  Entanglement between a stationary quantum system and a flying qubit is an
essential ingredient of a quantum-repeater network. It has been demonstrated
for trapped ions, trapped atoms, color centers in diamond, or quantum dots.
These systems have transition wavelengths in the blue, red or near-infrared
spectral regions, whereas long-range fiber-communication requires wavelengths
in the low-loss, low-dispersion telecom regime. A proven tool to interconnect
flying qubits at visible/NIR wavelengths to the telecom bands is quantum
frequency conversion. Here we use an efficient polarization-preserving
frequency converter connecting 854$\,$nm to the telecom O-band at 1310$\,$nm to
demonstrate entanglement between a trapped $^{40}$Ca$^{+}$ ion and the
polarization state of a telecom photon with a high fidelity of 98.2 $\pm$
0.2$\%$. The unique combination of 99.75 $\pm$ 0.18$\%$ process fidelity in the
polarization-state conversion, 26.5$\%$ external frequency conversion
efficiency and only 11.4 photons/s conversion-induced unconditional background
makes the converter a powerful ion-telecom quantum interface.
