字幕列表 影片播放 列印英文字幕 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… ;)

B2 中高級 薛定諤的貓如何遠距離傳送 (How to Teleport Schrödinger's Cat) 0 0 林宜悉 發佈於 2021 年 01 月 14 日 更多分享 分享 收藏 回報 影片單字