Before the results of an experiment have been obtained, how does one determine how to write down the initial state of the quantum system?(adsbygoogle = window.adsbygoogle || []).push({});

For the example of simple slit experiments (following Marcella's "Q.I. w/ slits") a particle emerging from slit A is in a position eigenstate, eg. [itex]|A> = \delta (y - y_A)[/itex]. For the double slit wealwaystake the superposition [itex]|\psi > = (|A>+|B>)/ \sqrt 2[/itex]. Interference fringes are obtained by measuring the momentum of this prepared state (or the position, after letting it evolve).

In contrast, the (more complex) quantum eraser experiments tend to assume a different initial state described by [itex]|\psi > = (|A>+e^{i \triangle \phi}|B>)/ \sqrt 2[/itex]. Various measurements then give rise to interference fringes ([itex]|A>+|B>[/itex]), anti-fringes ([itex]|A>-|B>[/itex]) and non-interference ([itex]|A>[/itex], or alternatively [itex]|B>[/itex]).

To me this seems to assume that the photon could not only have emerged from either part of the down-conversion crystal, but that it could have done so at an earlier (or later) time, and those four possible results or superpositions correspond to the different possible real/imaginary parts of [itex]|\psi >[/itex]? If so, it would seem to demand an explanation of why the photon couldn't also have emerged earlier (or later) from the second slit in the simple double-slit experiment? Is there a simpler way to prepare a state such as [itex]|\psi > = (|A>-|B>)/ \sqrt 2[/itex]?

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# Twin slits; state preparation

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