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With unlimited time, I'd put resources into the invention/improvement of a container which can be fed photons and is able to bounce them between mirrors for a long time, like days, and can be released at any time.

With that tech, I would build a delayed choice quantum eraser and set it up so that it produces with many photons an interference pattern or strips pattern by choice, representing a bit of information.

Then i would set up many of those devices in a row so that the results are representing bit strings for arbitrary information.

And I will use this time machine, which can send back information, to win the lottery and other stuff.

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    "which can be fed photons and is able to bounce them between mirrors for a long time, like days, and can be released at any time."

    Are you trying to get to a population inversion? This sounds like you are describing a laser.
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    @Demolishun no, a laser won’t help.
    I need to store phonons but they aren’t allowed to interact with anything because their entangled state must be preserved.

    As far as I know, photons can be stored only for a few seconds and only in small quantities with current tech.

    Storing photons in large amounts for a long time is the only technical hurdle which stands between such a time machine.
    That is, if my understanding of quantum physics is correct.
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