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A Bell Inequality for a Class of Multilocal Ring Networks


Michael R. Frey


Quantum networks with independent sources of entanglement (hidden variables) and nodes that execute joint quantum measurements can create strong quantum correlations spanning the breadth of the network. Understanding of these correlations has to the present been limited to standard Bell experiments with one source of shared randomness, bilocal arrangements having two local sources of shared randomness, and multilocal networks with tree topologies. We introduce here a class of quantum networks with ring topologies comprised of subsystems each with its own internally shared source of randomness. We prove a Bell inequality for these networks, and to demonstrate violations of this inequality, we focus on ring networks with three-qubit subsystems. Three qubits are capable of two non-equivalent types of entanglement, GHZ and W- type. For rings of any number N of three-qubit subsystems, our inequality is violated when the subsystems are each internally GHZ-entangled. This violation is consistently stronger when N is even. This quantitative even-odd difference for GHZ entanglement becomes extreme in the case of W-type entanglement. When the ring size N is even, our Bell inequality successfully detects the presence of W-type entanglement; when N is odd, the inequality consistently fails to detect its presence.
Quantum Information Processing


Bell inequality, Bell violation, hidden variables, multilocal network, nonlocality, ring network, shared randomness


Frey, M. (1970), A Bell Inequality for a Class of Multilocal Ring Networks, Quantum Information Processing (Accessed April 21, 2024)
Created June 20, 2017, Updated January 27, 2020