Persistent entanglement in arrays of interacting particles

Persistent entanglement in arrays of interacting particles

May 28, 2018 | Hans J. Briegel and Robert Raussendorf
This paper introduces a class of N-qubit entangled states that are generated in arrays of qubits with an Ising-type interaction. These states have a large amount of entanglement, as measured by their Schmidt measure, and a high persistency of entanglement, meaning that approximately N/2 qubits must be measured to disentangle the state. These states can be used as an entanglement resource to generate other multi-particle entangled states, such as generalized GHZ states. Entanglement is considered a resource for quantum information tasks. The paper defines two key properties of entangled states: maximal connectedness and persistency. Maximal connectedness refers to the ability to project any two qubits into a Bell state using local measurements on other qubits. Persistency measures the number of local measurements needed to disentangle the state. The paper shows that the introduced states are maximally connected and have a persistency equal to the floor of N/2. This persistency is also equal to the Schmidt measure of the state, indicating that these states are significantly more entangled than many known N-qubit states. The states are shown to be different from the GHZ and W classes of states. The paper also generalizes these results to higher dimensions, considering qubits arranged on a lattice. Cluster states, which are generated under a specific Hamiltonian, are shown to be maximally connected and have a persistency that depends on the cluster's shape. These cluster states can be used to generate other multi-particle entangled states through local measurements and classical communication. The paper concludes that these cluster states are a scalable resource for generating multi-qubit entangled states, and they can be experimentally realized in systems such as optical lattices. The results highlight the importance of entanglement in quantum information processing and the potential of cluster states as a resource for quantum computing and communication.This paper introduces a class of N-qubit entangled states that are generated in arrays of qubits with an Ising-type interaction. These states have a large amount of entanglement, as measured by their Schmidt measure, and a high persistency of entanglement, meaning that approximately N/2 qubits must be measured to disentangle the state. These states can be used as an entanglement resource to generate other multi-particle entangled states, such as generalized GHZ states. Entanglement is considered a resource for quantum information tasks. The paper defines two key properties of entangled states: maximal connectedness and persistency. Maximal connectedness refers to the ability to project any two qubits into a Bell state using local measurements on other qubits. Persistency measures the number of local measurements needed to disentangle the state. The paper shows that the introduced states are maximally connected and have a persistency equal to the floor of N/2. This persistency is also equal to the Schmidt measure of the state, indicating that these states are significantly more entangled than many known N-qubit states. The states are shown to be different from the GHZ and W classes of states. The paper also generalizes these results to higher dimensions, considering qubits arranged on a lattice. Cluster states, which are generated under a specific Hamiltonian, are shown to be maximally connected and have a persistency that depends on the cluster's shape. These cluster states can be used to generate other multi-particle entangled states through local measurements and classical communication. The paper concludes that these cluster states are a scalable resource for generating multi-qubit entangled states, and they can be experimentally realized in systems such as optical lattices. The results highlight the importance of entanglement in quantum information processing and the potential of cluster states as a resource for quantum computing and communication.
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