Citation: Cubitt, Toby S., et al. "Separable states can be used to distribute entanglement." Physical review letters 91.3 (2003): 037902.
Web: https://arxiv.org/abs/quant-ph/0302168
Tags: Information-theoretical
In this paper, the authors show that two quantum particles can become entanglement by sharing a particle which is never entanglement with the first two. Namely, there is a process whereby two unentangled particles can send back-and-forth a third particle which is at every step unentangled with the first two, and at the end they create entanglement between them. The idea here is as follows. Denote the source and target particles by A,B, and the mediating particle by C. At the first step, A talks to C and prepares a state with the following property: A is entangled with BC, but B is not entangled with AC and C is not entangled with AB. The nature of tripartite states is that such a configuration is possible, and can be obtained just by acting on AB. The particle C is then sent to B, and the entanglement between A and BC becomes entanglement between A and B, as desired.
This is a lovely little paper. The fact that this took a while to be discovered (and was only found by such a high-powered cast of authors!) demonstrates how subtle it can be to reason about quantum mechanics and cryptography in general. Fun!
The authors demonstrate several protocols to implement this phenomenon. One approach is a clean pure-quantum-information qubit example. Another approach is to use a Hamiltonian typical of trapped ion experiments. In this trapped ion example the analysis is performed using perturbation theory, so one concludes that the state is mildly non-separable. Adding a bit of noise (i.e. taking a convex combination with the maximally mixed state) turns approximately separable states into separable states, which shows that the trapped-ion example is not relying on the small amount of entanglement to get its power.