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Page 1: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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��

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�� ! "#

$%�& '&()**'++��

,- ./0123 0

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,>? ./< ,06B />/<AED,=FHG>/-7 .< /8I 5 JKB8 - /BC

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Page 2: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 3: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

�YZ ���[\����[][^� ��_�� [

��� �`

ab5 ..7 2B8 /5 >b5 ..3c 8 /5 >

,2/@7B >?156< ;B .7 /0c 7 .J7@8 2I @5 ..7 2B87? />J5 .0B8 /5 >

ab5 ..7 2B8 /5 >47@5 -7 .I

,2/@7B >?1568B d7B@8 /5 >85 .7@5 -7 .c 7 .J7@8@5 ..7 2B8 /5 >

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Page 4: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

�����Y� �

� ��`�� [[� �

0 1

0 1

10

1

0 1

11

0 1

0

noisy channel

Alice

Bob

time

a,2/@7<7 >?<6 /8<85 156

ab5 ..7 2B8 /5 >@5 ..3c 8 /5 >6I 8 ;7>5 /<I @ ;B >>7 2

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Page 5: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

Z� [_Z

� ��`�� [[� �

Alice

noisy channel

Bob

imperfect

entanglement

|0>

time

a,2/@7<7 >?<g 36 /8<85 156

ah>8B >i 27 07>8@5 ..3c 8 /5 >6I 8 ;7>5 /<I @ ;B >>7 2

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Page 6: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

k� ��� ��_�� [ml

n� ����o�[\

a@ 2B<< /@B 2 pp@5 ..7 2B8 /5 > q@5 ..7 2B8 /5 >

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Page 7: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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�Y� n� �`

ast� u� "+ 'u�v + t!+�# w

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ax�y ! t!+ 'u�v + t!+�# w

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Page 8: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

�� n� [_�n�_��_�\ `

encode

decode

Alice

noisy channel

Bob

perfect correlation

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ah..5 .b5 ..7@8 />i b5?7<A hbb<C

a{ 3B >83 0h..5 .b5 ..7@8 />i b5?7<A { hbb<C

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Page 9: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

��� �� ���Y_�[\�o��

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D~c

Alice

Bob

c

m

m

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Page 10: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

�� � ��_�n�_��_�\ `

}s bits

noisy channel

local operation

local operation

Alice

Bob

perfect correlation

ab5 ..7 2B8 /5 >.7c B /.7?B J87 .8 ;7@5 ..3c 8 /5 >

a,2/@7B >?1567�@ ;B >i 7�6 /8<85 .7@5 -7 .8 ;7@5 ..7 2B8 /5 >

 ,==G¡¢�D� �p>5 /<7 27<<@ 2B<< /@B 2@5 003 >/@B8 /5 >

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Page 11: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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s bitsnoisy channel

local operation

local operationB

ob

Alice

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Page 12: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

][^� ��_�� [

�� [������ [

,2/@7¥ /< ;7<858 .B >< 0/8�85 156� >5 /<7 27<< 2I

y t� u� "+ 'u�noisy channel

E

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c

m

m

t�y ! t!+ 'u�

}s bits

noisy channel

local operation

local operation

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ª ¦�7@5? />i p� q«A ¨§C

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�¦�/<8 /22B8 /5 >p

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Page 13: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

}s bits

noisy channel

local operation

local operation

noisy channelE

D~c

c

m

m

Quantum

Error C

orrecting Code

Error C

orrecting Code

Entanglem

ent Distillation P

rotocol

Correlation D

istillation Protocol

classical

quantum

s

statusw

ell−studied, w

ell−understood

less studied, fewer results

overheadc

m

preven

tiverep

arative

| | − | |

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Page 14: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

}s bits

noisy channel

local operation

local operation

noisy channelE

D~c

c

m

m

Quantum

Error C

orrecting Code

Error C

orrecting Code

Entanglem

ent Distillation P

rotocol

Correlation D

istillation Protocol

classical

quantum

s

statusw

ell−studied, w

ell−understood

less studied, fewer results

overheadc

m

preven

tiverep

arative

| | − | |

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Page 15: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 16: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

��� �� ���Y_�� [��

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E

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c

m

m

t�y ! t!+ 'u�

}s bits

noisy channel

local operation

local operation

>5 > �/>87 .B@8 /-7

/>87 .B@8 /-7

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Page 17: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

"An ounce of prevention is w

orth a pound of cure."

AE°±Dp�c 53 >? q�² 53 >@7<C

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Xz

Page 18: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

³´"µ ¶ "·�)¸st� u� "+ ') "'&¹) t+ %! s)¶ "º)¸(¶ t� »½¼

y t� u� "+ 'u�noisy channel

E

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c

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m

t�y ! t!+ 'u�

}s bits

noisy channel

local operation

local operation

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� -7 .;7B? q�

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Page 19: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 20: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

][^� ��_�� [

�� [������ [

y t� u� "+ 'u�noisy channel

E

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c

m

m

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}s bits

noisy channel

local operation

local operation

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Page 21: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

��� ^

$ÀÁA~}������C �2/>7B .hbbÂA~}���C �6 /8b �¢

message

k

checksum

kn

−k

message

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Page 22: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

an ounce

"An ounce of prevention is w

orth a pound of cure."

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Page 23: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

[_� [\ ��� [_

��_����_�� [

��_�

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Page 24: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

"In a corrupted quantum w

orld, prevention is useless, yet there is cure."

"An ounce of prevention is w

orth a pound of cure."

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Page 25: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

ËÌÍÍÎ ÏÐÑ ÒÌÓÔÒÕÑ ÒÏÏÐÑ ÒÌÓÖÐÕÌÍÎ ×ØØ ÏÒÙÐÑ ÒÌÓÕ

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st� u� "+ 'u�7>@5? />i 03<8c .7@7?78 ;7>5 /<7

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ÜÆ;B8 /J8 ;7>5 /<7 05?7 2/<? /á7 .7>8 ¿ÞÝ

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Page 26: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

� [o�

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0 1

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1

,.7B 2 �8 /07� -7 ./ãB6 27.B >?5 0<53 .@7

a-7 ./ãB6 27 25887 .I

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Page 27: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

� ä_�Z ��o�� [o�

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ner)B

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a47B 2 �8 /07-7 ./ãB6 27 pA B 205<8C 7-7 .I 5 >7@B ><778 ;7c 3 2<B .

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Page 28: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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ner)

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Page 29: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

ËÌÍÍÎ ÏÐÑ ÒÌÓåÎÙÌæÎ Íç�èÌÍåÐ ÓéÌêëÎÐÙÌÓÕ

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Alice (ow

ner)

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Page 30: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

��� �� ��ïY_ðñ [ñ [òó ôõò ö÷ø

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Page 31: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 32: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 33: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 34: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

óò PMó

[\OõM öO]óM ON P

^`_a[ò ôb

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Bob

perfect entanglement

perfect correlation

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ùkon��� ÿÿ�m � ����ü ÿ� � �ü� �� ÿ��T � �ü�

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Page 35: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

óò PMó

[\OõM öO]óM ON P

^[ò ôôOq[b

Alice

Bob

Eve

Ucorrupted entanglem

ent

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�� ������� � !!" �

7 r

Page 36: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

ööN öN öö[sM ON PqN ö

t[ ÷

Z RWW��� ��� ��� �ü ��� ÿ���� � ��� �ü�û ���

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Page 37: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

Z � �ü �w��x��ü ���ü �û �y� ��û ��û ����ü �û ������ �z� �� �ü �û�� ÿ

�� ������� � !!" �

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Page 38: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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n��û ���ü �û ���� �� ���� �û �

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k � ���� ��� �û ���� � ÿm

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k �� ���ü� ��û ��û ����ü� ÿ�� �m

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Z � �ü �w��x��ü ���ü �û �Z RWW��û � �ü� ÿ�

k � �z� �� �ü�û ��� �û�� ÿ�m

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Page 39: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 40: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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local operation

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Alice

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Page 41: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

����� ��������� � ���� �� ¡¡������ �� �¢� £¤ �� ����

}s bits

local operation

local operation

Alice

Bob

"noise model"

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Page 42: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 44: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 45: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 46: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 47: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 48: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 51: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 53: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 54: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 55: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 56: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 57: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 58: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 59: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 60: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 63: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 68: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 69: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 70: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 71: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 72: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 73: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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Page 79: P QSR P T - Carnegie Mellon School of Computer Scienceyangke/thesis/prop-slide.pdf · U U U U U U U U L L L L L L bounded corruption binary symmetric binary erasure tensor product

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