2002/04/02 by P. A. Zizzi, Zizzi, P. A.
Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Quantum Physics (quant-ph) #gr-qc #quant-ph
paper · pdf · doi:10.48550/arxiv.gr-qc/0204007
12 pages, 5 figures
arxiv created 2002/04/02 · arxiv updated 2009/11/30
A causal set C can describe a discrete spacetime, but this discrete spacetime is not quantum, because C is endowed with Boolean logic, as it does not allow cycles. In a quasi-ordered set Q, cycles are allowed. In this paper, we consider a subset QC of a quasi-ordered set Q, whose elements are all the cycles. In QC, which is endowed with quantum logic, each cycle of maximal outdegree N in a node, is associated with N entangled qubits. Then QC describes a quantum computing spacetime. This structure, which is non-local and non-casual, can be understood as a proto-spacetime. Micro-causality and locality can be restored in the subset U of Q whose elements are unentangled qubits which we interpret as the states of quantum spacetime. The mapping of quantum spacetime into proto-spacetime is given by the action of the XOR gate. Moreover, a mapping is possible from the Boolean causal set into U by the action of the Hadamard gate. In particular, the causal order defined on the elements of U induces the causal evolution of spin networks.