We experimentally quantify the contribution of magnetic dipole (MD) transitions to the near-infrared light emission from trivalent erbium-doped yttrium oxide (Er$^{3+}$:Y$_2$O$_3$). Using energy-momentum spectroscopy, we demonstrate that the $^4$I$_{
13/2}{to}^4$I$_{15/2}$ emission near 1.5 $mu$m originates from nearly equal contributions of electric dipole (ED) and MD transitions that exhibit distinct emission spectra. We then show how these distinct spectra, together with the differing local density of optical states (LDOS) for ED and MD transitions, can be leveraged to control Er$^{3+}$ emission in structured environments. We demonstrate that far-field emission spectra can be tuned to resemble almost pure emission from either ED or MD transitions, and show that the observed spectral modifications can be accurately predicted from the measured ED and MD intrinsic emission rates.
We provide a systematic way of constructing entanglement-assisted quantum error-correcting codes via graph states in the scenario of preexisting perfectly protected qubits. It turns out that the preexisting entanglement can help beat the quantum Hamm
ing bound and can enhance (not only behave as an assistance) the performance of the quantum error correction. Furthermore we generalize the error models to the case of not-so-perfectly-protected qubits and introduce the quantity infidelity as a figure of merit and show that our code outperforms also the ordinary quantum error-correcting codes.
