# VII. Quantum Networks – Using Dynamics to Restore and Extend Entanglement

Quantum networks use a continual dynamical sequence of entanglement to teleport a quantum state for purposes of communication. It works like this: suppose A, B, C, & D are qubits and we entangle A with B in one location, and C with D in another (most
laboratory quantum networks have used entangled photons from an EPR source for qubits). The two locations are 200km apart. Suppose the farthest we can send B or C without losing their quantum information to decoherence is 100km. So, we send B and C to a quantum repeater halfway in between. At the repeater station B and C are entangled (by performing a Bell state measurement, e.g. passing B and C thru a partially transparent mirror). Instantaneously, A and D will become entangled! Even if some decoherence sets in with B and C, when they interact at the repeater station full entanglement is restored. After that it does not matter what happens to B or C. They may remain entangled, be measured, or completely decohere – A and D will remain entangled 200km apart! This process can be repeated with N quantum repeaters to connect arbitrarily far away locations and to continually restore entanglement. It can also be applied in a multiple party setting (3 or more network endpoints). We could potentially have a vast number of locations entangled together at a distance – a whole quantum internet! When we are ready to teleport a quantum state, $\left|\phi\right>$, (which could be any number of qubits, for instance) over the network, we entangle $\left|\phi\right>$ with A in the first location and then D will instantaneously be entangled in a superposition of states at the second location – one of which will be the state $\left|\phi\right>$! In a multi-party setting, every endpoint of network receives the state $\left|\phi\right>$ instantaneously! Classical bits of information must be sent from A to D to tell which one of the superposition is the intended state. This classical communication prevents information from traveling faster than the speed of light – as required by Einstein‘s special theory of relativity.

Figure 18: A diagram of a quantum network from Centre for Quantum Computation & Communication Technology. EPR sources at either end are sources of entangled qubits where A&B and C&D are entangled. The joint measurement of B & C occurs at the quantum repeater in the middle entangling A & D at a distance.

Researchers further demonstrated experimentally that macroscopic atomic systems can be entangled (and a quantum network established) by transfer of light (the EM field) between the two systems (“Quantum teleportation between light and matter” – J. Sherson et al., 2006). In this case the atomic system was a spin-polarized gas sample of a thousand-billion ($10^{12}$) cesium atoms at room temperature and the distance over which they were entangled was about $\frac{1}{2}$ meter.