Entangled Space-Time

We illustrate the entanglement mechanism of quantum space-time itself. We consider a discrete, quantum version of de Sitter Universe with a Planck time-foliation, to which is applied the quantum version of the holographic principle (a Planckian pixel encodes one qubit rather than a bit). This results in a quantum network, where the time steps label the nodes. The quantum fluctuations of the vacuum are the connecting links of the quantum network, while the total number of pixels (qubits) of a spatial slice are the outgoing links from a node n. At each node n there is a couple of quantum gates, the Hadamard gate (H) and the controlled-not (CNOT) gate, plus a projector P. The Hadamard gate transforms virtual states (bits) into qubits, the projector P measures a qubit at the antecedent node, giving rise to a new bit, and the CNOT gate entangles a qubit at node n with the new bit at node n-1. We show that the above quantum-computational interpretation of space-time entanglement has a geometrical counterpart. In fact, the quantum fluctuations of the metric on slice n are such that a tiny wormhole will connect one Planckian pixel of slice n with one of slice n-1. By the quantum holographic principle, such a geometrical connection is space-time entanglement.