Quantum synchronization over quantum networks. (English) Zbl 1204.81039
Summary: We consider a network of quantum oscillators in which quantum states are distributed among connected nodes by means of unitary transformations. The distributed states interact with each local state according to a time-dependent interaction Hamiltonian, which is modeled by a Hermitian operator constructed in terms of the states themselves, thereby introducing nonlinear network interactions. For qubit nodes of differing natural frequencies, we show numerically that, for a sufficiently large coupling constant, synchronization of quantum nodes occurs in which the spins of all qubits are mutually aligned with a common frequency of oscillation, following initial transient configurations. We discuss the significance of quantum synchronization as a means to create copies of unknown quantum states.
MSC:
81P45 | Quantum information, communication, networks (quantum-theoretic aspects) |
81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
34B45 | Boundary value problems on graphs and networks for ordinary differential equations |
68M10 | Network design and communication in computer systems |