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).
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Patrascu, A.T. Entanglement, space-time and the Mayer-Vietoris theorem. J. High Energ. Phys. 2017, 46 (2017). https://doi.org/10.1007/JHEP06(2017)046
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DOI: https://doi.org/10.1007/JHEP06(2017)046