Teleportation

2 bits Teleportation BELL MEASUREMENT

Bell States spin rotation one spin rotation

2 bits BELL MEASUREMENT

The EPR- Bohm State David Bohm

Teleportation

The EPR State

Continuous Variables Teleportation unknown shift, kick L. Vaidman,PRA 49, 1473 (1994)

spin measurement  The EPR State = teleportation machine of a known spin up to a flip

spin measurement  The EPR State = teleportation machine of a known spin up to a flip

spin measurement  The EPR State = teleportation machine of a known spin up to a flip

Many-Worlds Interpretation spin measurement  mixture of and In the Universe is not moved from Alice to Bob  But in Teleportation it is moved!

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 Local Bell measurements split the nonlocal world and the branching is the carier of the huge amount of information.

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

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

Paradoxes in the context of the Aharonov-Bohm and the Aharonov-Casher effects

Mach Zehnder Interferometer

Aharonov-Bohm Effect:

SOLENOID 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. 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.

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.

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.

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.

Paradox I 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.

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

The relative phase is observable locally

EPR correlations are observable locally

RESULTS OF LOCAL MEASUREMENTS  RELATIVE PHASE 

PHOTON QUANTUM WAVE  EPR

LOCAL SPIN MEASUREMENTS  RELATIVE PHASE  PHOTON QUANTUM WAVE  EPR

INSTEAD OF REALISTIC EXPERIMENT: TWO-LEVEL ATOM PHOTON QUANTUM WAVE  EPR INSTEAD OF A SPIN IN THE MAGNETIC FIELD

REALISTIC EXPERIMENT: TWO-LEVEL ATOM INSTEAD OF A SPIN IN THE MAGNETIC FIELD PHOTON QUANTUM WAVE  EPR INSTEAD OF

REALISTIC EXPERIMENT: TWO-LEVEL ATOM INSTEAD OF A SPIN IN THE MAGNETIC FIELD PHOTON QUANTUM WAVE  EPR INSTEAD OF

HOW TO MAKE THE ANALOG OF THE SPIN MEASUREMENTS ON THE ATOM? ARE NOT MEASURABLE DIRECTLY ROTATION INSPACE COUPLING H TO A COHERENT STATE  ROTATION: REALISTIC EXPERIMENT: TWO-LEVEL ATOM INSTEAD OF A SPIN IN THE MAGNETIC FIELD PHOTON QUANTUM WAVE  EPR (RABI OSCILLATIONS):

The relative phase of a photon is observable locally

L. Hardy, Phys. Rev. Lett. (1994) The relative phase of a photon is observable locally

The relative phase of a charged pion is observable locally Y. Aharonov, and L. Susskind, Phys. Rev. 155, 1428 (1967) This is a gedanken experiment because such a coherent state is unstable

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)

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

The key to the resolution of the paradox is that the measuring device measuring relative phase “feels” the Aharonov-Bohm effect too.

The key to the resolution of the paradox is that a measuring device measuring relative the phase “feels” the Aharonov-Bohm effect too.

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

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 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 I 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.

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!?

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 AC dual to AB

Neutron slows down Neutron accelerates F x F x F x F x LINE OF CHARGE NEUTRON

It is a current loop I 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)

A moving current loop has an electric dipole moment The inhomogeneous electric field exerts force on the dipole E d F x The force exerted on the neutron T.H. Boyer, Am.J. Phys. 56, 688 (1988)

The forces exerted on the neutron can give energy for nothing! F x F x F x F x Paradox IV (Aharonov)

The forces exerted on the neutron can give energy for nothing!

F x V Paradox IV (Aharonov) The forces exerted on the neutron can give energy for nothing!

F x V dd Paradox IV (Aharonov)

dd The forces exerted on the neutron can give energy for nothing! Paradox IV (Aharonov) F x

dd The forces exerted on the neutron can give energy for nothing! Paradox IV (Aharonov) F x

dd The forces exerted on the neutron can give energy for nothing! Paradox IV (Aharonov) F x

dd The forces exerted on the neutron can give energy for nothing! Paradox IV (Aharonov) F x

dd The forces exerted on the neutron can give energy for nothing! Paradox IV (Aharonov)