Sharing nonlocality in a network using the quantum violation of chain network inequality

Abstract

Based on the quantum violation of suitable $n$-local inequality in a star network for arbitrary $m$ inputs, we demonstrate the sharing of nonlocality in the network. Such a network features an arbitrary $n$ number of independent sources, $n$ edge parties, and a central party. Each party receives arbitrary $m$ inputs. We consider two different types of sharing of nonlocality in the network. i) The symmetric case - when the sharing of nonlocality is considered across all edge parties. ii) The asymmetric case - when the sharing of nonlocality is considered across only one edge party. For simplicity, we first consider the bilocal scenario $(n=2)$ with three inputs $m=3$ and demonstrate that while in the symmetric case at most two sequential observers can share nonlocality, in the asymmetric case at most four sequential observers can share nonlocality. We extend the study to $n$-local scenario by assuming each party receives three inputs and show that in the symmetric case the result remains the same for any $n$, but in the asymmetrical case, an unbounded number of sequential observers can share nonlocality across one edge for a sufficiently large value of $n$. We further extend our result for arbitrary $m$ input in $n$-local scenario. We demonstrate that for $m\ge 4$, in the symmetric case at most one sequential observer can share nonlocality irrespective of the value of $n$. For the asymmetric case, we analytically show that there exists $n(k)$ for which an arbitrary $k$ number of sequential observers can share the nonlocality across one edge. The optimal quantum violation of $m$-input $n$-local inequality is derived through an elegant SOS approach without specifying the dimension of the quantum system.

arXiv commentarXiv admin note: text overlap with arXiv:2212.14325

References in corpus (39)

• Bell nonlocality
• Characterizing the nonlocal correlations of particles that never interacted
• Bilocal versus non-bilocal correlations in entanglement swapping experiments
• Multiple Observers Can Share the Nonlocality of Half of an Entangled Pair by Using Optimal Weak Measurements
• Genuine quantum nonlocality in the triangle network
• Nonlocal correlations in the star-network configuration
• Nonlinear Bell inequalities tailored for quantum networks
• Arbitrarily many independent observers can share the nonlocality of a single maximally entangled qubit pair
• Device-independent certification of entangled measurements
• Computationally Efficient Nonlinear Bell Inequalities for General Quantum Networks
• Sequential random access codes and self-testing of quantum measurement instruments
• Maximal violation of n-locality inequalities in a star-shaped quantum network
• Bilocal Bell inequalities violated by the quantum Elegant Joint Measurement
• Sharing of Non-Local Advantage of Quantum Coherence by sequential observers
• Unbounded sequence of observers exhibiting Einstein-Podolsky-Rosen steering
• Genuine multipartite nonlocality is intrinsic to quantum networks
• Experimental characterisation of unsharp qubit observables and sequential measurement incompatibility via quantum random access codes
• A neural network oracle for quantum nonlocality problems in networks
• Semi-device-independent self-testing of unsharp measurements
• Network Quantum Steering
• Classical simulation of entanglement swapping with bounded communication
• Bounding the sets of classical and quantum correlations in networks
• Facets of bipartite nonlocality sharing by multiple observers via sequential measurements
• Sharing non-locality and non-trivial preparation contextuality using same family of Bell expressions
• Sharing quantum nonlocality and genuine nonlocality with independent observables
• Correlations in star networks: from Bell inequalities to network inequalities
• Limitations on sharing Bell nonlocality between sequential pairs of observers
• Observation of nonlocality sharing via not-so-weak measurements
• Genuine Einstein-Podolsky-Rosen steering of three-qubit states by multiple sequential observers
• Quantum nonlocality in networks can be demonstrated with an arbitrarily small level of independence between the sources
• Quantum Correlations in Connected Multipartite Bell Experiments
• Maximal qubit violation of n-local inequalities in quantum network
• Recycling qubits for the generation of Bell nonlocality between independent sequential observers
• Generalized $n$-locality inequalities in star-network configuration and their optimal quantum violations
• Non-locality sharing for a three-qubit system via multilateral sequential measurements
• Characterizing nonlocal correlations through various $n$-locality inequlities in quantum network
• Network nonlocality sharing via weak measurements in the extended bilocal scenario
• Sharing nonlocality in quantum network by unbounded sequential observers
• Generalized $n$-locality inequalities in linear-chain network for arbitrary inputs scenario and their quantum violations

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