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There are basically three kinds of teleportation: the kind where the thing you want to teleport
is somehow instantly moved from one location to another perhaps by a loophole in the fabric
of spacetime or magic or something ; the kind where you disassemble the object and send
the pieces to the faraway location to be reassembled ; and the kind where you scan
the object in one place and just transmit the instructions for how to reassemble it
somewhere else using different molecules and atoms.
This last kind of teleportation kind of sounds like cloning, since couldn’t you just scan
the object and send instructions to reassemble a copy somewhere else without destroying the
original? But no, quantum mechanics prohibits exact copying of arbitrary objects , so any
method of teleportation governed by the physics in our universe will somehow alter or destroy
the original object. Which is kind of nice, because it bypasses those soul-searching,
paradox-inducing questions about which is the real "you" – the teleported you, or
the stuff that was left behind? – “no cloning” implies the teleported one is,
unequivocally, the real one. This isn't just science fiction\h– well,
human teleportation is, but physicists have successfully used this method to teleport
photons of light, electrons, even calcium atoms . In this video I'm going to show you
exactly how quantum teleportation works in the hopes of giving you a clearer picture
of what it can do, and what it can't. Physicists usually teleport small, quantum,
things in a superposition of several states, like an electron that's in a state of
spin up and spin down, or whatever. But we're going to use Schrödinger's cat, in a superposition
of alive and dead until you look inside the box, in which case the state collapses to
just one of the two options, alive, or dead – the math is the same, but c’mon, this
is the internet . Before we get into the details (and I promise,
there will be many), we need to talk for a second about quantum entanglement, because
it's the transmission mechanism that makes teleportation possible. Quantum particles,
as you may have heard, can be in multiple different states of existence at once, like
"spin up" and "spin down", or "alive" and "dead", or "exploded" and "not exploded."
Or if you have multiple particles, they can be in various different combinations of their
possible states of existence, like, heads and tails plus heads and heads. Saying two
or more particles are "entangled" just means that the states of the particles aren't independent
of each other. For example, if the gunpowder explodes, Schrödinger's cat will be dead,
and if the gunpowder doesn't explode, Schrödinger's cat will be alive, but the powder can't be
unexploded while killing the cat, and vice versa, so the alive or dead state of existence
of the cat is entangled with the exploded (or not) state of existence of the gunpowder.
Or two atoms can be entangled if the outer electron in one is always orbitingto the
left while the other is orbiting to the right, or vice versa, so even though either atom
could be in either state, they're always opposite, and if we know the state of one, we know the
state of the other. In general, if you have a set of fully entangled particles, you only need to know the states
of half of them to be able to infer the states of the other half. That's not the case with heads
and tails plus heads and heads –\hif the first coin turns out to be heads, we still
don't know what the second coin is, so they're not entangled.
Ok, so the reason we started talking about entangled pairs of objects is that , since
entanglement can be maintained over arbitrarily long distances, entangled particles are the
transmission mechanism for teleportation – send a pair
of entangled objects to two separate locations, and one of them is kind of like a mold or
scanner and "imprints" the state of the thing we want to teleport; the other object, because
it's entangled with the first, ends up as a kind of "negative" of that imprinted state.
That's basically it, but to see how teleportation works in detail, let's send Schrödinger’s
cat to the moon. Remember, Schrödinger's cat, hidden in its box, has some probability
of being alive , and some probability of being dead , so it's in a quantum superposition
of A times alive, plus B times dead, where we have no idea what the probabilities actually
are. In order to teleport the cat's state of existence
(A alive and B dead) to the moon, we need an entangled pair of particles, one here,
and one on the moon. Like, an entangled pair of fleas, each hidden in its own box, where
one flea is dead and one is alive, but we don't know which one, so they're in a superposition
of earth flea is alive and moon flea is dead, plus earth flea is dead and moon flea is alive.
Schrödinger's fleas! We're going to teleport the cat's state of existence to the flea on
the moon by putting the earth flea and the cat together in the same box, entangling them
in a particular way, and thus teleporting the cat’s state to the moon flea. And that’s
it! I know it sounds crazy, but if you replace cats and fleas with electrons or photons or
atoms, this is exactly what happens.
Here’s how teleportation works. The cat's initial life-or-death state is A
times alive plus B times dead. The entangled pair of fleas are initially in a state of
earth flea alive moon flea dead plus earth flea dead moon flea alive, in equal proportions.
So the cat together with the fleas is A times cat alive plus B times cat dead, times earth
flea alive times moon flea dead plus earth flea dead times moon flea alive. This seems
like a complicated situation, but it just means that if we were to look inside the boxes
, with probability A we'd see the cat alive and exactly one of the fleas dead (either
the moon flea or the earth flea), and with probability B we'd see the cat dead and still
exactly one of the fleas dead (either the moon flea or the earth flea). No teleportation,
just a cat and some fleas entangled with each other (but not with the cat). So we won't
look in the boxes like that. To start the teleportation process, we need
to get the cat also partially entangled with the fleas, and to do that we'll put the cat
and the earth flea inside the same box and look inside it in a sneaky, indirect way . What
I mean by indirect is that we can’t just open it up to see whether the cat and earth
flea are each alive or dead, since that would entirely collapse the superposition, either
killing or saving the cat (and flea), and resulting in a failed teleportation. Instead
we need a more subtle measurement that only partially collapses the superposition and
tells us just a little bit about both of them, but not everything. For example, we could
ask, "are they the same?”, which would mean that either both cat and earth flea are alive
or both are dead, but we don't know which. Or we could ask ”is only one of them dead?"
that is, one is dead while the other is alive, but we don't know which one. Or, “at least
one is dead”, which would mean either the cat is alive and the flea is dead, or the
cat is dead and the flea is alive, or both are dead, but we don’t know which. Or, "the
cat is not dead alone", which would mean either the cat is alive with the flea either alive
or dead, or the cat's dead and the flea is dead, too –\hbut again, we don’t know
which. You’ll notice that none of these four questions
on its own allows us to determine the full life or death situation of the cat and its
earthbound flea. "At least one is dead" tells us something about the cat and earth flea,
but not everything. The four questions taken together, however, are an alternative way
of fully specifying the cat and flea situation that we can use instead of “dead and dead”,
“alive and alive”, “alive and dead”, and “dead and alive”. For example, if the
cat is alive and the flea is dead , then we could write that – boringly – as “alive
times dead”, or in our sneaky indirect way as “the cat isn't dead alone” minus “the
cat and the flea are the same” (you can check to see that it works out). The sneaky
way to write “cat and flea are both alive” is – well, you could pause the video now
to try to figure it out on your own – or, wait for me to tell you it's “they’re
both the same” plus “they’re both different” minus “at least one is dead”. And the
sneaky way to write “cat is dead and flea is alive” is – “they’re both the same”
plus “they’re both different” minus “the cat isn’t dead alone”. And the
sneaky way to write “they’re both dead” is – “at least one is dead” minus “only
one is dead.” The point of all of this sneaky indirect questioning,
remember, is to bring the cat into entanglement with the fleas, which is what actually teleports
the cat’s life-or-death situation to the moon flea.
To see why this works, we'll have to write out the full state of the cat and both fleas
(remember from before, it was A times cat alive plus B times cat dead, all times earth
flea alive times moon flea dead plus earth flea dead times moon flea alive), and then
re-write this in terms of the sneaky questions. There’s going to be a bit of algebra and
distributing and such going on in the next little bit, but this is the part where the
teleportation actually happens, so it’s worth the effort!
First, we’ll write out the full state of the cat and both fleas so that we don’t
have any parentheses. That means distributing through the “A times cat alive plus B times
cat dead”, giving us “A times cat alive times earth flea alive times moon flea dead,
plus A times cat alive times earth flea dead times moon flea alive, plus B times cat dead
times earth flea alive times moon flea dead, plus B times cat dead times earth flea dead
times moon flea alive.” It's a mouthful. But we’re just getting started.
Now we need to entangle the cat and the earth flea, so we're going to re-write the cat and
earth flea parts in terms of our sneaky indirect questions – remember, where instead of "cat
alive times earth flea alive" (times moon flea dead), we have "both the same" plus "exactly
one alive" minus "at least one alive" (still all times moon flea dead). And instead of
"cat alive times earth flea dead" (times moon flea alive), we have "the cat isn't dead alone"
minus "both the same" (times moon flea alive). And instead of "cat dead times earth flea
alive" (times moon flea dead), we have "both the same" plus "exactly one alive" minus "the
cat isn't dead alone" (times moon flea dead). And instead of "cat dead times earth flea
dead" (times moon flea alive) we have "at least one is dead" minus "exactly one is dead"
(times moon flea alive). If we now sort through this big mess and group all the different
pieces together by the indirect questions, we find that we have four options: either
"at least one of cat and earth flea is alive" while the moon flea is in a superposition
of alive and dead, or "exactly one of cat and earth flea is alive" while the moon flea
is in a superposition of alive and dead, or "both are the same" while the moon flea is
in a superposition of alive and dead, or "the cat isn't dead alone" while the moon flea
is in a superposition of alive and dead. Notice a pattern? By re-framing the situation in
terms of the indirect questions, we've now put the moon flea, which started off entangled
to the earth flea, into one of several of possible superpositions of alive and dead,
each of which looks kind of like the original cat superposition, A alive and B dead!
There's one last step to complete the teleportation: now, finally, at the end, we actually look
(indirectly) into the cat/earth-flea box to collapse their combined wavefunction to just
one of the possible, sneaky, options. Like, maybe we look in (indirectly) and find out
that “the cat isn’t dead alone.” Then we know that the moon flea is in a superposition
of A alive minus B dead, which is almost exactly the same as the cat's original "A alive plus
B dead" state! All we need to do is switch B and minus B (which can be done by somebody
on the moon after we beam them the message about the cat not being dead alone), and the
moon flea IS in the state that the cat was originally. Successful teleportation!
If, instead, the cat and earth flea had been in the “at least one is dead“ state, then
the moon flea would be B times alive minus A times dead, and we could tell the person
on the moon to just swap B for A and minus A for B , and the moon flea would be in the
state the cat was originally. Successful teleportation! And there are simple swapping rules for each
of the other possible scenarios , so we can guarantee that, after the dust settles and
all is said and done, the cat's state of existence will be teleported to the moon.
At this point, you may be wondering about
two things. First, how is this teleportation if we didn't actually send a cat to the moon?
We just sent the life-or-death state the cat was in to a flea on the moon. Well, I used
fleas so the math would be easier to follow. But if, instead of fleas, we used two piles
of particles that you could in principle make a cat out of , and if we viewed our whole
cat as just a particular quantum cat-figuration of a pile of particles (which is, ultimately,
what it is), then by quantum teleporting the state of the pile that looks like a cat to
the blank canvas pile of particles on the moon (via the earth blank canvas pile), we
would indeed end up with a cat on the moon that is literally the same cat we started
with, while the particles that were originally the cat on earth would now be –\hwhat would
they be? That's the second thing you might be wondering.
What happens to the original cat on the earth? Well, in the case of teleporting a pile of
particles that look like a cat –\hI mean, are a cat - to the moon, well, after the teleportation
the pile of particles that originally was in the state of a cat will be in the most
mixed-up state possible for those particles, almost as if it had been put through a blender
and\hnot at all like a cat! To illustrate this a little more clearly,
if instead of a real cat we just teleported the word "cat" encoded as a quantum state
, after the teleportation the "cat" on earth would no longer be "C-A-T", but would in fact
be in a superposition of every single possible three-letter combination, all of them equally
likely. That is, it would be entirely jumbled and nothing like the original C-A-T whatsoever,
and there would be absolutely no confusion about which one –\hthe original cat or the
teleported cat – is the real cat. I mean, it's obvious – only one of them is a cat.
Of course, physicists haven’t succeeded in teleporting whole cats yet –\hor even,
for that matter, the word "CAT." It’s very hard to make an entangled pair of sufficiently
big piles of particles, and then have them stay entangled long enough to take one to
the moon. So far, only simple quantum states like those of a single photon or electron
have been teleported , and only as far as about 100km. So, teleportation teleportation
is a long way off. If only we had some way we could get there faster… ;)