Entanglement is a peculiar feature of quantum systems that makes them behave as if they were sitting directly next to each other even if they are kilometres away. Such behaviour does not occur in classical physics. Classical particles can affect each other through fields — such as the gravitational or electromagnetic field — but these fields propagate with the speed of light; the interaction between entangled particles, however, is instantaneous. Simply as if the distance between them did not exist.

Entanglement started to interest scientists in the early days of quantum physics (it was first mentioned by Erwin Schrödinger in 1935) but only in the 1990s, it was realised that entanglement can also be used as a resource for quantum communication. After some 20 years of intensive research, not much has been achieved in creating entanglement (over long distances as is needed for quantum communication) in the laboratory. The main problem is that the only system that we can send over such distances is light; if a system does not interact with light, it cannot be entangled with another system that is sitting far away.

One particular example of such a system is a superconducting circuit. These typically work at energies corresponding to microwave fields and microwaves cannot be transmitted as easily as light (at least in the quantum regime; the world is too hot for them and the signal they carry does not survive). But superconducting systems seem to be very well suited for quantum computing. And having a (quantum) computer which cannot communicate with other computers over (quantum) internet… well, what’s the point?

Naturally, scientists started looking for a way to connect superconducting circuits and light using a third system that can interact with both. There are several candidates for such an interface — sort of a quantum network card, if you like — and one of the most promising options is to use a mechanical oscillator for the task. Those can be relatively easily manufactures, well controlled, and they can strongly interact with both light and superconducting circuits.

What can we do with all that? Let us start with the simplest possible task — entangling two quantum bits formed by superconducting circuits^{1} and connected by light. There are many ways this can be done; we will use an approach where the light is used to measure the two qubits. A well-chosen measurement which reveals some joint property of the qubits can result in an entangled state; furthermore, it has the advantage that the right measurement outcome signals that the entangled state has been successfully created. (This is also a reminder of the importance measurements have in quantum physics that I wrote about before.)

Suppose we now start by preparing the qubits in such a state that each qubit has values 0 and 1 at the same time. Now, we let each qubit interact with a mechanical oscillator and the oscillators interact with a beam of light that we measure. If we build the system the right way, the measurement of light will tell us how many qubits have the value 1. It can happen that both or none have this value, which is uninteresting. But if exactly one of the qubits has the value 1 (the other, naturally, has the value 0), they are entangled because we cannot tell which qubit has which value. No matter how far apart they are, if we now measure one of the qubits to be in the state 0, the other will immediately end up having the value 1 and vice versa.

There is are many things one can do once the qubits are entangled — transfer quantum states using quantum teleportation, send encrypted messages using quantum key distribution, or try to confirm quantum mechanics by violating Bell’s inequality, for example.

Ultimately, people are interested in creating entanglement in more complicated systems; with superconducting circuits, it would be interesting to have many qubits entangled. There is one very practical reason for that: Superconducting quantum computers need to work at very low temperatures (only about 0.01 °C above absolute zero) and it is very difficult to cool things to such low temperatures. As a result, only small things can be successfully cooled. Future superconducting quantum computers therefore cannot be very large; to have one large, powerful quantum computer, it is then necessary to connect several such computers using entanglement. Then, the many small computers will behave as if they all were in the same large fridge, forming parts of a large quantum computer.

*This post aims to summarise the main results of a paper I wrote with my PhD advisor on the topic of generating entanglement of superconducting qubits using optomechanical systems. A free preprint can be found at arXiv.*

^{1} Superconducting qubits work similar as classical bits in a computer — there is a current running through a circuit and the value of this current determines the value of the bit. The only principal difference is that a classical bit has a value of either 0 or 1 whereas a quantum bit can also be in their superposition, having values 0 and 1 *simultaneously*.

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