Naimark extension for continuous variables

[atyy]

For discrete variables, a POVM on a system can be thought of as a projective measurement on the system coupled to an apparatus. This is called the Naimark extension. Is this also true for continuous variables?

http://arxiv.org/abs/1110.6815 (Theorem 4, p10)

 

[bhobba]

I would say yes.

Continuous variables are best handled by the Rigged Hilbert Space formalism which is simply a limit of the finite case.

Thanks
Bill

 

[atyy]

So presumably if I would like to make an "accurate" measurement of a system's position, in the Naimark extension I should not measure the position of the ancilla? The reason I'm thinking this is that the position of the ancilla will not have any eigenvectors in the Hilbert space, so one must measure some other observable of the ancilla that has eigenvectors in the Hilbert space?