When probe states are "classical", measurement accuracy is limited by the so-called standard quantum limit. Non-classical states, including squeezed states and entangled states, can be used to enhance the precision beyond the standard quantum limit, reaching the Heisenberg limit. But how do we measure whether a state is entangled in the first place? This is in itself another non-trivial quantum measurement situation. In principle, we can try to determine what the state of a quantum system is, and then from that try to estimate whether it is entangled or not. But this may not be very reliable. One other option is to test whether our quantum state violates a so-called Bell inequality. This will be illustrated by a recent experiment to verify that the orbital angular momentum of two photons, resulting from parametric down-conversion, was entangled in at least 11 x 11 dimensions.

When it comes to distinguishing between different quantum signal states e.g. in a communication situation, again, quantum measurements can be optimised in various ways. The optimal measurements go beyond standard projective measurements, in the eigenbasis of some observable. The resulting "generalised quantum measurements" are not merely theoretical constructs, but can be realised in a range of physical systems, including photons and trapped ions. This will be illustrated for example by looking at the case of distinguishing between two non-orthogonal states. Such a situation arises for example whenever two signal states have passed though a lossy channel, so that they are no longer perfectly distinguishable. Recent work on measurements for distinguishing between non-orthogonal quantum states includes optimising the measurements for when real and therefore imperfect detectors are used.