
arXiv: 1705.10776
We compute a momentum space version of the entanglement spectrum and entanglement entropy of general Young tableau states and one-point functions on Young tableau states. These physical quantities are used to measure the topology of the dual spacetime geometries in the context of gauge/gravity correspondence. The idea that Young tableau states can be obtained by superposing coherent states is explicitly verified. In this quantum superposition, a topologically distinct geometry is produced by superposing states dual to geometries with a trivial topology. Furthermore, we have a refined bound for the overlap between coherent states and the rectangular Young tableau state, by using the techniques of symmetric groups and representations. This bound is exponentially suppressed by the total edge length of the Young tableau. It is also found that the norm squared of the overlaps is bounded above by inverse powers of the exponential of the entanglement entropies. We also compute the overlaps between Young tableau states and other states including squeezed states and multi-mode entangled states which have similarities with those appeared in quantum information theory.
High Energy Physics - Theory, Quantum Physics, Mathematics - Operator Algebras, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), Mathematical Physics (math-ph), General Relativity and Quantum Cosmology, Yang-Mills and other gauge theories in quantum field theory, High Energy Physics - Theory (hep-th), Asymptotic procedures (radiation, news functions, \(\mathcal{H} \)-spaces, etc.) in general relativity and gravitational theory, Quantum coherence, entanglement, quantum correlations, Applications of Lie groups to the sciences; explicit representations, FOS: Mathematics, Quantization of the gravitational field, Operator Algebras (math.OA), Quantum Physics (quant-ph), Mathematical Physics, Gravitational interaction in quantum theory
High Energy Physics - Theory, Quantum Physics, Mathematics - Operator Algebras, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), Mathematical Physics (math-ph), General Relativity and Quantum Cosmology, Yang-Mills and other gauge theories in quantum field theory, High Energy Physics - Theory (hep-th), Asymptotic procedures (radiation, news functions, \(\mathcal{H} \)-spaces, etc.) in general relativity and gravitational theory, Quantum coherence, entanglement, quantum correlations, Applications of Lie groups to the sciences; explicit representations, FOS: Mathematics, Quantization of the gravitational field, Operator Algebras (math.OA), Quantum Physics (quant-ph), Mathematical Physics, Gravitational interaction in quantum theory
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