Quantum entanglement in the triangle network

Abstract

Beyond future applications, quantum networks open interesting fundamental perspectives, notably novel forms of quantum correlations. In this work we discuss quantum correlations in networks from the perspective of the underlying quantum states and their entanglement. We address the questions of which states can be prepared in the so-called triangle network, consisting of three nodes connected pairwise by three sources. We derive necessary criteria for a state to be preparable in such a network, considering both the cases where the sources are statistically independent and classically correlated. This shows that the network structure imposes strong and non-trivial constraints on the set of preparable states, fundamentally different from the standard characterization of multipartite quantum entanglement.

7 pages, 1 figure, see related work from Navascues et al.: arXiv:2002.02773, comments are welcome!

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• The Quantum Internet
• Entanglement detection
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• Information-Theoretic Implications of Quantum Causal Structures
• Theory-independent limits on correlations from generalised Bayesian networks
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Cited by in corpus (35)

• Bell nonlocality in networks
• Genuine Network Multipartite Entanglement
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• Deterministic distribution of multipartite entanglement and steering in a quantum network by separable states
• Network Quantum Steering
• Activation of genuine multipartite entanglement: Beyond the single-copy paradigm of entanglement characterisation
• Semidefinite programming relaxations for quantum correlations
• Symmetries in quantum networks lead to no-go theorems for entanglement distribution and to verification techniques
• Generalized $n$-locality inequalities in star-network configuration and their optimal quantum violations
• Understanding the interplay of entanglement and nonlocality: motivating and developing a new branch of entanglement theory
• Quantum-enhanced metrology with network states
• Characterizing nonlocal correlations through various $n$-locality inequlities in quantum network
• Experimental nonclassicality in a causal network without assuming freedom of choice
• Network Nonlocality via Rigidity of Token-Counting and Color-Matching
• Asymptotic survival of genuine multipartite entanglement in noisy quantum networks depends on the topology
• Certifying the Topology of Quantum Networks: Theory and Experiment
• Transformations of Stabilizer States in Quantum Networks
• No graph state is preparable in quantum networks with bipartite sources and no classical communication
• Quantum LOSR networks cannot generate graph states with high fidelity
• A generic framework for genuine multipartite entanglement detection
• Characterizing arbitrary quantum networks in the noisy intermediate-scale quantum era
• Metrological usefulness of entanglement and nonlinear Hamiltonians
• Quantum network-entanglement measures
• Metrology-assisted entanglement distribution in noisy quantum networks
• Finding maximal quantum resources
• Transformations in quantum networks via local operations assisted by finitely many rounds of classical communication
• Entanglement and the Path Integral
• Exploring Non-Multiplicativity in the Geometric Measure of Entanglement
• General spin systems without genuinely multipartite nonlocality
• Three Party Quantum Networks Created by Quantum Cloning
• Experimental verification of multi-copy activation of genuine multipartite entanglement
• Entanglement distribution in quantum networks via swapping of partially entangled pure states
• Robust Multipartite Entanglement Without Entanglement Breaking
• Features of preparable entangled states in Gaussian quantum networks
• Fully quantum inflation: quantum marginal problem constraints in the service of causal inference