4

3

In Nielsen and Chuang Quantum Computation and Quantum Information book section 2.2.6, a POVM of three elements are used to measure a single qubit in order to know for sure whether the state is $|0\rangle$ or $|+\rangle$ if the first two measurement results are obtained, and do not infer the state when the third result is obtained.

My question is: is it physically realizable to measure three possible results from a single qubit? I thought you can only get n bit of information measuring n qubits. Three outcomes is more than one bit.

Thanks for the explanation. Yes, you are right, from information theory point of view, it's still one bit information. Is it possible to give an example, for instance, use photon, to show a device with such a three element POVM? – czwang – 2019-11-17T06:39:14.227

Translating this into quantum world, Nielsen and Chuang's POVM works as projective measurements on 2 systems, and it seems to me that POVM measurement is constructed from projective measurements. Is this correct? – kludg – 2019-11-17T07:02:25.667