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Holography, Quantum Geometry, and Quantum Information Theory
Dipartimento di Astronomia dell' Università di Padova, Vicolo dell' Osservatorio, 5, 35122 Padova, Italy
Received: 1 November 1999; Accepted: 23 March 2000 / Published: 24 March 2000
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 labelled by the spin-½ 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.
Keywords: holography; quantum gravity; quantum Information
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Zizzi, P.A. Holography, Quantum Geometry, and Quantum Information Theory. Entropy 2000, 2, 39-69.
Zizzi PA. Holography, Quantum Geometry, and Quantum Information Theory. Entropy. 2000; 2(1):39-69.
Zizzi, P. A. 2000. "Holography, Quantum Geometry, and Quantum Information Theory." Entropy 2, no. 1: 39-69.