MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint

Quantum logic is undecidable

Tobias Fritz


We investigate the first-order theory of closed subspaces of complex Hilbert spaces in the signature $(\lor,\perp,0)$, where '$\perp$' is orthogonality. Our main result is that already its purely implicational fragment is undecidable: there is no algorithm to decide whether an implication between equations in the language of orthomodular lattices is valid in all complex Hilbert spaces. This is a simple corollary of a recent result of Slofstra in combinatorial group theory, and follows upon reinterpreting that result in terms of the hypergraph approach to contextuality.

Jul 20, 2016
Aug 8, 2016
MSC Codes:
03G12, 03B25, 46L99, 81P13
Quantum logic, orthomodular lattices, Hilbert lattices, decidability, restricted word problem, residually finite-dimensional C*-algebras, quantum contextuality

Related publications

2021 Repository Open Access
Tobias Fritz

Quantum logic is undecidable

In: Archive for mathematical logic, 60 (2021) 3/4, pp. 329-341