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arXiv:quant-ph/0304151 · Physical Review A

Mode entanglement and entangling power in bosonic graphs

Paolo Giorda, Paolo Zanardi A

Published Dec 18, 2003• 17 citations
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Abstract

We analyze the quantum entanglement properties of bosonic particles hopping over graph structures. Mode entanglement of a graph vertex with respect to the rest of the graph is generated, starting from a product state, by turning on for a finite time a tunneling along the graph edges. The maximum achieved during the dynamical evolution by this bipartite entanglement characterizes the entangling power of a given hopping Hamiltonian. We studied this entangling power as a function of the self-interaction parameters, i.e., nonlinearities, for all the graphs up to four vertices and for two different natural choices of the initial state. The role of graph topology and self-interaction strengths in optimizing entanglement generation is extensively studied by means of exact numerical simulations and by perturbative calculations

DOI
10.1103/physreva.68.062108

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We study a set of L spatial bosonic modes localized on a graph $\ensuremath{\Gamma}.$ The particles are allowed to tunnel from vertex to vertex by hopping along the edges of $\ensuremath{\Gamma}.$ We analyze how, in the exact many-body eigenstates of the system, i.e., Bose-Einstein condensates over single-particle eigenfunctions, the bipartite quantum entanglement of a graph vertex with respect to the rest of the graph depends on the topology of $\ensuremath{\Gamma}.$
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Quantum many-body Hamiltonians with two-body interactions can be represented by graphs, with sites as nodes and two-site couplings as edges. We investigate how the geometry of these graphs affects transport and entanglement growth. To do so, we study dynamics for quantum hopping on a random graph model with an effective range parameter. Tuning it, we interpolate between nearest-neighbor and all-to-all graphs, identifying a new localization regime that is robust in both single-particle and finite-density cases. This provides a model of Anderson localization induced by structural disorder, with implications for amorphous materials and tunable-range analog quantum simulators.