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Schlagwörter:
General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th,Quantum Physics, quant-ph
Zusammenfassung:
We introduce the geometric formulation of Quantum Mechanics in the quantum
gravity context, and we use it to give a tensorial characterization of
entanglement on spin network states. Starting from the simplest case of a
single-link graph (Wilson line), we define a dictionary to construct a
Riemannian metric tensor and a symplectic structure on the space of spin
network states, showing how they fully encode the information about
separability and entanglement, and, in particular, an entanglement monotone
interpreted as a distance with respect to the separable state. In the maximally
entangled gauge-invariant case, the entanglement monotone is proportional to a
power of the area of the surface dual to the link thus supporting a connection
between entanglement and the (simplicial) geometric properties of spin network
states. We extend then such analysis to the study of non-local correlations
between two non-adjacent regions of a generic spin network. In the end, our
analysis shows that the same spin network graph can be understood as an
information graph whose connectivity encodes, both at the local and non-local
level, the quantum correlations among its parts. This gives a further
connection between entanglement and geometry.
