Without knowing in advance that a physical system has been configured to do so, is it possible to determine whether that system is preforming, or has just performed a quantum computation?

That is, if I have an arbitrary system, $\mathbf{S}$, are there any

  • observations I can make on $\mathbf{S}$ which would tell me that it is currently preforming a quantum computation; or
  • are there any changes to the environment containing $\mathbf{S}$ which would indicate that that environment has observed the "output" (performed a measurement on) a system that had been preforming a quantum computation?

Or is there perhaps some other way?

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    $\begingroup$ Define "quantum computation." No, seriously, because depending on how you do so you might say that every system is always doing a quantum computation of its own dynamics. $\endgroup$ – Rococo Jul 8 at 15:50
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    $\begingroup$ To give a different perspective on @Rococo's comment, how would you determine is an arbitrary classical system is performing classical computation? $\endgroup$ – By Symmetry Jul 8 at 17:01
  • $\begingroup$ @Rococo: Good point. I guess that suggests (as By Symmetry) implies, that the answer is no: "doing a quantum computing" in the sense of the question (if it means anything) means that S is undergoing some evolution in the absence of any observation by the system of which the observer is a part. The question is effectively like asking whether it is possible to determine that S is or has been totally isolated (at least with respect to properties of S that are subsequently observed). $\endgroup$ – orome Jul 8 at 20:14

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