Entanglement, its generation, manipulation and fundamental understanding is at the very heart of quantum mechanics. The phrase entanglement was coined by Erwin Schrödinger in 1935 for particles that are described by a common wave function where individual particles are not independent of each other but where their quantum properties are inextricably interwoven 1 . Entanglement properties of two and three particles have been studied extensively and are very well understood. Entanglement of four 2 and five 3 particles was demonstrated experimentally. However, both creation and characterization of entanglement become exceedingly difficult for multi-particle systems. Thus the availability of such multiparticle entangled states together with the full information on these states in form of their 1

Teleportation of a quantum state encompasses the complete transfer of information from one particle to another. The complete specification of the quantum state of a system generally requires an infinite amount of information, even for simple two-level systems (qubits). Moreover, the principles of quantum mechanics dictate that any measurement on a system immediately alters its state, while yielding at most one bit of information. The transfer of a state from one system to another (by performing measurements on the first and operations on the second) might therefore appear impossible. However, it has been shown that the entangling properties of quantum mechanics, in combination with classical communication, allow quantum-state teleportation to be performed. Teleportation using pairs of entangled photons has been demonstrated, but such techniques are probabilistic, requiring post-selection of measured photons. Here, we report deterministic quantum-state teleportation between a pair of trapped calcium ions. Following closely the original proposal, we create a highly entangled pair of ions and perform a complete Bell-state measurement involving one ion from this pair and a third source ion. State reconstruction conditioned on this measurement is then performed on the other half of the entangled pair. The measured fidelity is 75%, demonstrating unequivocally the quantum nature of the process.

Today, ion traps are among the most promising physical systems for constructing a quantum device harnessing the computing power inherent in the laws of quantum physics 1,2 . For the implementation of arbitrary operations, a quantum computer requires a universal set of quantum logic gates. As in classical models of computation, quantum error correction techniques 3,4 enable rectification of small imperfections in gate operations, thus enabling perfect computation in the presence of noise. For fault-tolerant computation 5 , it is believed that error thresholds ranging between 10 −4 and 10 −2 will be required-depending on the noise model and the computational overhead for realizing the quantum gates 6-8 -but so far all experimental implementations have fallen short of these requirements. Here, we report on a Mølmer-Sørensen-type gate operation 9,10 entangling ions with a fidelity of 99.3(1)%. The gate is carried out on a pair of qubits encoded in two trapped calcium ions using an amplitudemodulated laser beam interacting with both ions at the same time. A robust gate operation, mapping separable states onto maximally entangled states is achieved by adiabatically switching the laser-ion coupling on and off. We analyse the performance of a single gate and concatenations of up to 21 gate operations.For ion traps, all building blocks necessary for the construction of a universal quantum computer 1 have been demonstrated over the past decade. Currently, the most important challenges consist of scaling up the present systems to a higher number of qubits and raising the fidelity of gate operations up to the point where quantum error correction techniques can be successfully applied. Although single-qubit gates are easily carried out with high quality, the realization of high-fidelity entangling two-qubit gates 11-16 is much more demanding because the inter-ion distance is orders of magnitude bigger than the characteristic length scale of any state-dependent ion-ion interaction. Apart from quantum gates of the Cirac-Zoller type 2,12 , where a laser couples a single qubit with a vibrational mode of the ion string at a time, most other gate realizations entangling ions have relied on collective interactions of the qubits with the laser control fields 11,[13][14][15] . These gate operations entangle transiently the collective pseudospin of the qubits with the vibrational mode and produce either a conditional phase shift 17 or a collective spin flip 9,10,18 of the qubits. Whereas the highest fidelity F = 97% reported until now 13 has been achieved with a conditional phase gate acting on a pair of hyperfine qubits in 9 Be + , spin-flip gates have been limited so far to F ≈ 85% (refs 11,14). All of these experiments have used qubits encoded in hyperfine or Zeeman ground states and a Raman transition mediated by an electric-dipole transition for coupling the qubits. Whereas spontaneous scattering from the mediating short-lived levels degrades the gate fidelity owing to the limited amount of laser power available in current experi...

We report the deterministic creation of maximally entangled three-qubit states-specifically the Greenberger-Horne-Zeilinger (GHZ) state and the W state-with a trapped-ion quantum computer. We read out one of the qubits selectively and show how GHZ and W states are affected by this local measurement. Additionally, we demonstrate conditional operations controlled by the results from reading out one qubit. Tripartite entanglement is deterministically transformed into bipartite entanglement by local operations only. These operations are the measurement of one qubit of a GHZ state in a rotated basis and, conditioned on this measurement result, the application of single-qubit rotations.