U2L1d.txt

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So first, let's do the measurement
Alice's measurement.
Alice's measurement.

And I think we talked about this basis of two cubits last time.
But measure in basis.

1 over root 2 0 0 plus 1 1.

And this state is often called phi plus.
I think the textbook uses a different name, but.

This is called phi minus.
1 over root 2 0 1 plus 1 0.
And this is psi plus.
And you can guess the last one.

0 1 minus 1 0.
And this is psi minus.
So it's easy to see that all four of these states
are orthogonal, because if you, you know,
multiply this state and this state, you get 1 minus 1,
which is zero.
If you multiply this state and this state, this and this--
no, the inter product of 0 0 with both 0 1 and 1 0 is zero,
so you get 0.
et cetera.
So because these four states are orthogonal,
you can do a measurement which returns
one of these four states.
So that's Alice's measurement.

Oh, wait.

I think I--
I think I want to keep this up.
And let's relabel this phi plus.

So I will draw a classical control in green.
And this is an XR because sigma x is an XR.
And this is a z.