Measurement and the creation/loss of information

[entropy1]

If we measure, say, the polarisation of a photon, the polarisation state of the photon collapses along the eigenvector of the observable corresponding to the measurement.

This may seem as a loss of information of the original polarisation (for it is now collapsed into another value). However, it can also be viewed as the creation of information (ie the measurement result).

What is the correct interpretation?

 

[Mentz114]

If we measure, say, the polarisation of a photon, the polarisation state of the photon collapses along the eigenvector of the observable corresponding to the measurement.

This may seem as a loss of information of the original polarisation (for it is now collapsed into another value). However, it can also be viewed as the creation of information (ie the measurement result).

What is the correct interpretation?

In this paper in section 5.4 you'll find a similar question discussed

Quantum mechanics: Myths and facts
Hrvoje Nikolic

http://arxiv.org/abs/quant-ph/0609163

 

[A. Neumaier]

If we measure, say, the polarisation of a photon, the polarisation state of the photon collapses along the eigenvector of the observable corresponding to the measurement.

This may seem as a loss of information of the original polarisation (for it is now collapsed into another value). However, it can also be viewed as the creation of information (ie the measurement result).

What is the correct interpretation?

Neither.

The polarization of a beam of light changes upon passing the polarizer. Typically part of the light is absorbed and the intensity of the output beam is dimmed by a factor determined from Malus'[/PLAIN] law. Interpreted in terms of photons (as clicks of a hypothetical detector at the end of the ingoing or outgoing beam) the rate of photons is proportional to the intensity. One cannot say what happens to a single photon. The conventional way to talk about the reduced rate is to say that the photon emerges in the state determined by the polarizer with a probability given by Malus' law, and is absorbed otherwise.

But to interpret this in terms of the Copenhagen interpretation (where states can collapse) one needs to work in Fock space, representing input and output as a superposition of the dark (or vacuum) state ##|0\rangle## containing no photon and the 1-photon state ##|1,\psi\rangle##, where ##\psi## is the incoming polarizaion state, projecting it upon passing the polarizer to another such superposition. Measurable (in principle - though never done in practice) in this setting is the amount of energy left in the polarizer, nothing else. I never saw anyone actually doing that - people pay only lipservice to Born's rule, a probabilistic version of Malus' law (which refers to intensity) and the associated postulates and argue about the situation in a heuristic way. (What is measured in practice is the rate of clicks at a detector at the end of the outgoing beam, upon which the photon disappears, so that Born's rule is not applicable.)

Moral: Don't take the postulates of quantum mechanics too seriously. They exist only to introduce the subject and to motivate the formalism. Once one has digested the real thing one always resorts to shut-up-and-calculate, and imports from experience the little bits needed to interpret the results in terms of experiments as one sees fit.