Characterizing nonlocal correlations through various $n$-locality inequlities in quantum network

Abstract

The multipartite quantum networks feature multiple independent sources, in contrast to the conventional multipartite Bell experiment involving a single source. So far, network nonlocality has been explored when each source produces a two-qubit entangled state. In this work, we demonstrate the network nonlocality when each party performs a black-box measurement, and the dimension of the system remains unspecified. In an interesting work, by considering each source produces two-qubit entangled states in the conventional bilocal scenario, Gisin \emph{et. al.} in https://doi.org/10.1103/PhysRevA.96.020304] demonstrated a correspondence between the violations of bipartite Clauser-Horne-Shimony-Halt inequality and the bilocality inequality. We introduce a variant of the sum-of-squares approach to reproduce their results without assuming the dimension of the system. We then generalize the argument for network nonlocality in star-network topology. Further, we propose a new set of $n$-locality inequalities in star-network configuration where each of the $n$ parties performs an arbitrary number of dichotomic measurements and demonstrate the above correspondence between the quantum violations of the $n$-locality inequalities and the chained Bell inequalities. A similar correspondence is demonstrated based on a recently formulated family of $n$-locality inequalities whose optimal quantum violation cannot be obtained when each source emits a two-qubit entangled state and requires multiple copies of two-qubit entangled states. Throughout this paper, each party in the network performs black-box measurements, and the dimension of the system remains unspecified.

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• Quantum Correlation Sharing: A Review On Recent Progress From Nonlocality To Other Non-Classical Correlations
• Sharing nonlocality in quantum network by unbounded sequential observers
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• Regarding the Maximal Qubit Violations of n-Locality in Star and Chain Networks
• Generalized $n$-locality inequalities in linear-chain network for arbitrary inputs scenario and their quantum violations
• Sharing nonlocality in a network using the quantum violation of chain network inequality
• Optimal quantum violations of n-locality inequalities with conditional dependence on inputs
• Nonlocal correlations in an asymmetric quantum network
• Device-independent certification of degeneracy-breaking measurements
• Robust self-testing and certified randomness based on chained Bell inequality