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U1L3c.txt
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#
# File: content-mit-8370x-subtitles/U1L3c.txt
#
# Captions for course module
#
# This file has 75 caption lines.
#
# Do not add or delete any lines. If there is text missing at the end, please add it to the last line.
#
#----------------------------------------
Let's go back to examples.
We have polarization of a photon.
And I said there were two basic states.
But of course, you know that a photon can have a lot
more than two polarizations.
So for example, you can have a diagonal polarization.
And what that is is equal to 1 over root
2 horizontal plus vertical.
Where of course this plus is a completely arbitrary
convention.
Equals 1/2 horizontal minus vertical.
Oh, we also have 1/2.
I said it was a complex vector space,
so you also have 1/2 horizontal minus I vertical.
Does anybody have a guess as to what this corresponds to?
Yeah?
Circular polarization.
So-- so this I guess is right circular polarization
and the other side would be left circular polarization.
And of course, if you rotate this by theta,
you want to have that is equal to cos theta--
OK.
Let's make that angle theta, because we
took cos theta times horizontal plus sine theta times vertical.
So this is an example of a quantum state space.
So the quantum state space that we'll
be using most of the time or much of the time--
actually, the quantum state space
we will be using most of the time is just a qubit
and we will use 0 and 1 as the basis vectors.
Spin 1/2 particle.
OK, so that's spin up.
And that's spin down.
But of course, we can also a particle
so it spins to the right.
Or actually, this is really the axis around which
it spins, so if you--
well actually, angular momentum of particles is very strange,
but this is equivalent to the axis around it spins
or analogous or something.
So if you have a spin up particle,
it's going around counterclockwise
assuming you can say it's going around anything at all.
And here, it's going around that way.
So this is equal to, by convention, plus spin down.
And we need to normalize it, so it's
1/2, and is equal to 1/2 spin up, minus spin down.
And there is also--
one is going into the board and out of the board
and into the board, which in Seth Lloyd's notes,
he uses is in and that is out.
And if you want to read Seth Lloyd's notes
and have a mnemonic for this, think of an arrow,
and here, you can see the head of the arrow pointing out,
and here, you can see the feathers on the arrow pointing
into the board.
And this is 1/2 up plus I down.
And this is minus.