Overlapping qubits from non-isometric maps and de Sitter tensor networks

The emergence of a local effective theory from a more fundamental theory of quantum gravity with seemingly fewer degrees of freedom is a major puzzle of theoretical physics. A recent approach to this problem is to consider general features of the Hilbert space maps relating these theories. In this work, we construct approximately local observables, or overlapping qubits, from such non-isometric maps. We show that local processes in effective theories can be spoofed with a quantum system with fewer degrees of freedom, with deviations from actual locality identifiable as features of quantum gravity. For a concrete example, we construct two tensor network models of de Sitter space-time, demonstrating how exponential expansion and local physics can be spoofed for a long period before breaking down. Our results highlight the connection between overlapping qubits, Hilbert space dimension verification, degree-of-freedom counting in black holes, holography, and approximate locality in quantum gravity.. Authors: Cao, ChunJun [University of Maryland, College Park, MD (United States); California Institute of Technology, Pasadena, CA (United States); Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)]; Chemissany, Wissam [University of Pennsylvania, Philadelphia, PA (United States)]; Jahn, Alexander [California Institute of Technology, Pasadena, CA (United States); Freie Universität Berlin (Germany)] (ORCID:0000000271420059); Zimborás, Zoltán [University of Helsinki (Finland); Algorithmiq Ltd, Helsinki (Finland); HUN-REN Wigner Research Centre for Physics, Budapest (Hungary)] (ORCID:000000022184526X). DOE Contract: SC0018407. Subjects: Quantum information; Theoretical physics