M1L7e.txt

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Here is the abstract of a paper.
So well, this was just 2008, so just a few years ago.
And what you see here is that here are,
1 meter apart, two ytterbium ions.
They emit light.
The light goes through an optical fiber.
And now after the beam splitter, when you detect one photon
you don't know which ion has emitted the photon.
So this is exactly this set-up, which I described.
Of course, in an optical fiber, you
have the two good polarizations are horizontal and vertical
in the polarization-maintaining fiber.
So therefore, the light, which originally
was emitted in a circular basis, angular momentum selection
rules, is transformed into linearly polarized light
using a qualitative plate.
Any questions?
Yes, Dickie.
To create the initial state, the [INAUDIBLE]
decays to one state or the other.
How do you make sure that the [INAUDIBLE] state is a pure
state and not a mixed state, that the coherence--

Good question.
So first of all, if you think about it,
you will discover more and more experimental challenges.
What people must have used there is sort of a strong laser
pulse, that you have more than overkill
to make sure that with a very, very short time window
both ions are excited.
The ions are in a pure state, and then they emit a photon.
And if you have one system prepared
which can emit a photon but it has a branching ratio of 50-50,
if it's an isolated system it will have a superposition
state of photon in one polarization,
let's say a sigma plus photon going
to a magnetic random number state m equals plus 1,
and the sigma minus photon going to m equals minus 1.
And this is a pure state.

The mixture only comes if, well, you're not careful.
If you have a magnetic field and you
don't shield your magnetic field well,
or you have some magnetized materials
and you were not aware of it, then that
means that you get different phase shifts, which
you can't calculate for.
So now you have a random phase.
You don't know it.
And if you have [INAUDIBLE], you have to trace out
or you have to average over the phase.
And then your pure state becomes a density matrix.
But the quantum mechanical process itself
of a particle having different branching ratios
is a pure system.
It undergoes unitary time evolution,
and it stays in a pure state.
And the state which is populated by two ions, both
emitting a photon simultaneously,
is exactly the state I've written down for you.
But you're absolutely right, that decoherence is an issue.
You have to be very careful with magnetic fields.
You probably want to work with atoms which are non-magnetic
or where the spin is only a nuclear spin, which
is much less sensitive to the magnetic field and so on.
Other questions?
So as far as soon as those detectors [INAUDIBLE],
then Bell's [INAUDIBLE] as derived
so that you can no longer make use of the [INAUDIBLE]?
No, no, wait.
Look here.
We have a state, which has atoms in a state and two photons.
So this state has four particles.
We detect two particles, which are the photons,
and the atoms are untouched.
The atoms are then afterwards in an entangled state.

So we have a [INAUDIBLE] system.
We do a measurement of part of the system.
And we have arranged things in a skillful way
that the moment we know the outcome of the measurement
is such and such, we know in which quantum state
the rest of the system is.
And this protocol means that the atoms
are left-- after the outcome of the measurement
is such and such, the atoms are left in a pure Bell state.