Effects of Topological Boundary Conditions on Bell Nonlocality
arXiv:2405.14587 · doi:10.1103/PhysRevA.110.032201
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.
arXiv comment10 + 7 pages, 10 figures, 1 table
References in corpus (35)
- A variational eigenvalue solver on a quantum processor
- Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
- Bell nonlocality
- Device-independent security of quantum cryptography against collective attacks
- Significant-loophole-free test of Bell's theorem with entangled photons
- A strong loophole-free test of local realism
- An Area Law for One Dimensional Quantum Systems
- The Variational Quantum Eigensolver: a review of methods and best practices
- Bell inequalities for arbitrarily high dimensional systems
- Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
- Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays
- Event-Ready Bell Test Using Entangled Atoms Simultaneously Closing Detection and Locality Loopholes
- Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
- Free randomness can be amplified
- The computational complexity of PEPS
- PEPS as ground states: degeneracy and topology
- Bell Correlations in a Bose-Einstein Condensate
- Detecting non-locality in multipartite quantum systems with two-body correlation functions
- Full randomness from arbitrarily deterministic events
- Self-testing protocols based on the chained Bell inequalities
- Classifying 50 years of Bell inequalities
- Nonlocality in many-body quantum systems detected with two-body correlators
- Device-independent quantum key distribution secure against adversaries with no long-term quantum memory
- Tropical Tensor Network for Ground States of Spin Glasses
- Efficient device-independent entanglement detection for multipartite systems
- Energy as a detector of nonlocality of many-body spin systems
- Matrix Product State and mean field solutions for one-dimensional systems can be found efficiently
- Translationally invariant multipartite Bell inequalities involving only two-body correlators
- Bounding the set of classical correlations of a many-body system
- Entanglement and Nonlocality in Infinite 1D Systems
- Bell correlations in a many-body system with finite statistics
- Trimer states with topological order in Rydberg atom arrays
- An Efficient Algorithm for approximating 1D Ground States
- Bell correlations at finite temperature
- Two Dimensional Translation-Invariant Probability Distributions: Approximations, Characterizations and No-Go Theorems