Entanglement Percolation with Bipartite Mixed States

Abstract

We develop a concept of entanglement percolation for long-distance singlet generation in quantum networks with neighboring nodes connected by partially entangled bipartite mixed states. We give a necessary and sufficient condition on the class of mixed network states for the generation of singlets. States beyond this class are insufficient for entanglement percolation. We find that neighboring nodes are required to be connected by multiple partially entangled states and devise a rich variety of distillation protocols for the conversion of these states into singlets. These distillation protocols are suitable for a variety of network geometries and have a sufficiently high success probability even for significantly impure states. In addition to this, we discuss possible further improvements achievable by using quantum strategies including generalized forms of entanglement swapping.

6+ pages, 5 figures; Published version

References in corpus (6)

• Entanglement Distribution in Pure-State Quantum Networks
• Entanglement percolation in quantum complex networks
• On the role of memory errors in quantum repeaters
• Multipartite entanglement percolation
• One-shot entanglement generation over long distances in noisy quantum networks
• Fidelity threshold for long-range entanglement in quantum networks

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• Long Distance Entanglement Generation in 2D Networks
• Long-distance entanglement generation with scalable and robust two-dimensional quantum network
• Percolation thresholds and connectivity in quantum networks
• Braess Paradox in a quantum network
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• Directed percolation effects emerging from superadditivity of quantum networks
• Upper Bound on Singlet Fraction of Two Qubit Mixed Entangled States
• Quantum entanglement percolation under a realistic restriction
• Entanglement percolation in random quantum networks
• The role of local and global geometry in quantum entanglement percolation