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Okay, so now in this video we are going to
finally complete the Quantum Teleportation

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Protocol. So in the last video, we saw how
to, how Alice could teleport a arbitrary

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qubit α0 + β1 to Bob. If she could do
this unrealistic thing of performing a

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CNOT with her qubit as a control bit and
Bob's qubit as a target bit. So, if she

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does that then she can entangle the two
qubits into this rectangle state, α0(0) +

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β1(1). And then, Alice measures her qubit
in the sign basis, and if she gets out

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from plus then Bob's qubit is in the, in
the desired state alpha zero + beta one.

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But if she gets out to minus, then Bob's
qubit is in a slightly related cube state

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alpha zero - beta one. So, well, Alice
calls up Bob and tells him which outcome

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she got and if the outcome was plus Bob,
Bob just uses his qubit as is, as is. If

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he got a minus, then he performs a
phase-flip on his, on his qubit using the

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Z gate, the phase-flip gate. Okay. So,
now, what, what this does is, it reduces

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our task of teleportation to somehow
creating this entangled state alpha zero,

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zero plus beta one but without the benefit
of a CNOT gate. And that's what we are

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going to do and once we do that, we'll
have our teleportation protocol completed.

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Okay. So, so what's our setup now? Our
setup is, that Alice has a qubit, alpha

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zero plus beta one, which we, let's, let's
think of you know, since we are going to

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be drawing a circuit, let's think of why
that can, that holds this qubit. But now,

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we are also going to assume that Alice and
Bob cannot, you know, they are too far

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apart to perform a, to perform a gate or
anything else. But we are going to assume

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that sometime in the past, they managed to
talk to each other enough to create a bell

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state, so they share a bell state. So
Alice has this qubit, and Bob has that

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qubit and these two qubits are entangled
with each other and they are in the states

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zero, zero plus one, one. So we think of
time as going from left to right so there

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are these three wires now that are
carrying these three qubits. Two of them

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entangled with eac h other and the third
one which is the one that Alice is started

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with, is the qubit that she wants to
eventually teleport to Bob. Okay. So what

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we want to do is, we want to use this bell
state to effectively apply a CNOT gate

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remotely. So how do we do this? Well,
let's start by well, Alice performs a CNOT

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from her qubit out you know, the unknown
qubit, the one she wants to teleport to

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her half of the bell state. Okay. So now,
let's try to understand what the state of,

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of the three qubits is after she does this
CNOT. Now so first, what was the state

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before she, she did this? Well, before she
did this, it was clearly, α0 + β1

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1/√2(00) + 1/√2(11). α/√2(000) +
α/√2(011) + β/√2(100) +

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β/√2(111). So that's the state of her
qubits, of the, of the three qubits,

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initially before the CNOT gate. Now what
happens after the CNOT gate is applied? So

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after we apply the CNOT, the CNOT is from
the first qubit to the second. So, in

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these first two cases, whether, whether
first qubit is zero, everything remains

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the same so you get α/√2(000) +
α/√2(011). And then in these two cases

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where the control bit is a one, the target
bit flips, so you get β/√2(110) +

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β/√2(101). Okay. So that's the state
that her, of, of the three qubits after

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the CNOT. Okay, so now let's, let's try to
understand what happens if we measure this

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middle qubit, what happens to the first
two, first and the third qubits? Do we

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magically end up in the desired state,
alpha zero, zero plus beta one, one, the

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entangled state that we want to get to.
Okay, so lets, lets try to see what

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happens. So, this was, this was the state
of our, of our three qubits, I have just

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rearranged the state a little bit. And,
now, what, what we, what we wish to do is,

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we wish to measure the middle qubit. So,
when we measure the middle qubit, the

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outcome is either, is either zero or one.
Now if it happens to be zero, which is,

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which is these red possibilities here,
then the remaining state of the other two

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qubits would be, zero, zero plus one, one
with amplitud e alpha and beta. So, you

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would get alpha zero, zero plus beta one,
one. On the other hand, if the middle

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qubit turns out to be one, if it's
measured to be one, then the, then the

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state of the remaining qubits, would be
one zero, be, let's see. Alpha times zero,

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one + beta times one, zero. Okay. So, at
this point, Alice picks up her phone,

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calls Bob and says, you know, I did the
measurement. The result was either zero or

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one. If the result is zero, then Bob can,
Bob needs to do nothing because, because,

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the, the two now share this, this
entangled state that we wanted, Alpha

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zero, zero plus beta one, one. On the
other hand, if the result is one, then,

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what Bob can do is, but he, he, you know,
they share the state alpha zero one plus

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beta one, zero. All he has to do is
perform a bit flip on his bit, and this

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will get transformed to alpha zero, zero
plus beta one, one. So, meaning, Alice

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makes a measurement on the second bit. She
calls up Bob. If the, if the bit is zero,

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Bob does nothing. If it's a one, then he
performs a bit flip or an x gate on his

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qubit. So now we have, we have reduced to
the case that we knew how to solve. So we,

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we are ready to see what the full quantum
teleportation protocol is. So here's the

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protocol. Alice starts with this qubit in
the unknown state, Psi. Alice and Bob

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share this bell state. So this is Alice's
qubit, that's Bob's qubit and they're

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entangled with each other. Now what Alice
does is, she performs a CNOT from her

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qubit to, to sorry, her unknown qubit to
her part of the bell state. She measures,

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she, she calls up, sends the results to
Bob. If it's a one, he performs a bit

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flip. Okay. So now, to deal with the first
and third qubits, Alice wants to measure

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her qubit in the, in the sign basis of the
Hadamard basis so what she does is, she

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first does a Hadamard transform, and then
she measures. So she is measuring in the

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plus-minus basis, she calls up Bob, tells
him what the result of that is, if it's,

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if the result is zero, Bob does nothing.
If it's one, then he performs a phas

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e-flip. And low and behold, his qubit is
now transformed into Alice's original

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qubit. In the meantime, Alice measured
both her cubits. And so this quantum state

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on these two qubits is completely
destroyed. And so, Alice's qubit got

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destroyed and later, after the phone call,
the, the and, and, and these two, the x,

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the potential x and Z gates, the, the, the
quantum state magically materializes at