Entanglement, space-time and the Mayer-Vietoris theorem

Abstract

Entanglement appears to be a fundamental building block of quantum gravity leading to new principles underlying the nature of quantum space-time. One such principle is the ER-EPR duality. While supported by our present intuition, a proof is far from obvious. In this article I present a first step towards such a proof, originating in what is known to algebraic topologists as the Mayer-Vietoris theorem. The main result of this work is the re-interpretation of the various morphisms arising when the Mayer-Vietoris theorem is used to assemble a torus-like topology from more basic subspaces on the torus in terms of quantum information theory resulting in a quantum entangler gate (Hadamard and c-NOT).

References in corpus (2)

• Entanglement, fidelity and topological entropy in a quantum phase transition to topological order
• Topological aspects of generalized gravitational entropy

Cited by in corpus (3)

• Grothendieck's point of view and complexity in the black hole paradox
• Multipartite entanglement via the Mayer-Vietoris theorem
• Cosmological constant as quantum error correction from generalised gauge invariance in double field theory