The Heisenberg limit is not a limit?

Question

This new Best-ever quantum measurement breaks Heisenberg limit

PHYSICISTS have made the most accurate quantum measurement yet, breaking a theoretical limit named for Werner Heisenberg.

Nature, DOI: 10.1038/nature09778

When an experiment breaks a theoretical limit we have to reassess what we are accustomed to know. Is it the case with this experiment? At what level ?

Answer 1

The use of the term "Heisenberg Limit" is somewhat misleading for outsiders (that is non-quantum Interferometers). If we recall the Heisenberg Uncertainty Principle is a limit on simultaneous measurement of two complementary variables. In the case of (quantum) metrology one is only interested in the measurement of a single variable to high accuracy, and this does not (directly) conflict with the HUP.

In the case of interferometry the variable of interest is $\Delta \Phi$ the phase difference between two waves detected in two arms. In basic interferometry there were some limits as to how accurately this could be measured:

Quantum Shot Noise : $\Delta \Phi = 1/N^{1/2}$

Heisenberg Limit : $\Delta \Phi = 1/N $

Here the N corresponds to how many quanta are required for the given accuracy, so the second is more accurate when it can be achieved, as was eventually done using entangled states, and perhaps squeezed light. If you cannot use these features of QM one gets just the Quantum Shot Noise accuracy.

Well a few years ago it was noticed that the assumption behind the Heisenberg limit calculation was that the Hamiltonian was quadratic in its (key) variables: this corresponded to the assumption of linearity amongst the measuring quanta. If the Hamiltonian could be made non-linear then an improvement on the Heisenberg limit would be possible.

This interaction between the measuring photons is discussed in the given paper, in Arxiv form here.