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Imagine I have a box, and in it, I have a photon in a superposition of state |1> and |0>. I look into the box and register that the photon is in state |1>.

Now, if I have ALL information in the universe, inside and outside the box, as well as the complete set of all physical laws (whether we've discovered them or not), can I deduce that the photon was previously in a superposition?

Qmechanic
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Trace Fleeman
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    A superposition of states is a state. The fact that the photon is in that state is a member of the set of ALL information in the universe. What deduction is required? – Alfred Centauri Mar 03 '15 at 12:58

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No. A single measurement can't tell you if the state was in a superposition or it was a pure state. In order to be able to do that you must have knowledge of how the state was prepared, which means you must have gauged your apparatus and therefore performed a statistically relevant number of measurements on the very same state many times and taken note of all the possible outcomes.

Now if someone gives you a black box with a photon inside and you perform a measurement you force the photon to collapse to one of its allowed pure states, so that every time you measure the state of the photon you will find the same result as the previous measurement.

Phoenix87
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  • What is this "measurement" you talk about which breaks time reversibility of the universe? – JiK Mar 03 '15 at 09:46
  • Isn't every superposition of pure states again a pure states? Usually, one distinguishes pure states from mixed states, where mixed states are due to lacking knowledge about the system. Every pure state can be expressed as the superposition of other pure states without losing information, though - unless you are using a different definition of pure state? – ACuriousMind Mar 03 '15 at 17:05
  • that's right. my point is that after the measurement it is no longer possible to reconstruct the "statistical" content of the original state w.r.t. to the "reference" pure states. – Phoenix87 Mar 03 '15 at 17:13