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cesiumfrog

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Before the results of an experiment have been obtained, how does one determine how to write down the initial state of the quantum system?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 we

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]?

*always*take 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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