"The Three-Body Problem" and Quantum Teleportation

I just finished reading the excellent Remembrance of Earth's Past trilogy¹ (perhaps more commonly known by the name of its first entry, The Three-Body Problem), a series of science-fiction novels about humanity's reaction to an alien civilisation's plan to invade Earth. In it, the author, Liu Cixin, tells an incredibely rich, nuanced and imaginative story about the future of humankind, in a way that I have never seen in science-fiction before. I was particularly impressed with his creative and unique inspirations drawn from real-world physics and astronomy, which rarely felt arbitrary or pseudo-scientific and made it apparent that he has a good amount of actual knowledge in these fields. One of the physical concepts that play an important role throughout the entire series stuck with me: quantum teleportation.

⚠ Major spoilers for the first entry of the trilogy ahead!

In 400 years, humanity will have a problem

The basic plot of The Three-Body Problem is this: a secret Chinese cold war-era project succeeds in establishing contact with the extraterrestrial system of Trisolaris, whose inhabitants are looking for a new planet to colonise due to the hostile conditions in their corner of space. Through this contact, Earth's location is exposed to the Trisolarans, who immediately head for the solar system in order to conquer it and destroy humankind. But there's a twist: even though they are vastly superior to Earth in terms of technology, their spaceships still need around 400 years to arrive, inadvertently giving humans time to prepare.

Obviously it is in Trisolaris' best interest to prevent Earth from making significant technological progress during this time. A lot could happen in 4 centuries, and the aliens do not have capacities to achieve scientific breakthroughs of their own while on their voyage. To tamper with and monitor human progress, they need to interact with Earth remotely. What makes this difficult, however, is that the speed of exchanging information is capped by the speed of light, as the specific theory of relativity tells us. While that is pretty fast to us, the Trisolarans are so far away from Earth that this still means years of delays between messages. Any sort of coordinated real-time influence on Earth using classical communication is therefore impossible. So, given that they are not on Earth yet and the effectiveness of classical communication depends on human cooperation, how could they possibly make sure that Earth stays inferior until they get there?

The aliens have a cheat code

One of the major mysteries throughout The Three-Body Problem, especially before the future invasion of the alien species becomes known to the public, is the inexplicable and abrupt halt of progress made in research across the entire world. The results of controlled experiments in particle accelerators suddenly become arbitrary, unpredictable and seem to contradict what we thought were laws of nature. After a while, it's clear that Trisolaris has something to do with this, but how? Later, towards the end of the book, we get an answer: sophons.

Sophons are essentially supercomputers in the form of a single proton, i.e. the size of subatomic particles. Because they're so tiny, Trisolaris is able to accelerate them to a much higher speed than the Trisolaran fleet and consequently have them arrive much sooner on Earth. A handful of protons are, of course, not really detectable, so, initially, nobody is aware of their presence. Their primary task is the disruption of experimental physics relating to particles (by simply messing with the experiments on a subatomic level), which explains the aforementioned problems in human research. The explanation for how these devices have been built by Trisolaris is cool, but not of relevance in this post.

Interestingly, the sophons are not some kind of fully autonomous AI, but actually directly controlled by Trisolaris, in real time. They can collect incredibly detailed information from anywhere in the world and share them with Trisolaris instantaneously, i.e., with no delay. That is why they're a sort of cheat code: nothing humans say or do is secret anymore, the hostile aliens are always watching and listening. This incredible disadvantage requires humanity to come up with all kinds of crazy and unique strategies to respond to the threat.

But wait a second, didn't I just say that information can't be transmitted faster than the speed of light? How can Trisolaris see what's going on on Earth in real time if they're so far away?

Quantum magic mechanics

It's a bit of a sci-fi trope at this point. When in doubt, just call something "quantum" to lend it scientific credibility in the eyes of a layperson. And indeed: sophons, the proton supercomputers of Trisolaris, supposedly communicate in real time through the use of quantum entanglement, according to the book's explanation. So there you have the answer: they defy the laws of physics "because quantum". But there's actually something more to this.

You see: quantum mechanics, i.e. our idea of how subatomic physics work, is weird. Very weird. So weird in fact, that world renowned physicists have said things like "I think I can safely say that nobody understands quantum mechanics". Certainly weird enough for Albert Einstein to think that our understanding of it can't be right, despite it being supported by experiments.

There are essentially two things that make the theory of quantum mechanics weird:

1. Quantum mechanics is not realistic in the philosophical sense: observing a system influences its state, which means that there is no state independent from observation. In other words: what you measure will never be what it was before you measured it. This conflicts with our intuitive reasoning that the result of a measurement must already exist before measuring.
   • this non-realism comes from the concept of superposition, the idea that a quantum system can be in multiple states at once
2. Quantum mechanics is not local in the sense of the theory of relativity: interacting with one system can influence another system instantaneously, no matter how far apart they are. Remember that relativity forbids anything travelling faster than the speed of light. But if I interact with a particle and that influences a particle on the other end of the universe without delay, something has happened that does not respect this speed limit!
   • this non-locality comes from the concept of entanglement, the idea that two quantum systems can be physically separate but still influence each other

Aha! There is quantum entanglement again, the explanation for sophons in The Three-Body Problem. The surface-level idea of how it might be used by sophons to transfer information instantaneously is pretty simple:

1. You take two quantum particles (such as photons or protons)
2. You entangle these particles such that the state of one determines that of the other
3. You keep one and send the other off to Earth
4. Now when the one on Earth is observed/measured, you instantaneously (faster than light!!!) see the result on your side.

Now just expand this system, use more entanglement and more particles and you've built an information teleporter. Is that right?

Einstein was wrong

As described earlier, quantum mechanics is neither realistic nor local, two very important cornerstones of what we now call classical physics. You could say that classical theories, i.e. theories that conform to the principles of realism and locality, are "reasonable". The output is always determined by the input, you can view systems in isolation etc. This is nice.

Einstein wanted to have a classical theory for quantum systems, so he was convinced that there had to be something missing from quantum mechanics as we know it. To put Einstein's thoughts very bluntly: surely, there must be some piece we're missing that, if added to quantum mechanics, would make the whole thing... make sense? That piece would then give us a theory that does not conflict with the theory of relativity (which is both realistic and local). This idea became known as the Einstein-Podolsky-Rosen (EPR) paradox. Although like most things we call "paradoxes" it wasn't actually one; it was an argument that if the entire physical world can be modeled classically, quantum mechanics must be incomplete.

How do you respond to an argument like that? We never found a missing piece, which seems to suggest there isn't one. But how do we know for sure that we're not missing something from quantum mechanics?

Physicist John Bell gave us an answer: he took the EPR paradox ("there must be a quantum theory that adheres to realism and locality") and derived a mathematical inequality from it. This gave him the following proposition: "If there is a classical theory for quantum systems, then this inequality must be true" and conversely "If this inequality is not true, there is no classical theory for quantum systems".

At first, this answered the EPR paradox only via thought experiment; later, it was confirmed in the real world as well. Bell and physicists after him were able to show that the inequality he derived from the EPR paradox was not true for quantum systems. Thus, the efforts to find a quantum theory that "makes sense" in the framework of classical physics had been futile. This is Bell's theorem: in order to model how quantum systems work, your theory must be either non-realistic or non-local (or both). There cannot possibly be a quantum theory like Einstein imagined.²

Quantum information theory ruins all the fun

Remember when I described how sophons might use quantum entanglement for information transfer?

1. You take two quantum particles (such as photons or protons)
2. You entangle these particles such that the state of one determines that of the other
3. You keep one and send the other off to Earth
4. Now when the one on Earth is observed/measured, you instantaneously (faster than light!!!) see the result on your side.

Well, as it turns out, this is actually the simplified version of what Bell did to answer the EPR paradox. The specifics of it are a bit more complex, of course (how to you entangle two quantum states? How do you separate them? How do you actually measure them?) but the essence is there. Except for one crucial part that I conveniently left out.

Imagine you are Trisolaris. You built your sophons and sent them to Earth. Now you want the sophons to tell you what is happening on Earth. Let's make this very simple: say that you want the sophons to collect a single bit of information, e.g. you want them to the answer to the question "does pineapple belong on pizza?" Yes or no – 1 or 0. The sophons are supposed to send you that single bit, instantaneously using quantum teleportation. Thanks to the setup described above, the sophon has one of the entangled particles and you have the other. These two particles form a Bell pair.

On its own, that is not very useful yet. You now have a channel for communication – if the sophon measures its side, the result appears on your side – but the answer to the actual question is still missing from the mix. To actually include the bit of information in the transfer, the sophon must encode it using another particle and then entangle that new particle with its existing part of the Bell pair. This way, your part of the Bell pair becomes (indirectly) entangled with the actual bit of information. But here is where the problem arises.

The sophon's measurement of its two particles affects your side of the channel, yes. However, because the sophon entangled the bit of information and its part of the Bell pair (which is in superposition), the outcome of its measurement are completely random! It could measure 0 and 0, 0 and 1, 1 and 0 or 1 and 1. Depending on this result, what you see on your side changes as well. If the sophon happens to measure 0 and 0, you see exactly the bit of information it wanted to transfer. If it measures something else, you have to make an adjustment in your calculation specific to what the sophon measured in order to actually get the answer. Unfortunately, you don't know what the sophon measured, so you don't know what adjustments you need to make to reconstruct the bit of information, so you're left with no information gained at all.

This is where quantum teleportation fails to work as instant communication. Yes, quantum teleportation is actually real – but without knowing two additional (classical) bits of information from the other side, it's utterly useless. The solution to make it usable, therefore, is for the sophon to send you its two measurement results through a non-quantum channel first – only then can you interpret the data it teleported to you through the entangled particles. The inability to communicate by only using quantum mechanics is called the no-communication theorem.

But if the sophon has to send you two bits using classical communication first, your overall communication is again restricted by the speed of light! Shucks. Your evil plan to invade Earth has been foiled by quantum information theory.

The fact that we can't just use quantum mechanics to transmit information faster than light willy-nilly is probably a good thing, and not just because it means that the Trisolarans won't be able to spy on us:

[The ability to transmit quantum states faster than light] would be rather peculiar, because the theory of relativity implies that faster than light information transfer could be used to send information backwards in time.³

Quantum mechanics may be weird, but I'm glad we dodged that bullet.