Universal quantum theory contains twisted logic

TL;DR

This paper reveals that quantum theory's universal application leads to a twisted logical structure where local consistency does not guarantee global consistency, impacting how we understand measurement outcomes and state distinguishability.

Contribution

It uncovers a new logical manifestation of quantum theory's counterintuitive nature, demonstrated both theoretically and experimentally, highlighting the impossibility of certain logical deductions.

Findings

Heisenberg's uncertainty principle causes logical deduction impossibilities.

Experimental validation using polarization-encoded single-photon qubits.

Overlooking this structure suggests false possibilities in state discrimination.

Abstract

Quantum theory is notoriously counterintuitive, and yet remains entirely self-consistent when applied universally. Here we uncover a new manifestation of its unusual consequences. We demonstrate, theoretically and experimentally (by means of polarization-encoded single-photon qubits), that Heisenberg's uncertainty principle leads to the impossibility of stringing together logical deductions about outcomes of consecutive non-compatible measurements. This phenomenon resembles the geometry of a Penrose triangle, where each corner is locally consistent while the global structure is impossible. Besides this, we show how overlooking this non-trivial logical structure leads to the erroneous possibility of distinguishing non-orthogonal states with a single measurement.