Fig. 4: Multi-phonon entanglement generation and tomography.
From: Deterministic multi-phonon entanglement between two mechanical resonators on separate substrates
a Illustration of N00N (N = 2) state generation process. We first generate an entangled qutrit state \((\left\vert fg\right\rangle+\left\vert gf\right\rangle )/\sqrt{2}\) (\(\left\vert f\right\rangle\) is the qubit 2nd excited state), followed by a two-step swap from the qubits into the mechanical resonators, yielding a \((\left\vert 20\right\rangle+\left\vert 02\right\rangle )/\sqrt{2}\) N00N state. The corresponding pulse sequence is shown in b; following state preparation, tomography is performed in a manner analogous to that for the Bell state tomography. c, d Qubit coincidence probability measurements and corresponding joint resonator population distribution. For the N00N N = 2 state, the oscillations in Peg and Pge are approximately \(\sqrt{2}\) faster than for the analogous Bell state measurements in Fig. 3b; Pee remains zero as expected. Qubit populations for each data point are extracted from 5,000 repetitions. e Density matrix resulting from Wigner tomography of multi-phonon entangled state, with a state fidelity \({{{{\mathcal{F}}}}}=0.748\pm 0.008\) to the ideal \((\left\vert 20\right\rangle+\left\vert 02\right\rangle )/\sqrt{2}\) N00N state; measured density matrix ρ is shown with solid color bars, while dashed outlines show the simulated result (see Methods).
