The Quantum Internet (Patreon)

When we finally have a quantum internet you’ll be able to simultateously like and dislike this video. But we don’t. So I hope you like it.

The world is widely regarded as being well and truly into the digital age, also called the information age. No longer are economies and industries solely characterised by the physical goods they produce, and in fact some of the largest companies in the world produce no physical goods at all: digital information is a commodity in its own right. As discussed in a previous episode, this worldwide digital economy is fundamentally reliant on certain cryptographic processes. Currently these processes work in the realm of classical cryptography, but one day soon this may not be enough and so quantum cryptographic methods and algorithms are being developed. However, it’s one thing to design a protocol, it’s something else entirely to build a system to support it. To understand what needs to be done we need to get to the foundations of quantum mechanics - we need to talk about quantum information theory.

First plain-old non-quantum information theory - the study of the creation, storage, and transmission of information, typically in the form of classical bits, 1’s and 0’s. Claude Shannon started it all with his 1948 paper “A Mathematical Theory of Communication”, which quantified the rate of digital information that can be transferred without error given the amount of noise in a communication channel. Information theory has since blossomed into a full science, ultimately connecting the concept of information and certain fundamentals of physics - such as entropy, and also quantum theory.

Quantum information theory parallels classical information theory, but instead of using classical bits, it deals bits of quantum information - qubits. Qubits enjoy all of the weirdness of quantum mechanics - they can be in a superposition of many states at once, defined only when they are measured, two qubits can be entangled with each other, so both of their states are determined when one is measured; they can even be teleported. Qubits are also subject to some fundamental restrictions, which I’ll get to. Those restrictions, on top of all the weirdness, define the challenge of transmitting and storing quantum information.

But first, a reminder why we want to muck around with quantum info in the first place. First there’s the whole quantum computer thing - in those, the ability for a qubit to hold many simultaneous states can lead to massive speed-ups in certain types of computing. Partly motivated by the cryptography-cracking power of the quantum computer, we also want to think about a quantum internet. In fact we already did. In our episode on quantum key distribution we talked about two schemes for sharing cryptographic keys that should be far more secure than classical counterparts. But these only work if you can actually send entangled quantum states between parties - that means transmitting qubits over long distances perfectly intact.

So ultimately what is preventing from us just setting up these networks and getting on with it? We can already send photons of light very long distances using lasers or fiber optics - and those photons are pretty quantum. The problem is that to transmit quantum information we have to pay attention to individual photons - quanta of light. To transfer classical information using light, each bit is encoded with many photons, and many can be lost or altered en route without compromising the signal. If too many photons are going to be lost you can just run the channel through a repeater, which reads the signal and boosts it with extra photons.

It’s much harder to transmit single photons in a way that perfectly maintains their quantum state. And it’s fundamentally impossible to boost that signal by duplicating those photons. This impossibility is referred to as the no-cloning theorem. It simply states that: “you cannot take a quantum state and copy it perfectly to end up with two copies of the same state existing at the same time”. This is connected to the law of conservation of quantum information, which we’ve talked about before - it comes from the fact that every quantum state in the universe must be perfectly traceable - single quantum state to single quantum state - both forwards and backwards in time. That prohibits a quantum state vanishing, but also splitting in two - or being copied.

The no cloning theorem means that as soon as you try to read a qubit, which you have to do at some point to make the copy, you disturb the state in such a way that you will never end up with two exact copies of the same quantum state. Plus, even if you could copy it, you wouldn’t really be able to transmit an entangled quantum state because the act of reading in the state to copy it would destroy the entanglement through a phenomenon called decoherence.

While it’s impossible to copy a qubit, it IS possible to overwrite one - and it can be overwritten with exactly the same state but in a completely different location. In other words, qubits can be teleported. This doesn’t allow faster-than-light communication because a classical, sub-light-speed channel is still needed to extract the information. But quantum teleportation DOES allow us to massively extend the range over which we can send an intact qubit. No copying or boosting needed.

Think of it like this. Two people, let’s say Bill and Ted, are connected by a classical channel and a quantum channel. The classical channel can be anything - a fibre optic cable, a telephone wire, the Pony Express, whatever, while the quantum channel needs to carry intact quantum states - so probably fibre optics. A pair of entangled particles are created, and Bill and Ted receive one each via the quantum channel. Bill has qubit A and Ted has qubit B. Now, say Bill wants to send a message to Ted, and that message is stored as the state of a third qubit – qubit C. That would be only one bit of information, but you could always use more qubits. To send that message, Bill performs a particular type of measurement on his qubits called a Bell measurement. Performing this measurement simultaneously on A and C entangles these qubits but breaks the entanglement between A and B. However qubit B then has to be in whatever state C was in prior to the measurement. 

Let’s look at a more concrete example – although I have to add that this is way oversimplified. Qubits A and B could be the polarization states of two photons. They’re entangled so that they have opposite polarization, say one is vertical the other is horizontal. Measure one and you immediately know the other. Now Bill takes photon A and entangles it with photon C using a Bell measurement so that now A and C have opposite polarization. Photon B, which was opposite to A, must now be the same polarization as the original photon C. At this point the original quantum state of photon C has been almost completely teleported to photon B. The reason it’s incomplete is that there is more to the quantum state of C than simply the aspect of the polarization that is fixed by the entanglement. The remaining information of the quantum state is actually obtained by observing the outcome of the process that generates the entanglement itself. 

This measurement outcome is encoded in two classical bits which Bill sends to Ted along the classical channel. Using the information in these two bits Ted can then calibrate a measurement of his own on his qubit B, after which that qubit will be in the state qubit C was at the start. A minor technical caveat that you we are only using photonic qubits then it's not so easy to perform a Bell measurement that will give all of the information we need for this final step, but it's definitely possible for matter qubits.

Combined with a quantum key distribution protocol, this can give us a mechanism for secure communication. It can also be used to transmit quantum information over longer distances than we could normally send entangled particles. Just position repeaters along the quantum channel between Bill and Ted. Bill performs the above trick with the nearest repeater, that repeater communicates with the next repeater, and so on until we reach Ted – who should still get a copy of the original qubit C. In principle this can be done without the quantum channel ever becoming un-quantum. Which means it stays secure.

OK, sounds easy, right, but there are complications. It’s pretty much impossible to do all the transmissions, entanglements, and measurements in perfect synchrony. Quantum states have to somehow be stored – by Bill, by Ted, and by the repeaters in between. This typically means transferring a quantum state between a photon and a matter particle – say, an electron whose up or down spin direction can be entangled with the polarization state of a photon. But storing delicate quantum states for any length of time is hard work – especially if you don’t want insanely expensive supercooled devices.

Experimentalists have of course come up with a number of ingenious solutions, ranging from storing entangled photon quantum states in a cloud of caesium atoms, a kind of quantum atomic disk drive, or the spin-state of a single electron in a nitrogen atom embedded in diamond crystal. In the future, if entangled states can be maintained for long periods, it may be possible for two people to hold a large array of mutually entangled qubits, which they could use to communicate by exchanging classical Bell measurement data. This could also be done between many individuals and a centralized node – a sort of quantum switchboard.

There are also proposals for removing the need for physical storage all together, with repeaters that are entirely photonic. These are great because they’re much, much faster than repeaters that have to transfer quantum states between photons and matter particles.

So the current state of the art is that entangled quantum states have been transmitted with photons using fibre optics, lasers. Some researchers have even succeeded in bouncing entangled photons off a satellite. These photons can then transfer their entangled states into a variety of matter storage systems, which may eventually serve as repeaters to extend the range and connect a network of these quantum channels. 

Reliability and speed are not where we need them to be, but the progress is fast. We currently live in the information age, but it’s a classical information age. We’ve gotten pretty far sending streams of 1’s and 0’s round the world, but if we could build truly quantum networks we’ll also be able to build the next generation of cryptographic protocols, distributed quantum computers, as well as achieve new levels of atomic clock synchronization and extreme precision in our interferometric telescopes. The quantum information age is around the corner. I’m guessing we’ll go with “quantum age” - as the quantum internet enables us to take advantage of the incredible properties of our quantum space time.