Effects of Topological Boundary Conditions on Bell Nonlocality

Autor: Emonts, Patrick, Hu, Mengyao, Aloy, Albert, Tura, Jordi
Rok vydání: 2024
Předmět:
Zdroj: Phys. Rev. A 110, 032201 (2024)
Druh dokumentu: Working Paper
DOI: 10.1103/PhysRevA.110.032201
Popis: Bell nonlocality is the resource that enables device-independent quantum information processing tasks. It is revealed through the violation of so-called Bell inequalities, indicating that the observed correlations cannot be reproduced by any local hidden variable model. While well explored in few-body settings, the question of which Bell inequalities are best suited for a given task remains quite open in the many-body scenario. One natural approach is to assign Bell inequalities to physical Hamiltonians, mapping their interaction graph to two-body, nearest-neighbor terms. Here, we investigate the effect of boundary conditions in a two-dimensional square lattice, which can induce different topologies in lattice systems. We find a relation between the induced topology and the Bell inequality's effectiveness in revealing nonlocal correlations. By using a combination of tropical algebra and tensor networks, we quantify their detection capacity for nonlocality. Our work can act as a guide to certify Bell nonlocality in many-qubit devices by choosing a suitable Hamiltonian and measuring its ground state energy; a task that many quantum experiments are purposely built for.
Comment: 10 + 7 pages, 10 figures, 1 table
Databáze: arXiv