U2L1b.txt

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So what is teleportation?
Well, Charlie Bennett named it teleportation,
which I find invariably brings up,
you know images, of Star Trek.
Although, you know, Star Trek, they were transporters and not
teleporters.

Anyway how does-- what is teleportation?
Well, so some time from the past, Alice and Bob
have acquired an entangled pair of qubits,
and let's say 0, 0 plus 1, 1.

And Alice has an unknown--

unknown qubit.

Let's call this zeta.

Well-- so this is AB, AB.

So what Alice does is she performs
a measurement on her half of the entangled pair
and this unknown qubit.

And this leaves Bob with a qubit in some state.

Let's call it zeta prime.
And Alice gets two bits out of this measurement.

Two-- well, she's measuring two qubits, which
is a four-dimensional quantum state,
so she gets one of four results, which is two bits.
So she sends these two bits to Bob,
and then he performs a unitary.
Let's call this B1, B2.
He performs a unitary that depends on B1 and B2
on zeta prime.
And miraculously, he gets back the original unknowing qubit.

So you can send one qubit over a telephone line with two bits
if the sender and receiver have an EPR pair.
Now remember, in my first lecture,
I said you could not send qubits over a telephone line.
Because if you did, you could clone, because zeta
goes into a classical channel.
A classical channel can be duplicated.
So if all the information about zeta
were in this classical channel, you could clone the qubit.
And we know that's not allowed.
But here, Alice and Bob also have this EPR pair.
And anyone-- any eavesdropper can
listen in on this conversation and get the two bits.
But if without the other half of the EPR pair,
they can't recreate zeta.