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In the literature of the quantum eraser experiment it is argued that the change in statistics of the system from non-interference to interference is due to the erasing of "distinguishing information". The preparation of the experiment almost always introduces and then erases this information via a pair of unitary actions on the system. In the specific case that the interference effect is a second order effect of single photon interference, by destroying/creating the interference one is causing a physical disturbance to the system in that it changes the measurable statistics of the system, it destroys/creates the interference pattern that is collected at a single detector/screen. If it is distinguishing information that causes this physical change, if this physical change happens in the absence of a physical cause, is it not the case that this is a violation of the law of conservation of energy? There is no "driving force". It might only be the configuration of the statistics of the system that changes (from interference to non-interference or vica versa), but certainly this is a physical change that is measurable, so it should require energy and momentum to "push" the statistics in the right direction(away from or towards constructive interference). Distinguishing information does not provide this driving force.

And I know the generalized set of rules as to why quantum mechanics is suppose to be energy and momentum conserving, it has to do with the invariance of H under dislacements. This does not explain the specific case of quantum erasure which seemingly defies conservation.

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In the quantum eraser experiment, the interference is re-created logically, not physically. It is re-created by conditioning on some observable which is measured after the interference pattern has failed to appear on the detector. This doesn't require any energy.

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There is a misunderstanding here.

If the beam(s) are not changed at the origin, they deliver the same energy on the screen whether one sees interference or not. It just has a different spatial distribution.

Conservation of energy says that the energy of the beam(s) should equal the energy absorbed by the screen in total plus the energy reflected. It has nothing to do with the patterns of deposition.

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My problem concerns how the beam changes its spatial distribution, without energy. Obviously, to change the distribution (from non-interference to interference) so that the particles are detected in bands of constructive interference would require a push away from the destructive interference positions. There must be a driving force behind this change. However, in the quantum eraser it is claimed that only the "in principle knowability of distinguishing information" is accountable for this change in statistics. There is no "driving force". This is a violation of conservation. – Thomas Leibniz May 2 '13 at 13:06
You have a wrong understanding of conservation of energy and of the interference phenomenon. As I say in my answer the distribution of energy on the screen, as long as the input and ouput are equal is irrelevant. Conservation means the energy budget, in-out=0. . spatial distribution just might make difficult integrating the out, but a calorimeter could take care of that. Nothing is moving, in the sense of a horizontal force, when interference appears. – anna v May 2 '13 at 20:00
lets take the one photon at a time double slit experiment… . The interference builds up slowly, but the energy of the electron is the same, and conserved if the absorption of the screen is measured. The same energy electrons through only one slit would not show interference, but would deliver the same energy. what has happened is that the boundary conditions are different, no energy is necessary to produce the effect:a different solution for the same energy content is picked for each case by nature. – anna v May 2 '13 at 20:08

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