Circuiti ottici integrati per l'informazione quantistica

7/29/2019 Circuiti ottici integrati per l'informazione quantistica

1/23


2/23


3/23


4/23


5/23

H H1H2

H = H1 H2

H1 H2


6/23

|0i |1i H

{|0i1 |0i2 , |0i1 |1i2 , |1i1 |0i2 , |1i1 |1i2}

|iH

|i =1X

i,j=0

cij |ii1 |ji2

|i =Xi,j

cij |iji .

|i1 H1|i2 H2

|1i = 1p2

(|01i + |11i)

|1i = 1p2

(|0i + |1i) |1i .

|2i = 1p2

(|00i + |11i)


7/23

SA B O

x

y

z

B A

A B

12

|i = 1p2

(|01i |10i),

|0i |1iz +1

1

z

(A)z = +1 |01i

(B)z = 1

|i = 1p2

(|+i |+i),

|+

i= 1p

2(|0

i+ |1

i) |

i= 1p

2(|0

i |1

i)

x x +1 1(A)x = +1

(B)x = 1 x z

[x,z] = i~y


8/23

0 1

n 2n

12 |0i |1i

|i = |0i+ |1i ,

||2+||2

= 1 {|0i , |1i}

|i = cos 2

|0i + ei sin 2

|1i ,

0

0

2

=Xi

pi |ii hi| .


9/23

= |i h| T r = T r(2) = 1T r = 1 T r(2) < 1

=

||2

||2

.

AB =

0BB@

0 0 0 00 12 12 00 12 12 00 0 0 0

1CCA .

AB =Xi

pi |aiiA hai|A |biiB hbi|B Xi

piAi Bi .

U U = U1 0

U

0 = UU

.

|i =r

1 + z

2|0i + x + iyp

2(1 + z)|1i

n

U(n, ) = ei

2n~.

x

x


10/23

_

x

y

z

1

0

n

n n

|i =2n1Xi=0

ci |ii ,

2n1Xi=0

|ci|2

= 1

n = 2 |i

|i = c0 |1i+ c1 |2i + c2 |2i + c3 |3i = c00 |00i + c01 |01i + c10 |10i + c11 |11i .

2n


11/23

2n

n

2n2n2 2 4 4

H =1

p2 1 1

1 1 .

{|0i , |1i}{|+i , |i}

H|0i = 1p2

(|0i + |1i) |+i ,

H|1i = 1p2

(|0i |1i) |i .

H2 = I (H) = H H

{|+i , |i} {|0i , |1i} .

Rz() =

1 00 ei

.


12/23

|0i ei|1

i |i

z

2

|1i |0i

|1i

|00i =

2664

1000

3775 , |01i =

2664

0100

3775 ,

|10i =

2664

0010

3775 , |11i =

2664

0001

3775 ,

4

4

CNOT =

2664

1 0 0 00 1 0 00 0 0 10 0 1 0

3775 .


13/23

(CNOT)2 = I

CNOT( |0i + |1i) |0i = |00i + |11i ,

|0i |1i


14/23


15/23

|i

|i = |Hi + |Vi ,

|Hi |Vi

x2 =

4

|i = |1it1 + ei |1it2 ,


16/23

nf nc

max c = arcsinncnf

OUT1

Interactionlength

IN1IN2

OUT2

i

i

i l

16 m 3.5 m

16 m


17/23

T0

VA

C1

T1

VB

C0

1/2

1/3

1/3

1/3

1/2

1/2 1/3

1/2 = 0.4 0.6

3/2 = 0.27 0.4

|0iC |0iT |0iC |1iT|1iC |0iT |1iC |1iT

|0iC 98.5%94.3 0.2%

T0 T1

|11iT0T1 ! (|20iT0T1 |02iT0T1)/p

2,

VB C1VB C1 VB C1

T0 T1T0 T1

|20i |02i92%


18/23

.

.

.

.

0,2

0,4

0,6

0,8

1,0

00

01

10

11

Input Oupu

t

P

0,2

0,4

0,6

0,8

1,0

00

01

10

11

Outpu

t

P

Input

0,2

0,4

0,6

0,8

1,0

00

01

10

11

Input Oupu

t

P

00

01

10

0,2

0,4

0,6

0,8

1,0

00

01

10

11

Input Oupu

t

P

00

01

10

11

00

01

10

11

11

00

01

10

11

0,2

0,4

0,6

0,8

1,0

00

01

10

11

Input Oupu

t

0,2

0,4

0,6

0,8

1,0

00

01

10

11

Input Oupu

t

P

00

01

10

11

00

01

10

11

HHHA B C

| |


19/23

> 1 nm

DL

WP

PBS

IF

PC

SMF

CNOT

INC

OUTC

OUTT

SPCMMMFWP

PBS

INT

PPDC1 PPDC3

PPDC2

WPC

C

|

|

|

|

|

|

|

||

||

|

|

|

|

|

= 806nm


20/23

TH = 0 TV =23

TH =13 TV = 1

|0iC = |ViC |1iC = |HiC |0iT = |AiT |1iT = |DiT |Ai = 1p2(|Hi+ |Vi)|Di = 1p

2(|Hi |Vi)

. . .

1

0.75

0.5

0.25

0

1

0.75

0.5

0.25

OutputOutput

Input

Input

+

+

+

+0

1

100

+1

+1

+0

+0

1

0.75

0.5

0.25

0

0

0.25

0.5

|11

|11

|10

|10

|01

|01

|00

|11|10

|01|00

|00

|11|10

|01|00

|+iC |0iT+

|0iC |0iT |0iC |1iT|1iC |0iT |1iC |1iT94.0 0.4%

|iC |0iT , |iC |1iT|i = 1p

2(|0i |1i)


21/23

|i = 1p2

(|0iC |0iT|1iC |1iT |i = 1p2(|0iC |1iT|1iC |0iT91.2 0.5%

87.7 0.7%


22/23


23/23

a

Circuiti ottici integrati per l'informazione quantistica

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