz2c=">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</latexit>

j0iBH2

<latexit sha1_base64="fi59Qw5xi9LUcuJMrUX2lNakWI=">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</latexit><latexit sha1_base64="j0DXLfk+2S9fRzprzVtK9L5Jeck=">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</latexit><latexit sha1_base64="j0DXLfk+2S9fRzprzVtK9L5Jeck=">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</latexit><latexit sha1_base64="j0DXLfk+2S9fRzprzVtK9L5Jeck=">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</latexit>

step 0 step 1 step 2

BH JR ER BH JR ER BH JR ER

swap swap swap

Entanglement of BH is transferred to Radiation by SWAP operations

|ψ0⟩ = 1 √ 2

  • |10⟩ + |01⟩
  • BH12|0⟩JR|00⟩ER12.

|ψ2⟩ = 1 √ 2 |00⟩BH12|0⟩JR

  • |10⟩ + |01⟩
  • ER12.

→ |ψ1⟩ = 1 √ 2 |0⟩BH1|0⟩JR

  • |01⟩ + |10⟩
  • BH2,ER1|0⟩ER2.

QIST2019-talk.key - 2019612

slide-11
SLIDE 11

11

jBHj D 26

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jJRj D 21

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jERj D 26

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Our circuit model

13 qubits

This circuit is just one example realizing basic features of Hawking radiation and black hole evaporation

QIST2019-talk.key - 2019612

slide-12
SLIDE 12

12

Result and interpretation

Page curve negativity between BH, JR

separable

  • Information contained in BH is transferred to Radiation

Shape of Page curve depends on frequency of mode “firewall” structure but classical correlation remains (separable state)

  • After Page time, BH:JR becomes separable for low frequency modes

M4!  0:041

QIST2019-talk.key - 2019612

slide-13
SLIDE 13

13

Before Page time After Page time

j0i

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j0i

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BH ER JR ER BH JR

U

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BH JR ER BH JR ER

creation of Hawking pair

BH JR ER

swap

BH JR ER BH JR ER ER BH JR ER ER

GHZ type

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CNOT-U gates create GHZ type state exact GHZ state TH ! 1

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U=H

(maximally entangled) BH:ER pair is created as a entangled pair After successive application of CNOT-U gate, GHZ type state is created

step 4

QIST2019-talk.key - 2019612

slide-14
SLIDE 14

14

After Page time

As 1 and 2 are maximally entangled, 1 and 3 cannot establish new correlation due to monogamy of entanglement

negativity between BH, JR

CNOT-U gate tries to establish a new correlation between GHZ type state and previously generated Hawking pair

BH ER BH ER JR ER

CNOT-U

Monogamous property of multipartite state is related to emergence of separable state (firewall)

BH: JR becomes separable for M4!  0:041

step 5

3 1 2

E1j23 E12 C E13

QIST2019-talk.key - 2019612

slide-15
SLIDE 15

Summary

15

  • Circuit model of BH evaporation
  • Formation of GHZ type state after Page time

emergence of separable state between BH & R for low frequency modes

  • We observed effect of multipartite entanglement (monogamy) 


is a reason why the separable state (firewall-like structure) emerges
 in our evaporation model.

  • Different evolution scenario of evaporation

initial condition, structure of circuit A pair of qubit detectors cannot reveal entanglement beyond super horizon scale

  • Entanglement harvesting in de Sitter space

Local noise of de Sitter space kills quantum correlation (but this is related to monogamy of entanglement) This behavior can be understood from monogamy of qubit-qubit-environment (quantum field)

A B

r negativity

rp

rmax D 2H 1

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QIST2019-talk.key - 2019612