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U2L1g.txt
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#
# File: content-mit-8370x-subtitles/U2L1g.txt
#
# Captions for course module
#
# This file has 143 caption lines.
#
# Do not add or delete any lines. If there is text missing at the end, please add it to the last line.
#
#----------------------------------------
Fact-- if you do the circuit without the extra Hadamard,
zeta plus 0 become 0 plus zeta.
So this with a plus here and a 0 here swaps the zeta down here.
So this just teleports the zeta there.
So you can see this does teleportation.
You need to check that this entry comes down here,
and you also need to check that this entry and this entry
are constant, independent of what this guy is.
Because if they weren't, then this state
would be entangled with these states
and it wouldn't be teleportation.
Well, it's fairly easy to show this.
I mean, what you need to do is zeta equals alpha
0 plus beta 1.
So let's look at what happens when we put 0 plus 0 in--
0 plus 0.
Well, the first thing we do is a control NOT here.
And that's 0.
Well, wait-- no.
There's an easier way of thinking about this.
Well this control NOT does nothing
because the top state is 0.
And here, we apply a control NOT and we apply another control
NOT, so that does nothing as well.
So the only operation here, we have a 0 controlling NOT
into another 0, which gives us a 0.
So 0 plus 0.
Now, the next one is a little more complicated--
1 plus 0.
So after this, the state is 1 00 plus 111.
And now we're doing that.
Well, what does this do?
It x-- it control NOT's or XR's the first qubit
into the second qubit.
So after this guy, this state is 110 plus--
110 plus 101.
And now we do that again.
So it becomes 111 plus--
OK, I'm running out of room here.
So but you can see that here it's 111 plus 101.
And the last thing is this guy.
So what that does is take the last qubit and XR it with
the first qubit, so that becomes 011 plus 001.
And that's here.
And this is 0 plus 1.
So 1 plus 0 became 0 plus 1.
And now the last thing we get is a Hadamard and a measurement.
So you can see that both of these states
are plus right before they're measured,
which means all measurement values are equally likely.
And if you go back to our teleportation circuit--
are the first way of analyzing teleportation,
you would have seen that all teleportation
values were equally likely.
So that is the way of using the circuit
to analyze how to teleport--
to show this teleportation circuit actually
teleports the first qubit to the last qubit,
which means that the original teleportation circuit, which
I've now erased, also did.
OK.
That's-- yeah?
So the measurement is there to tell you what you teleported?
Well, the measurements are necessary
in the original teleportation circuit
because, well, you need to get information
from Alice to Bob somehow.
And in teleportation, they don't have a classical channel
between them, so the only thing they can send
is classical information.
So let's write down the original teleportation circuit
and go over it.
So we had psi plus 0.
Measurements and-- so this first thing
is done before these two qubits get
distributed to Alice and Bob.
So Alice-- so Bob owns everything here and Alice
owns everything up here.
And the only thing going from Alice to Bob
are these two green classical bits.
So Alice and Bob are in two different labs
with a classical telephone line between them,
over which they can send classical bits.
So the reason you did this measurement
was to convert the information into classical information,
which then can be sent to Bob over a telephone line
or-- yeah?
So in the idealized version of the circuit,
these measurements are no longer necessary?
In the idealized version, oh--
oh, you mean in this--
yeah, in this version of the circuit,
you don't need those measurements.
OK.
Yeah.
But I kept them because they were in the original version,
and I also wanted to show that this circuit made
all four measurement outcomes equally likely, which--
well, which was necessary for the original teleportation.
Good question.
Yeah?
Sorry, just one last question.
For the circuit that we have on the top right there--
Yeah
--we start after the first CNOT.
It looks like the operation that we're describing
is like a totally non-local thing between Alice and Bob,
right?
It's just some unitary that has these--
like that controlled-Z gate, which is a non-local operation.
Right.
So this is a non-local-- yeah, so this and this
are non-local operation between Alice and Bob.
And yet, it turns out to do the same thing, which
is local operations and classical communication.
Right.
And so is there--
If someone just hands you a unitary,
is there some way to tell whether or not
that can be done?
Well, the only reason we could do that, really,
is these two measurements afterwards,
which we could commute back over this state and that gate.