“We present a novel twist present in quantum mechanics, absent in its classical counterpart: We are able to show that very natural, reasonable questions about quantum measurement are, intriguingly, undecidable,” Eisert told Phys.org. “At the same time, the corresponding classical problem is decidable.”An early thought: assuming quantum involvement in brain cells, does this have relevance to the question of free will?
The problem in question involves a measurement device that generates any one of multiple outputs depending on the outcome of the measurement. The output state is then fed back into the device as the input, leading to a new output, and the process repeats. The question is whether there exist any finite sequences of measurement outcomes that never occur.
“The problem as such is simple - merely asking whether certain outcomes can occur in quantum measurements,” Eisert said.
When using a classical measurement device, the physicists show that they can always find an algorithm that can answer whether or not any outputs with zero probability exist. So in a classical context, the problem is decidable.
However, when using a quantum measurement device, the physicists show that there cannot be an algorithm that always provides the correct answer, and so the problem becomes undecidable. The scientists explain that the undecidability arises from interference in the quantum device, implying that, at least in this scenario, undecidability appears to be a genuine quantum property.
Tuesday, July 10, 2012
Should I be surprised? - I can't decide