T. Körber

Scalable multiparticle entanglement of trapped ions

The generation, manipulation and fundamental understanding of entanglement lies at the very heart of quantum mechanics. Entangled particles are non-interacting but are described by a common wavefunction; consequently, individual particles are not independent of each other and their quantum properties are inextricably interwoven. The intriguing features of entanglement become particularly evident if the particles can be individually controlled and physically separated. However, both the experimental realization and characterization of entanglement become exceedingly difficult for systems with many particles. The main difficulty is to manipulate and detect the quantum state of individual particles as well as to control the interaction between them. So far, entanglement of four ions or five photons has been demonstrated experimentally. The creation of scalable multiparticle entanglement demands a non-exponential scaling of resources with particle number. Among the various kinds of entangled states, the ‘W state’ plays an important role as its entanglement is maximally persistent and robust even under particle loss. Such states are central as a resource in quantum information processing and multiparty quantum communication. Here we report the scalable and deterministic generation of four-, five-, six-, seven- and eight-particle entangled states of the W type with trapped ions. We obtain the maximum possible information on these states by performing full characterization via state tomography, using individual control and detection of the ions. A detailed analysis proves that the entanglement is genuine. The availability of such multiparticle entangled states, together with full information in the form of their density matrices, creates a test-bed for theoretical studies of multiparticle entanglement. Independently, ‘Greenberger–Horne–Zeilinger’ entangled states with up to six ions have been created and analysed in Boulder.

Deterministic quantum teleportation with atoms

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.

Robust state preparation of a single trapped ion by adiabatic passage

We report adiabatic passage experiments with a single trapped ion. By applying a frequency-chirped laser pulse with a Gaussian amplitude envelope, we reach a transfer efficiency of 0.99(1) on an optical transition from the electronic ground state S1/2 to the metastable state D5/2. This transfer method is shown to be insensitive to the accurate setting of laser parameters, and therefore is suitable as a robust tool for ion-based quantum computing.

Quantum computing with trapped ions

The paper reports on the investigation of single Ca/sup +/ ions and crystals of Ca/sup +/ ions confined in a linear Paul trap. These are also investigated for quantum information processing. Recent experimental advancements towards a quantum computer with such a system are also discussed.

QUANTUM COMPUTATION WITH TRAPPED IONS

Trapped ions can be prepared, manipulated and analyzed with high fidelities. In ad-dition, scalable ion trap architectures have been proposed (Kielpinski et al., Nature417, 709 (2001).). Therefore trapped ions represent a promising approach to large scalequantum computing. Here we concentrate on the recent advancements of generatingentangled states with small ion trap quantum computers. In particular, the creationof W–states with up to eight qubits and their characterization via state tomography isdiscussed.Keywords: entanglement; quantum information; ion traps

ENTANGLEMENT OF TRAPPED IONS

We report on the scalable and deterministic generation and tomographic characterization of entangled states of up to 8 trapped ions and experiments towards entangling ions and photons.

Teleportation with atoms

The teleportation of an atomic state accomplishes the complete transfer of information from one particle to another, employing the non‐local properties of quantum mechanics. Recently, two groups have achieved the deterministic teleportation of a quantum state between a pair of trapped ions. Following closely the original proposal of Bennett et al., a highly entangled pair of ions is created, a complete Bell‐state projective measurement involving the source ion and one of the entangled pair is carried out, and state reconstruction conditioned on this measurement is performed on the other half of the entangled pair.

CONTROLLING THREE ATOMIC QUBITS

We present a series of experiments where up to three ions held in a Paul trap are entangled, a given number of ions is selectively read out while conditional singlequantum-bit (qubit) operations are performed coherently on the remaining ion(s). Using these techniques, we demonstrate also a state transfer of a quantum bit from one ion to another one using two measurements and entanglement between an auxiliary ion and the target ion ‐ also known as teleportation.

Observation of very long-lived entanglement

We report on the preservation of bi-partite entanglement in an ion trap for over 10 seconds.

Application of process tomography to quantum teleportation

Three Ca-40 ions trapped in a linear Paul trap serve as a three-qubit register that can be manipulated by series of suitably tailored laser pulses. We implement deterministic quantum teleportation in the following way: First, we create a maximally entangled pair of ions that will be shared between the sending and the receiving party. Next, the third quantum bit is prepared in an arbitrary quantum state that will be teleported to the quantum bit of the receiver (the target). This is done by measuring the quantum bits of the sender in a basis of maximally entangled states and depending on the measurement result - applying one out of four unitary transformations to the target qubit. This teleportation protocol can be completely characterized by preparing six different input states and tomographically reconstructing the corresponding output states. The information obtained in this way is used for reconstructing the quantum process with the help of a maximum-likelihood technique.