The Walker speaks its graph: global and nearly-local probing of the tunnelling amplitude in continuous-time quantum walks. (English) Zbl 1507.82011
Summary: We address continuous-time quantum walks on graphs, and discuss whether and how quantum-limited measurements on the walker may extract information on the tunnelling amplitude between the nodes of the graphs. For a few remarkable families of graphs, we evaluate the ultimate quantum bound to precision, i.e. we compute the quantum Fisher information (QFI), and assess the performances of incomplete measurements, i.e. measurements performed on a subset of the graph’s nodes. We also optimize the QFI over the initial preparation of the walker and find the optimal measurement achieving the ultimate precision in each case. As the topology of the graph is changed, a non-trivial interplay between the connectivity and the achievable precision is uncovered.
MSC:
| 82B10 | Quantum equilibrium statistical mechanics (general) |
| 82B41 | Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics |
| 81P45 | Quantum information, communication, networks (quantum-theoretic aspects) |
| 81P15 | Quantum measurement theory, state operations, state preparations |
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