U1L4d.txt

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And there's one more thing I want
to say about tensor products state of two-qubits
before I go onto the no cloning theorem.
Inner products of two-qubits.

So suppose two-qubits are in a separable state.
Well, the inner product, alpha, psi, phi
is equal to some psi i star [INAUDIBLE] sub i 0, 2, 3.

Or maybe I should say i equals 0, 0, 2, 1, 1.

But if phi is equal to phi 1 tensor phi 2 and psi is
equal to psi 1 tensor psi 2, phi psi
is equal to phi 1 psi 1, the inner producer of the first two
times the inner product of the second.

Why is this?
Well, psi is equal to--

OK.

Let's say psi 1 is equal to alpha 1,
or psi a equal-- oh, no.
Psi 1 equals alpha 1, beta 1, gamma 1, delta 1.
And psi 2 equals alpha 2 beta 2, gamma 2, delta 2.

And that equals, of course, this.
Then, psi 1, psi 2, is equal to, well, alpha 1,
gamma 1, alpha 2, gamma 2 plus alpha 1, delta 1, alpha
2, delta 2.
So that would be alpha 1 star gamma 1, alpha 2 star gamma 2
plus alpha 1 star delta 1, alpha 2 star delta 2 plus
beta 1 star gamma 1, beta 2 star gamma 2 plus--

did I do this completely wrong?

Alpha 1-- yeah.
I did.

I'm putting the complex conjugates in the wrong things.

Plus beta 1 star delta 1 star, beta 2, delta 2,
which if you look at it just factors.

I have an alpha 1 star alpha 2.
Star alpha 2, and you have beta 1 star beta 2, gamma 1
star gamma 2 plus delta 1 star delta 2, which
equals psi 1 phi 1a psi 1 psi 2 a times psi 1 psi 2, so b.

So that's a proof of this.