[katieHaylor (OP)]

Tilo asks:

Can we entangle an already entangled particle?

What do you think?

[jeffreyH]

That will be multipartite entanglement. I haven't read much about it but there is a wikipedia article.
https://en.m.wikipedia.org/wiki/Multipartite_entanglement

[evan_au]

Yes, it is possible to entangle multiple particles.

In fact, it is essential for making a useful quantum computer, where data is computed using "quantum bits" or "qubits"..
- One of the earliest demonstrations of "useful" quantum computing was a 4-qubit computer that managed to factor 15 into 3 x 5.
- But the power of a quantum computer goes up exponentially with the number of qubits
- It is estimated that a 50-qubit quantum computer would be more powerful than a computer which could be conceivably constructed on Earth
- This state is given the bold name "quantum supremacy"
- Of course, this only applies to algorithms that can take advantage of quantum weirdness; we don't have quantum-optimised algorithms for many real-world problems.
- And it still wouldn't be able to factor a 1000-bit public key used for commercial encryption

See: http://spectrum.ieee.org/computing/hardware/google-plans-to-demonstrate-the-supremacy-of-quantum-computing