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Author(s): H. Häffner (corresponding author) [1, 3]; W. Hänsel [1]; C. F. Roos [1, 3]; J. Benhelm [1, 3]; D. Chek-al-kar [1]; M. Chwalla [1]; T. Körber [1, 3]; U. [...]

Author(s): M. Riebe [1]; H. Häffner [1]; C. F. Roos [1]; W. Hänsel [1]; J. Benhelm [1]; G. P. T. Lancaster [1]; T. W. Körber [1]; C. Becher [1]; F. [...]

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. [ABSTRACT FROM AUTHOR]

Quantum networks promise to provide the infrastructure for many disruptive applications, such as efficient long-distance quantum communication and distributed quantum computing 1,2 . Central to these networks is the ability to distribute entanglement between distant nodes using photonic channels. Initially developed for quantum teleportation 3,4 and loophole-free tests of Bell's inequality 5,6 , recently, entanglement distribution has also been achieved over telecom fibres and analysed retrospectively 7,8 . Yet, to fully use entanglement over long-distance quantum network links it is mandatory to know it is available at the nodes before the entangled state decays. Here we demonstrate heralded entanglement between two independently trapped single rubidium atoms generated over fibre links with a length up to 33 km. For this, we generate atom-photon entanglement in two nodes located in buildings 400 m line-of-sight apart and to overcome high-attenuation losses in the fibres convert the photons to telecom wavelength using polarization-preserving quantum frequency conversion 9 . The long fibres guide the photons to a Bell-state measurement setup in which a successful photonic projection measurement heralds the entanglement of the atoms 10 . Our results show the feasibility of entanglement distribution over telecom fibre links useful, for example, for device-independent quantum key distribution 11-13 and quantum repeater protocols. The presented work represents an important step towards the realization of large-scale quantum network links., (© 2022. The Author(s).)

Quantum computers have the potential to perform certain computational tasks more efficiently than their classical counterparts. The Cirac-Zoller proposal for a scalable quantum computer is based on a string of trapped ions whose electronic states represent the quantum bits of information (or qubits). In this scheme, quantum logical gates involving any subset of ions are realized by coupling the ions through their collective quantized motion. The main experimental step towards realizing the scheme is to implement the controlled-NOT (CNOT) gate operation between two individual ions. The CNOT quantum logical gate corresponds to the XOR gate operation of classical logic that flips the state of a target bit conditioned on the state of a control bit. Here we implement a CNOT quantum gate according to the Cirac-Zoller proposal. In our experiment, two 40Ca+ ions are held in a linear Paul trap and are individually addressed using focused laser beams; the qubits are represented by superpositions of two long-lived electronic states. Our work relies on recently developed precise control of atomic phases and the application of composite pulse sequences adapted from nuclear magnetic resonance techniques.

Determining classically whether a coin is fair (head on one side, tail on the other) or fake (heads or tails on both sides) requires an examination of each side. However, the analogous quantum procedure (the Deutsch-Jozsa algorithm) requires just one examination step. The Deutsch-Jozsa algorithm has been realized experimentally using bulk nuclear magnetic resonance techniques, employing nuclear spins as quantum bits (qubits). In contrast, the ion trap processor utilises motional and electronic quantum states of individual atoms as qubits, and in principle is easier to scale to many qubits. Experimental advances in the latter area include the realization of a two-qubit quantum gate, the entanglement of four ions, quantum state engineering and entanglement-enhanced phase estimation. Here we exploit techniques developed for nuclear magnetic resonance to implement the Deutsch-Jozsa algorithm on an ion-trap quantum processor, using as qubits the electronic and motional states of a single calcium ion. Our ion-based implementation of a full quantum algorithm serves to demonstrate experimental procedures with the quality and precision required for complex computations, confirming the potential of trapped ions for quantum computation.