Relativistic Relativistic Quantum Information Quantum Information George E.A. Matsas George E.A. Matsas Instituto de F Instituto de F í í sica Te sica Te ó ó rica/Unesp rica/Unesp
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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)
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