Quantum measurement occurrence is undecidable
Abstract
In this work, we show that very natural, apparently simple problems in quantum measurement theory can be undecidable even if their classical analogues are decidable. Undecidability hence appears as a genuine quantum property here. Formally, an undecidable problem is a decision problem for which one cannot construct a single algorithm that will always provide a correct answer in finite time. The problem we consider is to determine whether sequentially used identical Stern-Gerlach-type measurement devices, giving rise to a tree of possible outcomes, have outcomes that never occur. Finally, we point out implications for measurement-based quantum computing and studies of quantum many-body models and suggest that a plethora of problems may indeed be undecidable.
Cite
@article{arxiv.1111.3965,
title = {Quantum measurement occurrence is undecidable},
author = {J. Eisert and M. P. Mueller and C. Gogolin},
journal= {arXiv preprint arXiv:1111.3965},
year = {2012}
}
Comments
4+ pages, 1 figure, added a proof that the QMOP is still undecidable for exponentially small but nonzero probability