Measurement of quantum state Consider a particle in a box system. Assume its state to be a superposition of the ground and the first excited energy states. Consider two observers A and B (rest of the world). A made the measurement of the energy of the system and got energy corresponding to one of the states. Consider two scenarios:


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*A made the measurement and B is not aware of it at all. For B would the state still be the superimposed state?

*A made the measurement and B know(s) but is unaware of the result. Would it be ok to say that for B the state of the system is still the same as it was initially?
Are these two scenarios equivalent?
 A: It sounds to me like you're asking about "Quantum Bayesianism", or "QBism" as it's called by David Mermin, one of its principal proponents, e.g.,
http://arxiv.org/abs/1311.5253
Or you can google those two terms in quotes for lots more references. Is that what you're talking about? And do their interpretations answer your questions?
A: A measurement is a form of interaction.  A's interaction with the state is information that B is not unaware of.  Which is equivalent to say that A's interaction is information that B cannot use.  Thus, your two statements are equivalent in that the best B can do is use the information about the state that he does have to make a prediction.  A practical example of this makes the situation more clear.
Consider an experiment where A measured the spin of an unpolarized particle to be +1/2 in the z-direction.  B is unaware of A's measurement.  B subsequently measures the z-direction spin and finds it to be +1/2.  This is a reasonable from a prediction using the superimposed state (unpolarized) state with 50% probability of being +1/2 and 50% probability of being -1.2
Now consider the same situation but with B being aware of A's measurement but unaware of the result.  It remains that the best B can do is still make a probabilistic prediction.
Now consider the same experiment repeated over and over again.  On B's measurement after A's measurement, B will see that 50% of the time the particle is +1/2 and 50% of the time the particle is -1/2.  Thus, to B, the state is a superposition as expected.  However, if A were to join B on the subsequent measurement and tell B of his early results, then B could use the collapsed state and predict the correct spin 100% of the time (since A already measured it).  But, both predictions accurately conform to the results of the experiment, however one prediction (A's prediction) contains more knowledge about the system.
A: The relevant issue is not what B knows, but rather whether the content of the measurement result has affected B. If the content of the result has affected B then B will not be able to arrange interference between the different results of that measurement. For example, suppose that the information about the result has been displayed on a computer screen and the light from the screen has interacted with B's skin while his back is turned, then he will not be able to produce interference between the results.
See papers about decoherence such as
C. Jess Riedel, Wojciech H. Zurek, Quantum Darwinism in an Everyday Environment: Huge Redundancy in Scattered Photons, Phys. Rev. Lett. 105, 020404 (2010)
http://arxiv.org/abs/1001.3419.
There is a slight complication. When two systems are entangled the correlations between them are explained by decoherent systems carrying quantum information in observables in such a way that the content of the information doesn't change the expectation values of those observables.  See David Deutsch, Patrick Hayden, 'Information Flow in Entangled Quantum Systems', Proc. R. Soc. Lond. A 456(1999):1759-1774. available at http://arxiv.org/abs/quant-ph/9906007. And also David Deutsch, 'Vindication of quantum locality', Proc. R. Soc. A 468(2012), 531-544. available at http://arxiv.org/abs/1109.6223.
A: It shouldn't make a difference because in both cases the particle is measured.
This kind of question can be rather muddy -  physicists try to stay away from using the words 'observer' and 'measurement' in quantum mechanics because they raise more questions than they answer.
At any rate, most physicists prefer 'interaction with a macroscopic system'.
