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

We construct approximately local observables, or "overlapping qubits", using non-isometric maps and show that processes in local effective theories can be spoofed with a quantum system with fewer degrees of freedom, similar to our expectation in holography. Furthermore, the spoofed system naturally deviates from an actual local theory in ways that can be identified with features in quantum gravity. For a concrete example, we construct two MERA toy models of de Sitter space-time and explain how the exponential expansion in global de Sitter can be spoofed with many fewer quantum degrees of freedom and that local physics may be approximately preserved for an exceedingly long time before breaking down. We highlight how approximate overlapping qubits are conceptually connected to Hilbert space dimension verification, degree-of-freedom counting in black holes and holography, and approximate locality in quantum gravity.