Relativistic Relativistic Quantum InformationQuantum Information

George E.A. MatsasGeorge E.A. MatsasInstituto de FInstituto de Fíísica Tesica Teóórica/Unesprica/Unesp

MotivationMotivation

H

UNITARY

MotivationMotivation

H

UNITARY

QFT Curved Spacetimes

MotivationMotivation

H

UNITARY

NON UNITARY

QFT Curved Spacetimes

MotivationMotivation

H

UNITARY

CLASSICAL APARATUS

QFT Curved Spacetimes

MotivationMotivation

H

UNITARY

CLASSICAL APARATUS

QFT Curved Spacetimes

Relativistic Quantum Information

�� AndrAndréé Landulfo (PhD)Landulfo (PhD)�� Adriano Torres (PhD)Adriano Torres (PhD)�� Katja Ried (MSc)Katja Ried (MSc)

StudentsStudents

Sistema de 2 partSistema de 2 partíículas c/ spin total nuloculas c/ spin total nulo

0=== zyx SSS

02 =S

Desigualdades de BellDesigualdades de Bell

Medida de PolarizaMedida de Polarizaçãçãoo

POLARÍMETROS

0=== zyx SSS

02 =S

+ +

1±

−

1±

−

Medida de PolarizaMedida de Polarizaçãçãoo

+

−

1+ 1−

0=== zyx SSS

02 =S

BellBell

��““For me, it is so reasonable to assume that the photons in those experiments carry with them programs, which have been correlated in advance, telling them how to behave.””

��John S. Bell (1928John S. Bell (1928--1990)1990)

DescriDescriçãção Clo Cláássica (intuitiva)ssica (intuitiva)

DescriDescriçãção Clo Cláássica (intuitiva)ssica (intuitiva)

DescriDescriçãção Clo Cláássica (intuitiva)ssica (intuitiva)

DescriDescriçãção Clo Cláássica (intuitiva)ssica (intuitiva)

+

1+ 1−

−

T.V.O.L.

M.Q.

MecMecâânica Qunica Quâânticantica T.V.O.L ???T.V.O.L ???⊂

Teoria de VariTeoria de Variááveis Ocultasveis Ocultasc

b

1 2

z

# P 1 2

N1 [+z,+b,+c] [-z,-b,-c]

N2 [+z,+b,-c] [-z,-b,+c]

N3 [+z,-b,+c] [-z,+b, -c]

N4 [+z,-b,-c] [-z,+b,+c]

N5 [-z,+b,+c] [+z,-b,-c]

N6 [-z,+b,-c] [+z,-b,+c]

N7 [-z,-b,+c] [+z,+b,-c]

N8 [-z,-b,-c] [+z,+b,+c]

zc

b

Teoria de VariTeoria de Variááveis Ocultasveis Ocultas

1 2

z

# P 1 2

N1 [+z,+b,+c] [-z,-b,-c]

N2 [+z,+b,-c] [-z,-b,+c]

N3 [+z,-b,+c] [-z,+b, -c]

N4 [+z,-b,-c] [-z,+b,+c]

N5 [-z,+b,+c] [+z,-b,-c]

N6 [-z,+b,-c] [+z,-b,+c]

N7 [-z,-b,+c] [+z,+b,-c]

N8 [-z,-b,-c] [+z,+b,+c]

b

Teoria de VariTeoria de Variááveis Ocultasveis Ocultas

b

1 2

# P 1 2

N1 [+z,+b,+c] [-z,-b,-c]

N2 [+z,+b,-c] [-z,-b,+c]

N3 [+z,-b,+c] [-z,+b, -c]

N4 [+z,-b,-c] [-z,+b,+c]

N5 [-z,+b,+c] [+z,-b,-c]

N6 [-z,+b,-c] [+z,-b,+c]

N7 [-z,-b,+c] [+z,+b,-c]

N8 [-z,-b,-c] [+z,+b,+c]

b

Teoria de VariTeoria de Variááveis Ocultasveis Ocultasc

1 2

# P 1 2

N1 [+z,+b,+c] [-z,-b,-c]

N2 [+z,+b,-c] [-z,-b,+c]

N3 [+z,-b,+c] [-z,+b, -c]

N4 [+z,-b,-c] [-z,+b,+c]

N5 [-z,+b,+c] [+z,-b,-c]

N6 [-z,+b,-c] [+z,-b,+c]

N7 [-z,-b,+c] [+z,+b,-c]

N8 [-z,-b,-c] [+z,+b,+c]

z

1 2

Teoria de VariTeoria de Variááveis Ocultasveis Ocultasc+

b−

# P 1 2

N1 [+z,+b,+c] [-z,-b,-c]

N2 [+z,+b,-c] [-z,-b,+c]

N3 [+z,-b,+c] [-z,+b, -c]

N4 [+z,-b,-c] [-z,+b,+c]

N5 [-z,+b,+c] [+z,-b,-c]

N6 [-z,+b,-c] [+z,-b,+c]

N7 [-z,-b,+c] [+z,+b,-c]

N8 [-z,-b,-c] [+z,+b,+c]

1 2

# P 1 2

N1 [+z,+b,+c] [-z,-b,-c]

XX [+z,+b,-c] [-z,-b,+c]

N3 [+z,-b,+c] [-z,+b, -c]

XX [+z,-b,-c] [-z,+b,+c]

N5 [-z,+b,+c] [+z,-b,-c]

XX [-z,+b,-c] [+z,-b,+c]

N7 [-z,-b,+c] [+z,+b,-c]

XX [-z,-b,-c] [+z,+b,+c]

Teoria de VariTeoria de Variááveis Ocultasveis Ocultasc+

b−

1 2

# P 1 2

N1 [+z,+b,+c] [-z,-b,-c]

XX [+z,+b,-c] [-z,-b,+c]

XX [+z,-b,+c] [-z,+b, -c]

XX [+z,-b,-c] [-z,+b,+c]

N5 [-z,+b,+c] [+z,-b,-c]

XX [-z,+b,-c] [+z,-b,+c]

XX [-z,-b,+c] [+z,+b,-c]

XX [-z,-b,-c] [+z,+b,+c]

Teoria de VariTeoria de Variááveis Ocultasveis Ocultasc+

b−

1

2

φ

φ1a

12ˆˆ ba = 21

ˆˆ ab =

2b

ClauserClauser--HorneHorne--ShimonyShimony--HoltHolt

1

2

φ

φ1a

12ˆˆ ba = 21

ˆˆ ab =

2b

ClauserClauser--HorneHorne--ShimonyShimony--HoltHolt

N a1

a2b1

b2

1 +1 -1

1

2

φ

φ1a

12ˆˆ ba = 21

ˆˆ ab =

2b

ClauserClauser--HorneHorne--ShimonyShimony--HoltHolt

N a1

a2b1

b2

1 +1 -1

2 +1 -1

1

2

φ

φ1a

12ˆˆ ba = 21

ˆˆ ab =

2b

ClauserClauser--HorneHorne--ShimonyShimony--HoltHolt

N a1

a2b1

b2

1 +1 -1

2 +1 -1

3 -1 -1

4 +1 -1

5 -1 +1

...

1.000.000 +1 -1

1b1a

2a

2b

ClauserClauser--HorneHorne--ShimonyShimony--HoltHolt

φ

φ

N a1

a2b1

b2

1 +1 -1

2 +1 -1

3 -1 -1

4 +1 -1

5 -1 +1

...

1.000.000 +1 -1

1 2

φ

φ

ClauserClauser--HorneHorne--ShimonyShimony--HoltHolt

1a2a 1b

2b

2)( ≤φF

ÁREA PROIBIDA PARA T.V.O.L.

φ

φ

2)( ≤φF

T.V.O.L.

M.Q.ÁREA PROIBIDA PARA T.V.O.L.

MecMecâânica Qunica Quâânticantica T.V.O.L T.V.O.L ⊂

T.V.O.L.M.Q.

AREA PROIBIDA PARA T.V.O.L.

MecMecâânica Qunica Quâânticantica T.V.O.L T.V.O.L ⊄

EXPERIEXPERIÊÊNCIANCIAVERE DICTUM FINALVERE DICTUM FINAL

AREA PROIBIDA PARA T.V.O.L.

( )2121

ˆˆˆˆ2

1zzzz +⊗−−−⊗+=Ψ

Estado Emaranhado

0=== zyx SSS

02 =S

COMPATÍVEL c/ MECÂNICA QUÂNTICA

φ

φ

��““Unperformed Unperformed experiments have no experiments have no resultsresults.””

��Asher Peres (1934Asher Peres (1934--2005)2005)

PeresPeres

OneOne--particle angular momentum particle angular momentum

???2222

zyx LLLL ++=

4/15)12/3)(2/3(2 =+=L

2/3=l

2/3,2/1 ±±=iL

Relativistic Quantum Entanglement Relativistic Quantum Entanglement

( )XX dd vtg 1−−=α

QUANTUM MECHANICAL + RELATIVITY RESULT

φ

´´´,

,

´ ssp

sp

ptr rrr

rr

→

Λ↓

´

,

s

ssp ptr

r

rrr

Λ↓

→

Quantum Teleportation Quantum Teleportation

userwww.sfsu.edu

classical signal

⟩⟩⊗−⟩⟩⊗=⟩ CBCBBC 0|1|2

11|0|

2

1|ψ⟩+⟩=⟩ AAA 1|

2

10|

2

1|ϕ

Bell measurement

Teleportation for accelerated qubits Teleportation for accelerated qubits

userwww.sfsu.edu

end of acceleration

beginning of acceleration

classical signal

⟩⟩⊗−⟩⟩⊗=⟩ CBCBBC 0|1|2

11|0|

2

1|ψ⟩+⟩=⟩ AAA 1|

2

10|

2

1|ϕ

Bell measurement

TIM

E

Minkowski vacuum

Unruh effect

TIM

E

userwww.sfsu.edu

end of acceleration

beginning of acceleration

classical signal

⟩⟩⊗−⟩⟩⊗=⟩ CBCBBC 0|1|2

11|0|

2

1|ψ⟩+⟩=⟩ AAA 1|

2

10|

2

1|ϕ

Bell measurement

Sudden death of the entanglement between the qubits

userwww.sfsu.edu

end of acceleration

beginning of acceleration

classical signal

⟩⟩⊗−⟩⟩⊗=⟩ CBCBBC 0|1|2

11|0|

2

1|ψ⟩+⟩=⟩ AAA 1|

2

10|

2

1|ϕ

Bell measurement

Teleportation fidelity

Teleportation around Black HolesTeleportation around Black Holes

userwww.sfsu.edu

classical signal

⟩+⟩=⟩ AAA 1|2

10|

2

1|ϕ

Bell measurementend of acceleration

beginning of acceleration

⟩⟩⊗−⟩⟩⊗=⟩ CBCBBC 0|1|2

11|0|

2

1|ψ

Q. Information and Black HolesQ. Information and Black Holes

Q. Information and Black HolesQ. Information and Black Holes

)( +− ℑ−≡ JMBBlack Hole:

Event Horizon: MJH I& )( +− ℑ≡

Space

Time

Black Hole and Q. MechanicsBlack Hole and Q. Mechanics

Entropy: bhbh AG

kcS

h4

3

=

Temperature: 08

3

=== JQGMk

cTbh π

h

Area: 016 2 === JQMAbh π

Information Loss in Black HolesInformation Loss in Black Holes

Is there any problem?Is there any problem?

��““I think of my lifetime as I think of my lifetime as divided into three periods. In divided into three periods. In the first I was in the grip that the first I was in the grip that everything is everything is ParticlesParticles...I call ...I call my second period my second period ““Everything Everything is is FieldsFields..””..Now I am in the ..Now I am in the grip of a new vision, that grip of a new vision, that everything iseverything is InformationInformation””

��John A. Wheeler (1911John A. Wheeler (1911--2008)2008)