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Transcript of Teleportation
![Page 1: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/1.jpg)
Teleportation
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2 bits
Teleportation
BELL MEASUREMENT
![Page 3: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/3.jpg)
Bell States
1 2 1 2
1 2 1 2
1 2 1 2
1 2 1 2
1
21
21
21
2
1 2EPR
EPR
EPR z
EPR
EPR
x
y
spin rotation
one spin rotation
![Page 4: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/4.jpg)
2 bits
BELL MEASUREMENT
1 1 2 3 2 3
1
2
1 2 1 2 3 3
1 2 1 2 3 3
1 2 1 2 3 3
1 2 1 2 3 3
![Page 5: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/5.jpg)
The EPR-Bohm State
1 2 1 2 1 2 1 2
10, 0
2x x z zEPR
1 2EPR
David Bohm
![Page 6: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/6.jpg)
iBELL
EPR
x
x
3i Teleportation
3i
![Page 7: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/7.jpg)
The EPR State
1 2 1 20, 0EPR q q p p
1q 2q
1q a 2q aEPR
![Page 8: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/8.jpg)
The EPR State
1 2 1 20, 0EPR q q p p
1q 2q
1q EPR 1
* q
![Page 9: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/9.jpg)
The EPR State
1q 2q
EPR
1 2 1 20, 0EPR q q p p
![Page 10: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/10.jpg)
,a bBELL
EPR
,a b
Continuous Variables Teleportation
unknown *
ab
ab
ab
shift , kick a b
( )ibqe q a
L. Vaidman,PRA 49, 1473 (1994)
1 2 1 2, ,a b q q a pBELL p b
![Page 11: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/11.jpg)
1 2EPR
spin measurement
The EPR State = teleportation machine of a known spin up to a flip
![Page 12: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/12.jpg)
1 2EPR
spin measurement
The EPR State = teleportation machine of a known spin up to a flip
![Page 13: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/13.jpg)
1 2EPR
spin measurement
The EPR State = teleportation machine of a known spin up to a flip
![Page 14: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/14.jpg)
Many-Worlds Interpretation
1 2EPR
spin measurement
mixture of and
In the Universe is not moved from Alice to Bob
But in Teleportation it is moved!
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Teleportation
In all worlds!
mixture of and and and But after rotation we get
The information sent is only about in which world we are
i
Local Bell measurements split the nonlocal world and thebranching is the carier of the huge amount of information.
![Page 16: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/16.jpg)
We cannot measure (scan) Ψ Too much information to send We cannot clone Ψ
We do not scan Ψ
Why teleportation is possible?
We do not clone Ψ
![Page 17: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/17.jpg)
We cannot measure (scan) Ψ Too much information to send We cannot clone Ψ
We do not scan Ψ
Why teleportation is possible?
We do not clone Ψ
Most of information is in branching of the world
![Page 18: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/18.jpg)
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Paradoxes in the context of the Aharonov-Bohm
and the Aharonov-Casher effects
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Mach Zehnder Interferometer
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Mach Zehnder Interferometer
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Mach Zehnder Interferometer
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Mach Zehnder Interferometer
1| | |
2a b
1| | |
2a b
1| | |
2a b
1| | |
2a b
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Aharonov-Bohm Effect:
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SOLENOID
Aharonov-Bohm Effect
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Aharonov-Bohm Effect
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1| | |
2a b
1| | |
2a b
1| | |
2a b
1| | |
2a b
Aharonov-Bohm Effect
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1| | |
2a b
1| | |
2a b
The solenoid causes a relative phase, but the time when the phase is gained depends on the choice of gauge, and therefore, it is unobservable.
Aharonov-Bohm Effect
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21| | |
2
ia e b
2ie
Aharonov-Bohm Effect The solenoid causes a relative phase, but the time when the phase is gained depends on the choice of gauge, and therefore, it is unobservable.
![Page 32: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/32.jpg)
21| | |
2
ia e b
2ie
Aharonov-Bohm Effect The solenoid causes a relative phase, but the time when the phase is gained depends on the choice of gauge, and therefore, it is unobservable.
![Page 33: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/33.jpg)
1| | |
2a b
1| | |
2a b
Aharonov-Bohm Effect
A
The solenoid causes a relative phase, but the time when the phase is gained depends on the choice of gauge, and therefore, it is unobservable.
![Page 34: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/34.jpg)
1| | |
2a b
1| | |
2a b
Aharonov-Bohm Effect
A
The solenoid causes a relative phase, but the time when the phase is gained depends on the choice of gauge, and therefore, it is unobservable.
![Page 35: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/35.jpg)
Paradox I
1| | |
2a b
1| | |
2ia e b
At every place on the paths of the wave packets of the electron there is no observable action, but nevertheless, the relative phase is obtained.
![Page 36: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/36.jpg)
The relative phase is observable locally, therefore the time of change of the relative phase can be observed, in contradiction with the fact that it is a gauge dependent property.
Paradox II
1| | |
2a b
1| | |
2ia e b
1| | |
2ia e b
ie
![Page 37: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/37.jpg)
1| | |
2ia e b
The relative phase is observable locally
![Page 38: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/38.jpg)
1 1| | | |1 | 0 | 0 |1
2 2i i
A B A Ba e b e
| |1 Aa | |1 Bb
Ax Bx
A B
x
1| | |
2ia e b
1| | | |
2i
A B A Be
The relative phase is observable locally
EPR correlations are observable locally
![Page 39: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/39.jpg)
Ax Bx
A B
x
t
0
1| | | | |
2i
EPR A B A Be
A B
RESULTS OF LOCAL MEASUREMENTS RELATIVE PHASE
(| ,| ) 0,z A z Bprob 2|1 |
(| ,| ) 0,...8
i
x A x B
eprob
![Page 40: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/40.jpg)
1 1| | | |1 | 0 | 0 |1
2 2i i
A B A Ba e b e
| |1 Aa | |1 Bb
Ax Bx
A B
x
t
0
PHOTON QUANTUM WAVE EPR
1| | |
2ia e b
![Page 41: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/41.jpg)
Ax Bx
A B
x
t
0
1 1| | | | | |
2 2i i
A B A Ba e b e
PHOTON QUANTUM WAVE EPR
![Page 42: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/42.jpg)
Ax Bx
A B
x
t
0
1 1| | | | | |
2 2i i
A B A Ba e b e
h B
B
B
PHOTON QUANTUM WAVE EPR
![Page 43: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/43.jpg)
Ax Bx
A B
x
t
0
1 1| | | | | |
2 2i i
A B A Ba e b e
h B †ˆ ˆ| | | |A BH H a a
B
B
1 1|1 | 0 | 0 |1 | | | | | |
2 2i i
A B A B A B A B A Be e
PHOTON QUANTUM WAVE EPR
![Page 44: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/44.jpg)
Ax Bx
A B
x
t
0
1 1| | | | | |
2 2i i
A B A Ba e b e
B
B
h B †ˆ ˆ| | | |A BH H a a
1 1|1 | 0 | 0 |1 | | | | | |
2 2i i
A B A B A B A B A Be e
LOCAL SPIN MEASUREMENTS RELATIVE PHASE
PHOTON QUANTUM WAVE EPR
![Page 45: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/45.jpg)
Ax Bx
A B
x
t
0
1 0h E E h B INSTEAD OF
REALISTIC EXPERIMENT: TWO-LEVEL ATOM | |
| |
z
z
e
g
PHOTON QUANTUM WAVE EPR
INSTEAD OF A SPIN IN THE MAGNETIC FIELD
![Page 46: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/46.jpg)
Ax Bx
A B
x
t
0
REALISTIC EXPERIMENT: TWO-LEVEL ATOM INSTEAD OF A SPIN IN THE MAGNETIC FIELD
| |
| |
z
z
e
g
PHOTON QUANTUM WAVE EPR
†ˆ ˆ| | | |A BH H a g e a e g
1 1|1 | 0 | 0 |1 | | | | | |
2 2i i
A B A B A B A B A Be g g e g e g e
†ˆ ˆ| | | |A BH H a a
1 1|1 | 0 | 0 |1 | | | | | |
2 2i i
A B A B A B A B A Be e
1 0h E E h B INSTEAD OF
![Page 47: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/47.jpg)
Ax Bx
A B
x
t
0
REALISTIC EXPERIMENT: TWO-LEVEL ATOM INSTEAD OF A SPIN IN THE MAGNETIC FIELD
| |
| |
z
z
e
g
PHOTON QUANTUM WAVE EPR
†ˆ ˆ| | | |A BH H a g e a e g
1 1|1 | 0 | 0 |1 | | | | | |
2 2i i
A B A B A B A B A Be g g e g e g e
†ˆ ˆ| | | |A BH H a a
1 1|1 | 0 | 0 |1 | | | | | |
2 2i i
A B A B A B A B A Be e
1 0h E E h B INSTEAD OF
![Page 48: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/48.jpg)
†ˆ ˆ| | | |H a g e a e g
HOW TO MAKE THE ANALOG OF THE SPIN MEASUREMENTS ON THE ATOM?
1 1| (| | ), | (| | )
2 2x xe g g e ARE NOT MEASURABLE DIRECTLY
ROTATION IN | |e g SPACE
COUPLING H TO A COHERENT STATE | , | | 1 | |2| |
!
n
e nn
†ˆ | |a ROTATION:
| |
| |
cos(| | ) sin(| | )
sin(| | ) cos(| | )i
i
t t
t t
REALISTIC EXPERIMENT: TWO-LEVEL ATOM INSTEAD OF A SPIN IN THE MAGNETIC FIELD
| |
| |
z
z
e
g
PHOTON QUANTUM WAVE EPR
(RABI OSCILLATIONS):
![Page 49: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/49.jpg)
1| | |
2ia e b
| a |b
The relative phase of a photon is observable locally
![Page 50: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/50.jpg)
L. Hardy, Phys. Rev. Lett. (1994)
1| | |
2ia e b
2| |
4 2( )
| '!
nn
e an
| a |b
2| |
4 2( )
| '!
nn
e bn
The relative phase of a photon is observable locally
![Page 51: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/51.jpg)
1| | |
2ia e b
2| |
2 | '!
nn
e an
| a |b
2| |2 | '
!
nn
e bn
The relative phase of a charged pion is observable locallyY. Aharonov, and L. Susskind, Phys. Rev. 155, 1428 (1967)
2| |2| |
!
n
e q nen
This is a gedanken experiment because such a coherent state is unstable
![Page 52: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/52.jpg)
| a |b
The relative phase of an electron is not observable locally
But it is observable, if we have a positron in a superposition with a known phase.
Y. Aharonov, and L. Vaidman, PRA 61, 2108 (2000)
1| | |
2ia e b
1| | ' | '
2a b
| 'b | 'a
![Page 53: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/53.jpg)
The relative phase is observable locally, therefore the time of change of the relative phase can be observed in contradiction with the fact that it is gauge dependent property.
Paradox II
1| | |
2a b
1| | |
2ia e b
1| | |
2ia e b
ie
![Page 54: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/54.jpg)
1| | |
2a b
1| | |
2ia e b
1| | |
2ia e b
ie
The key to the resolution of the paradox is that the measuring device measuring relative phase “feels” the Aharonov-Bohm effect too.
ie
![Page 55: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/55.jpg)
1| | |
2ia e b
ie
2| |
2 | '!
nn
e an
2| |
2 | '!
nnie e b
n
The key to the resolution of the paradox is that a measuring device measuring relative the phase “feels” the Aharonov-Bohm effect too.
2 2| | | | 2
2 2 | | ( 2 ) 1| ' | ' | ' | '
! ! ! 2
ie
ni nn nn n i
ee a e b e a e b
n n n
![Page 56: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/56.jpg)
The relative phase of the measuring device which measures the relative phase of the particle also depends on the chosen gauge. In fact, local outcomes are not influenced by the solenoid, only their interpretation is. Even the interpretation is gauge dependent.
Paradox II - resolution
1| | |
2a b
1| | |
2ia e b
1| | |
2ia e b
ie
![Page 57: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/57.jpg)
1| | |
2a b
1| | |
2a b
A
Paradox II - resolution The relative phase of the measuring device which measures the relative phase of the particle also depends on the chosen gauge. In fact, local outcomes are not influenced by the solenoid, only their interpretation is. Even the interpretation is gauge dependent.
![Page 58: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/58.jpg)
1| | |
2a b
1| | |
2a b
A
Paradox II - resolution The relative phase of the measuring device which measures the relative phase of the particle also depends on the chosen gauge. In fact, local outcomes are not influenced by the solenoid, only their interpretation is. Even the interpretation is gauge dependent.
![Page 59: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/59.jpg)
Paradox I
1| | |
2a b
1| | |
2ia e b
At every place on the paths of the wave packets of the electron there is no observable action, but nevertheless, the relative phase is obtained.
![Page 60: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/60.jpg)
LINE OF CHARGE
NEUTRON
Aharonov-Bohm Effect Aharonov-Casher Effect
SOLENOID
ELECTRON
The Aharonov-Casher Effect is dual to the Aharonov-Bohm Effect
due to symmetry in electron neutron interaction
The motion of the electron should be identical to the motion of the neutron, but the neutron feels force!?
![Page 61: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/61.jpg)
ELECTRON
The motion of the electron is identical to the motion of the neutron
Paradox III The motion of the electron inside the interferometer is the same with or without the solenoid
ELECTRON
NEUTRON
LINE OF CHARGE
NEUTRON
0F
0F
AC dual to AB
![Page 62: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/62.jpg)
Neutron slows down
Neutron accelerates
Fx Fx
Fx Fx
LINE OF CHARGE
NEUTRON
0F
![Page 63: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/63.jpg)
It is a current loopI
The force exerted on the neutron
N
S
A neutron is not two magnetic monopoles
The model of the magnetic moment of a neutron
T.H. Boyer, Am .J. Phys. 56, 688 (1988)
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c
Vd
A moving current loop has an electric dipole moment
The inhomogeneous electric field exerts force on the dipole
EdF
E
d
Fx
d
V
The force exerted on the neutron
V
T.H. Boyer, Am .J. Phys. 56, 688 (1988)
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The forces exerted on the neutron can give energy for nothing!
Fx Fx
Fx Fx
Paradox IV (Aharonov)
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Paradox IV (Aharonov)
The forces exerted on the neutron can give energy for nothing!
![Page 67: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/67.jpg)
FxV
Paradox IV (Aharonov)
The forces exerted on the neutron can give energy for nothing!
![Page 68: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/68.jpg)
FxV
c
Vd
d EdF
d
V
V
The forces exerted on the neutron can give energy for nothing!
Paradox IV (Aharonov)
![Page 69: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/69.jpg)
c
Vd
d EdF
d
V
V
The forces exerted on the neutron can give energy for nothing!
Paradox IV (Aharonov)
Fx
![Page 70: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/70.jpg)
c
Vd
d EdF
d
V
V
The forces exerted on the neutron can give energy for nothing!
Paradox IV (Aharonov)
Fx
![Page 71: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/71.jpg)
c
Vd
d EdF
d
V
V
The forces exerted on the neutron can give energy for nothing!
Paradox IV (Aharonov)
Fx
![Page 72: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/72.jpg)
c
Vd
d EdF
d
V
V
The forces exerted on the neutron can give energy for nothing!
Paradox IV (Aharonov)
Fx
![Page 73: Teleportation](https://reader033.fdocuments.in/reader033/viewer/2022061518/56813391550346895d9a9d76/html5/thumbnails/73.jpg)
c
Vd
d EdF
d
V
V
The forces exerted on the neutron can give energy for nothing!
Paradox IV (Aharonov)