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arXiv · 2405.14587

Effects of Topological Boundary Conditions on Bell Nonlocality

Patrick Emonts·Mengyao Hu·Albert Aloy·Jordi Tura
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Abstract

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.

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Patrick Emonts, Mengyao Hu, Albert Aloy, Jordi Tura. 2024-05-23. Effects of Topological Boundary Conditions on Bell Nonlocality. https://doi.org/10.1103/physreva.110.032201

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