Holography, Quantum Geometry, and Quantum Information Theory

TL;DR

This paper explores the holographic principle through quantum bits, linking quantum geometry with information theory, and models early universe inflation as a quantum computational process with emergent micro-causality.

Contribution

It introduces a novel framework connecting holography, quantum geometry, and quantum information, applying it to de Sitter horizons and early universe inflation.

Findings

Quantum states associated with surfaces punctured by spin networks.

Emergence of discrete micro-causality from entropy increase.

Decoherence of the quantum history at the end of inflation.

Abstract

We interpret the Holographic Conjecture in terms of quantum bits (qubits). N-qubit states are associated with surfaces that are punctured in N points by spin networks' edges labeled by the spin-1/2 representation of SU(2), which are in a superposed quantum state of spin "up" and spin "down". The formalism is applied in particular to de Sitter horizons, and leads to a picture of the early inflationary universe in terms of quantum computation. A discrete micro-causality emerges, where the time parameter is being defined by the discrete increase of entropy. Then, the model is analysed in the framework of the theory of presheaves (varying sets on a causal set) and we get a quantum history. A (bosonic) Fock space of the whole history is considered. The Fock space wavefunction, which resembles a Bose-Einstein condensate, undergoes decoherence at the end of inflation. This fact seems to be responsible for the rather low entropy of our universe.