WEBVTT
Kind: captions
Language: en-US
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So far, most of our discussion has involved waves
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and superposition and interference
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in ways that are almost entirely classical,
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except for measurement,
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where we talked about the state collapsing,
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and the idea that
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n qubits results in
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to entries in our state vector.
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Two qubits requires four of our dials,
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three of our qubits requires eight of our dials, and so on.
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Each of these dials represents our
quantum amplitude for the corresponding state,
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so the absolute value of the square of the
amplitude of each is the probability that
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we will measure that value
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if we measure the whole register.
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So far, so good.
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Now, we're going to step out into the realm
of really hair-raising quantum phenomena.
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We're going to talk about “quantum entanglement”,
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the idea that worried Albert Einstein so much
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that he figured that maybe quantum mechanics as a theory
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wasn't yet complete and correct.
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We'll get to that in a minute.
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First, let's assume we have quantum entanglement
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and talk about its effect on measuring quantum states.
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Then, we'll talk a little about
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how we can make entanglement
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and how we can tell that it's real.
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After you finish this video,
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there is more information in the accompanying article,
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covering the important concept of Bell pairs.
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There is also information on some
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of the most recent experimental demonstrations
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that quantum entanglement is real.
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If you have two or more qubits,
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their states can be correlated in a way that classical systems can't replicate.
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Let's take an example.
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Suppose our two qubits have two states,
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which we'll call “up” and “down.”
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Here is up.
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This can be our zero state, ket 0
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and here is down
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– this can be our one state
– ket one.
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If we have two qubits, for example,
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maybe one of them is always up and the other
is down.
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Let me bring in my student,
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Shin Nishio, so we can demonstrate.
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One state would be this one.
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We can write that as |↑↓⟩ or |01⟩
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and the other state is this one,
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naturally, we can write that as |↓↑⟩ or |10⟩.
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In fact, it doesn't actually matter
what write inside the ket.
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We could write a picture with our faces inside of it.
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Now let's take those two states and put them in superposition.
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Remember, this is two qubits,
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but we have to normalize the state,
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just like we did with one qubit.
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We will take it and put it over a square root of 2 like in this equation.
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Now, each qubit is in superposition.
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The first qubit is in a state that is 50% zero and 50% one.
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The second qubit is also in a state that's
50:50
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but the states of the two quibits are
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random but not independent.
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This is critical.
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This is the essence of quantum entanglement.
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Okay, I can hear you thinking,
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how would this
show up in the real world?
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How can we tell if this rather esoteric concept of entanglement is real?
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Earlier, we saw how to measure multi-qubits states.
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What happens with this entangled quantum state if we measure it?
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Of course, the system collapses into one of the states
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that has a probability that’s greater than zero.
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With two qubits, there are four possible states,
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just like with two classical bits:
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00, 01,
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10, and 11.
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In the case of our entangled state,
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only two of those four have probabilities that are non-zero:
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01 and 10.
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When we measure
the state, we will find either 01 or 10,
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but never 00 or 11,
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even though each qubit individually
seems to be 50:50.
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This is what we mean when
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we say that they are random but not independent.