Entanglement of Trapped-Ion Clock States

A M{\o}lmer-S{\o}rensen entangling gate is realized for pairs of trapped $^{111}$Cd$^+$ ions using magnetic-field insensitive "clock" states and an implementation offering reduced sensitivity to optical phase drifts. The gate is used to generate the complete set of four entangled states, which are reconstructed and evaluated with quantum-state tomography. An average target-state fidelity of 0.79 is achieved, limited by available laser power and technical noise. The tomographic reconstruction of entangled states demonstrates universal quantum control of two ion-qubits, which through multiplexing can provide a route to scalable architectures for trapped-ion quantum computing.