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 – 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 – if 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 – but 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 – what 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 – I 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 not 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 – the 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 – or 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… ;)
Mr Crayola Marker needs some hand lotion for those fingers.
Using cats and fleas as examples really clashed with the technical part of the video. The title talks about teleporting a cat, but really the technical part is describing teleporting a qubit in the form of a live-or-dead state. ...I don't even want to think about how complicated the unitary operation that rotates between live-cat and dead-cat must be.
Personally, I think the best way to explain quantum teleportation is as a quantum version of the one-time pad.
I still did not understand (still trying though)
Edit: parenthesis added
I think the video did a fairly good job of getting the concepts across, but I kind of wish minutephysics would stop doing so many videos on quantum teleportation/quantum entanglement/anything with the word quantum in it all the time. Sure that stuff is cool, but there are so many other cool physics topics that he could portray in his videos.