Generalized $n$-locality inequalities in linear-chain network for arbitrary inputs scenario and their quantum violations

Abstract

Multipartite nonlocality in a network is conceptually different from standard multipartite Bell nonlocality. In recent times, network nonlocality has been studied for various topologies. We consider a linear-chain topology of the network and demonstrate the quantum nonlocality (the non-$n$-locality). Such a network scenario involves $n$ number of independent sources and $n+1$ parties, two edge parties (Alice and Charlie), and $n-1$ central parties (Bobs). It is commonly assumed that each party receives only two inputs. In this work, we consider a generalized scenario where the edge parties receive an arbitrary $n$ number of inputs (equals to a number of independent sources), and each of the central parties receives two inputs. We derive a family of generalized $n$-locality inequalities for a linear-chain network for arbitrary $n$ and demonstrate the optimal quantum violation of the inequalities. We introduce an elegant sum-of-squares approach enabling the derivation of the optimal quantum violation of aforesaid inequalities \emph{without} assuming the dimension of the system. We show that the optimal quantum violation requires the observables of edge parties to mutually anticommuting. For $n=2$ and $3$, the optimal quantum violation can be obtained when each edge party shares a two-qubit entangled state with central parties. We further argue that for $n\ge 2$, a single copy of a two-qubit-entangled state may not be enough to exhibit the violation of $n$-locality inequality, but multiple copies of it can activate the quantum violation.

References in corpus (41)

• Bell nonlocality
• Secure device-independent quantum key distribution with causally independent measurement devices
• Characterizing the nonlocal correlations of particles that never interacted
• Bilocal versus non-bilocal correlations in entanglement swapping experiments
• Beyond Bell's Theorem: Correlation Scenarios
• Genuine quantum nonlocality in the triangle network
• Nonlocal correlations in the star-network configuration
• Nonlinear Bell inequalities tailored for quantum networks
• Polynomial Bell inequalities
• The Inflation Technique for Causal Inference with Latent Variables
• Computationally Efficient Nonlinear Bell Inequalities for General Quantum Networks
• Beyond Bell's Theorem II: Scenarios with arbitrary causal structure
• All entangled pure quantum states violate the bilocality inequality
• Full network nonlocality
• Experimental demonstration of non-bilocal quantum correlations
• Experimental non-locality in a quantum network
• Maximal violation of n-locality inequalities in a star-shaped quantum network
• Bilocal Bell inequalities violated by the quantum Elegant Joint Measurement
• Constraints on nonlocality in networks from no-signaling and independence
• Towards device-independent information processing on general quantum networks
• Semidefinite tests for quantum network topologies
• Bounding the sets of classical and quantum correlations in networks
• Sharing non-locality and non-trivial preparation contextuality using same family of Bell expressions
• Bell-type Inequalities for Arbitrary Non-Cyclic Networks
• Correlations in star networks: from Bell inequalities to network inequalities
• Optimal quantum preparation contextuality in $n$-bit parity-oblivious multiplexing task
• Experimental bilocality violation without shared reference frames
• 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
• Characterizing Quantum Networks: Insights from Coherence Theory
• Nonlocality for Generic Networks
• Device-independent certification of Hilbert space dimension using a family of Bell expressions
• Generalized $n$-locality inequalities in star-network configuration and their optimal quantum violations
• Device-independent quantum key distribution based on Bell inequalities with more than two inputs and two outputs
• Characterizing nonlocal correlations through various $n$-locality inequlities in quantum network
• Non-Local Boxes for Networks
• Network Nonlocality via Rigidity of Token-Counting and Color-Matching
• Preservation of quantum non-bilocal correlations in noisy entanglement-swapping experiments using weak measurements
• Revealing Quantum Advantage in a Quantum Network
• Spreading Nonlocality in Quantum Network

Cited by in corpus (2)

• Regarding the Maximal Qubit Violations of n-Locality in Star and Chain Networks
• Sharing nonlocality in a network using the quantum violation of chain network inequality