Entanglement, space-time and the Mayer-Vietoris theorem

Andrei T. Patrascu

doi:10.1007/jhep06(2017)046

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arXiv · 1703.09610

Entanglement, space-time and the Mayer-Vietoris theorem

Andrei T. Patrascu

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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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Andrei T. Patrascu. 2017-06-10. Entanglement, space-time and the Mayer-Vietoris theorem. https://doi.org/10.1007/jhep06(2017)046

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