  Conventional information processors freely convert information between
different physical carriers to process, store, or transmit information. It
seems plausible that quantum information will also be held by different
physical carriers in applications such as tests of fundamental physics,
quantum-enhanced sensors, and quantum information processing.
Quantum-controlled molecules in particular could transduce quantum information
across a wide range of quantum-bit (qubit) frequencies, from a few kHz for
transitions within the same rotational manifold, a few GHz for hyperfine
transitions, up to a few THz for rotational transitions, to hundreds of THz for
fundamental and overtone vibrational and electronic transitions, possibly all
within the same molecule. Here, we report the first demonstration of
entanglement between states of the rotation of a $\rm^{40}CaH^+$ molecular ion
and internal states of a $\rm^{40}Ca^+$ atomic ion. The qubit addressed in the
molecule has a frequency of either 13.4 kHz or 855 GHz, highlighting the
versatility of molecular qubits. This work demonstrates how molecules can
transduce quantum information between qubits with different frequencies to
enable hybrid quantum systems. We anticipate that quantum control and
measurement of molecules as demonstrated here will create opportunities for
quantum information science, quantum sensors, fundamental and applied physics,
and controlled quantum chemistry.
