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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 cloningimplies 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 deadthe 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 teleportationsend 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 askis 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. Youll 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 ofdead and dead”,

  • alive and alive”, “alive and dead”, anddead and alive”. For example, if the

  • cat is alive and the flea is dead , then we could write thatboringlyasalive

  • times dead”, or in our sneaky indirect way asthe cat isn't dead aloneminusthe

  • cat and the flea are the same” (you can check to see that it works out). The sneaky

  • way to writecat and flea are both aliveiswell, you could pause the video now

  • to try to figure it out on your ownor, wait for me to tell you it's “theyre

  • both the sameplustheyre both differentminusat least one is dead”. And the

  • sneaky way to writecat is dead and flea is aliveis – “theyre both the same

  • plustheyre both differentminusthe cat isn’t dead alone”. And the

  • sneaky way to writetheyre both deadis – “at least one is deadminusonly

  • 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, well 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 were 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 questionsremember, 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

  • thatthe 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 theat least one is deadstate, 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 catis the real cat. I mean, it's obviousonly 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… ;)

There are basically three kinds of teleportation: the kind where the thing you want to teleport

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薛定諤的貓如何遠距離傳送 (How to Teleport Schrödinger's Cat)

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    林宜悉 發佈於 2021 年 01 月 14 日
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