Quantum measurement occurrence is undecidable

TL;DR

This paper demonstrates that certain natural problems in quantum measurement theory are fundamentally undecidable, highlighting a uniquely quantum form of computational intractability with implications for quantum computing and many-body physics.

Contribution

It introduces the undecidability of a quantum measurement problem, showing a stark contrast with classical analogues and revealing a new quantum property.

Findings

Quantum measurement outcome problems can be undecidable.

Undecidability in quantum measurement differs from classical cases.

Implications for quantum computing and many-body physics are discussed.

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.