When we finally have a super-fast quantum internet, you’ll simultaneously like and dislike this blogging post. But we don’t yet. So I hope you like it. Now we are in the age of information or data. No longer are economies and industries solely characterized by the physical products they produce for customers. Of course, a number of the biggest companies in the world produce no physical products at all. Digital information could be a commodity in its title.

## Needs of Quantum internet

The digital economy worldwide is essentially based on different cryptographic processes. Such processes operate in the realm of classical cryptography, but this will saturate the process. Quantum cryptographic methods and algorithms will be the only option then.

Designing a protocol is one thing, and creating a system to support it is entirely something else. To know more about it, we’d like to urge the foundations of quantum physics – we need to speak about quantum information theory.

First, In plain-old classical information theory, we do the study of the creation, storage, and transmission of data, in the form of classical bits, 1’s and 0’s.

## Classical information theory

Claude Shannon began it all along with his 1948 paper “A Mathematical theory of communication,” which quantified the speed of transmission of digital information. We can transmit digital data without error if a given amount of noise is present in the communication channel. Information theory has since blossomed into a full modern science, by connecting the concept of information and certain fundamentals of quantum physics, like entropy and quantum theory.

## Quantum information theory

Quantum information theory parallels classical information theory, but rather than using classical bits. It deals with bits of quantum information, which is qubits. Qubits enjoy all of the weirdness of quantum physics – they can be in a superposition of the many states at once, defined if they’re measured, two qubits can entangle with one another, so both of their states we can determine when one is measured. They can even be part of teleportation.

#### Restrictions of qubits

Qubits are subject to some fundamental restrictions. Those restrictions, on top of all the weirdness, define the challenge of transmitting and storing quantum information using quantum bits. But first, a reminder of why we wish to muck around with quantum info in the first place.

First, there’s the entire quantum computer thing – in those, the power for a qubit to carry many simultaneous states can result in massive speed-ups in certain computing forms. Partly motivated by the cryptographic-cracking power of the quantum computer, we also want to consider a quantum internet.

Quantum cryptographic key distribution for sharing cryptographic keys, will be way more secure than classical counterparts. But these only work if you can send entangled quantum states between parties – meaning transmitting qubits over long distances perfectly intact.

## Challenges of the quantum internet

So ultimately, what’s preventing us from just fitting these networks and getting on with it? We can already send digital data in the forms of 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’ve to concentrate on individual photons – quanta of light. When we transmit classical information using light, we do encode each data with many photons, and lots of are often lost or altered on the way without compromising the signal. If too many photons are lost, you can just run the channel through a repeater or signal booster, which reads the signal and boosts it with extra added photons.

#### No cloning theorem

It’s much harder to transmit and receive a single photon in a way that perfectly maintains their actual quantum state. And it’s fundamentally impossible to boost that signal by duplicating those photons with their actual state. It is merely because of the no-cloning theorem. It says, “You can’t pick a quantum state and replicate it exactly the same, and end up with two identical copies of the same quantum state that exist simultaneously.”

It has a connection with the law of conservation of quantum information. It comes from the fact that each quantum state in the universe must be entirely traceable – single quantum state to only quantum state – both forwards and backward in time. That prohibits a quantum state vanishing, but also splitting in two or being replicated.

The no-cloning theorem implies that as soon as you are trying to read a qubit, which you have to do to create the copy, you disturb the state in such a way that you will never end up with two exact replicas of the same quantum state. Plus, even if you could copy it, you wouldn’t be able to transmit an entangled quantum state because the act of reading in the state to copy it might destroy the entanglement through a phenomenon called decoherence.

## What is the solution?

While it’s impossible to repeat a qubit, it’s possible to overwrite one – and we can overwrite it with precisely the same state but in a very completely different location. In other words, we can teleport qubits. This process doesn’t allow faster-than-light communication nor teleportation of actual matter, because a traditional, sub-light-speed channel is still needed to extract the data. But quantum information theory does will enable us to massively extend the range over which we can send a perfectly intact qubit.

No copying or boosting needed.

## Example

Consider it this way: Two people, such as Jack and Joe, are connected by a classical channel and a quantum channel. The classical channel may be anything – a fiber optic cable, a telegraph wire, the pony Express, whatever, while the quantum channel needs to carry intact quantum states – so it’s probably fiber optics. A pair of entangled quantum particles are generated, and Jack and Joe receive one each via the quantum channel. Jack has qubit A, and Joe has qubit B.

Now, say Jack wants to send a message to Joe, which is stored as the state of a 3rd qubit – qubit C. That will be only 1 bit of information, but you may always use more qubits. Jack executes a specific type of measurement on its qubits are known as bell measurements to send that message.

Performing this test on A and C at the same time interferes with these qubits, thus eliminates the interferences between A and B. However, qubit B then must be in whatever state C was in before the measurement.

Let’s look at a more concrete example – although I’ve got to mention that this can be way oversimplified. Qubit A and qubit B could be the polarization states of two photons. We can entangle them to have opposite polarization, say one is vertical, and the other is horizontal. Measure one, and you immediately know the opposite. Now Jack takes photon A and entangles it with photon C employing a Bell measurement so that now A and C have opposite polarization qubits. Photon B, which was opposite to A, must now be the identical polarization because the original photon C. At now, the initial quantum state of photon C, which contains the message, has been almost wholly teleported to photon B.

The reason it’s an incomplete explanation is that there’s more to the quantum state of C than merely the aspect of polarization fixed by the entanglement. The remaining information of the quantum state is obtained by observing the result of the method that generated the entanglement.

This measurement result is encoded in two classical bits that Jack sends to Joe along the conventional channel.

Joe will then calibrate a calculation of his own qubit B using the information in those two bits, after which the qubit would be the state of qubit C was at the beginning.

A minor technical caveat is that we are only using photonic qubits. It is not very easy to perform a Bell measurement, which will give all of the data we need for this final step, but all of this is often definitely possible with matter qubits. Combined with a quantum key distribution protocol, this could provide a mechanism for secure communication. It may be used to transmit quantum information over longer distances than we could generally send entangled particles.

Repeaters are present along the quantum channel between Jack and Joe. Jack performs the above trick with the closest repeater. That repeater communicates with the subsequent repeater, so on until we reach Joe – who should still get a duplicate of the original qubit C. In theory, this may be done without the quantum channel ever becoming un-quantum. Which implies it stays secure.

OK, sounds easy. But there are complications. It’s pretty much impossible to do all the transmissions, entanglements, and measurements in perfect synchrony. Quantum states should somehow be stored – by Jack, by Joe, and by the repeaters in between. It means transferring a quantum state between a photon and a matter particle – say, an electron whose up or down spin direction will be entangled with the photon’s polarization state.

But storing delicate quantum states for any length of time is tough work – especially if you don’t want expensive, supercooled devices. After all, experimentalists have come up with a variety of ingenious solutions, starting from storing entangled photon quantum states in a cloud of cesium atoms, a form of a quantum atomic disc drive, or the spin-state of one electron in a nitrogen atom embedded in the diamond crystal.

Suppose we can maintain the entangled states for long periods. In that case, it should be possible for two people to carry a vast array of mutually entangled qubits, which they may use to communicate by exchanging classical Bell measurement data. It might even be done between many individuals in a centralized node – a sort of quantum switchboard. There are proposals for removing the need for physical storage altogether, with repeaters that are entirely photonic.

These are great because they’re much faster than repeaters that need 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 fiber optics and lasers.

Some researchers have even succeeded in bouncing entangled photons off a satellite. These photons can then transfer their entangled states into a range of matter storage systems, which can eventually serve as repeaters to increase the range and connect a network of these quantum channels. Reliability and speed aren’t where we need them to be, but the progress is fast.

We currently sleep in the information age, but it’s a classical modern era. We’ve gotten pretty far sending streams of 1’s and 0’s around the world. Still, suppose we could build genuinely quantum networks. In that case, we’ll even be able to create the following generation of cryptographic protocols, distributed quantum computers, and achieve new levels of atomic clock synchronization and extreme precision in our interferometric telescopes.

The quantum information age is knocking our door. I’m guessing we’ll go with “quantum age” – because the quantum internet enables us to take advantage of the incredible properties of our quantum space-time.

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