Quantum wires: prime numbers make the difference

LP12825 - Imagine a bunch of people forming a line. By talking to each of the their neighbours, they help Alice, at one end, in passing a message to Bob, at the other end. Like a sort of bucket brigade. If all do their job correctly, the message should reach Bob independently of the number of people in line. However, if we substitute people with (interacting) “talking” quantum particles, a new analysis shows that this is not the case, and that the number of people is crucial. Lines of this type are called quantum wires: they model the transfer of information between quantum particles and appear in a variety of nanodevices engineered and natural. It is known since a decade that perfect communication in quantum wires is impossible beyond three particles. But now we know that if we include an arbitrarily small imperfection, and if we wait long enough, then the message is very likely to reach Bob, exactly when the length of the wire is very special: a power of two, a prime or twice a prime. This peculiar phenomenon is due to interference effects. So, if the wire is composed by 9 particles, which is not one of these numbers, Alice better invites an extra particle to join the line and then get to 10 – which is twice a prime. The result opens up the possibility of employing quantum dynamics to design “natural algorithms” for probing the arithmetic structure of numbers