The square root of a number operator is Hermitian and therefore in principle, it should be possible to measure it in a laboratory. Also, the number operator itself, say for photons, can be estimated using counting statistics. So, is there a way to measure the square root of the number operator experimentally in the same spirit? I am also aware of the statement that there are Hermitian operators which can not be measured in a laboratory.
Dear Aleksei,
Thank you for your response. Here is what I think-
In quantum mechanics, a measurement is peformed using a measuring device whch is itself a quantum system (Consider for example von Neumann measurement model). One couples the measuring device with the system to be measured, such that the interaction Hamiltonian contains the operator to be measured and the conjugate observable to the measuring device's meter along with a coupling parameter. In laboratory one need to simulate the unitary generated by above interaction Hamiltonian. And in general, one simulates the required unitary using quantum gates. For continuous variables one usually does a homodyne or hetrodyne kind of measurement. I am asking specifically, what could be a homodyne measurement or something to measure square root of number operator? Or what are the quantum gates that will simulate the above unitary generated via interaction Hamiltonian?
For me, calibrating scale of a measuring device seems to be possible only when one knows the relation between what is being measured and what exactly one wanted to know. Here in my question the relation is known. So your answer may qualify to be a solution. But I wanted to ask, whether there is a direct way to get the desired outcome imprinted on the meter by coupling square root of number operator itself to the measuring apparatus. In this case intuition is not rquired to interpret the results as it is what it is.
Regards,
Uttam
Dear Charles Francis,
Am glad and suprised to see you here considering the foundation of QM. I would like to use your presence to invite to take part in a discussion on sci.physics.research
Called Diffraction of a particle. You took part in a similar discussion some time ago on a thread Action withot interaction. Your opinion was very close to m.ine as far I can judge. SO I would be happy to see your comments there.
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