Okay, hello, welcome again.

So we are just in the process of discussing the various options you have for bail test

experiments and I was just giving a brief overview of what are the options of just producing

these singlet states.

And for example we mentioned scattering of particles or just taking the electrons out

of an helium atom or then the more relevant options like parametric down conversion for

example or photons emitted from a cascade in an atom.

And I want to conclude this brief overview by just pointing out qubits because nowadays

you have these artificial quantum systems that can be fabricated with the desired parameters

and you can tune the parameters even in situ in the experiment and you can then apply pulses

to these qubits and manipulate them at will and provide interactions between the qubits

so you have all the flexibility.

And among the many, many possible things you can do in particular obviously you can produce

an entangled state.

I mean if you have a qubit setup where you wouldn't be able to produce an entangled state

it would be a very bad qubit setup indeed.

So let me just briefly mention the options here.

Okay so the point about qubits is that in contrast to all the other examples we have

mentioned you have full control, you can easily manipulate them, you can easily read them

out because that is part of the definition of what is a good qubit.

And I just mentioned two examples.

One of the examples would be ions that is charged atoms in a trap and if you place two

of them inside a trap and you choose them such that they have spin one half then there

are ways to manipulate them such that you create an entangled state.

Another example I want to mention are superconducting qubits.

So if you design an electrical circuit and cool it to sufficiently low temperatures then

it will often go superconducting and then you could have structures such as the one

I am drawing right now.

So you would have two qubits which are basically just metallic boxes that are cut in two halves

and then qubit pairs will be able to turn between the two halves and this under the

right conditions can then be a two level system.

And if you have two of these superconducting qubits and for example couple them via a metallic

strip that is a resonator for microwaves then again you have a situation where you can actually

very easily engineer entangled states of the qubits.

And there are just very many other examples for example you can have electron spins and

quantum dots or you can have the excitations and excitonic quantum dots and many other

examples.

Now let me just briefly mention how you would go about creating an entangled state for example

in such a situation you can easily have an effective coupling between the two qubits

that is mediated by this microwave resonator and the Hamiltonian for this effective coupling

would contain an interaction term that goes by for example sigma x1 times sigma x2 where

1 and 2 refer to the two qubits.

And so what that does is for example if you have an excitation in qubit 1 and no excitation

in qubit 2 then applying the Hamiltonian would just flip the excitation to the other qubit.

Now this in itself after you flip the excitation to the other qubit that wouldn't be an entangled

state but let's see so the interaction as I said can take up down that is excited ground

state into the down up state and the point is that in these circuits you can easily switch

the interactions or at least switch on and off effectively the interaction for example

this interaction will be effective only if the two qubits are resonant because only then

this is a process that conserves the energy of the original Hamiltonian and so just by