H. J. Briegel

We review and discuss the potential of using measurement-based elements in quantum communication schemes, where certain tasks are realized with the help of entangled resource states that are processed by measurements. We consider long-range quantum communication based on the transmission of encoded quantum states, where encoding, decoding and syndrome read-out are implemented using small-scale resource states. We also discuss entanglement-based schemes and consider measurement-based quantum repeaters. An important element in these schemes is entanglement purification, which can also be implemented in a measurement-based way. We analyze the influence of noise and imperfections in these schemes, and show that measurement-based implementation allows for very large error thresholds of the order of 10\% noise per qubit and more. We show how to obtain optimal resource states for different tasks, and discuss first experimental realizations of measurement-based quantum error correction using trapped ions and photons.

We report on the experimental violation of multipartite Bell inequalities by entangled states of trapped ions. First we consider resource states for measurement-based quantum computation of between 3 and 7 ions and show that all strongly violate a Bell-type inequality for graph states, where the criterion for violation is a sufficiently high fidelity. Second we analyze GHZ states of up to 14 ions generated in a previous experiment using stronger Mermin-Klyshko inequalities, and show that in this case the violation of local realism increases exponentially with system size. These experiments represent a violation of multipartite Bell-type inequalities of deterministically prepared entangled states. In addition, the detection loophole is closed.

Measurement-based quantum computation (MBQC) represents a powerful and flexible framework for quantum information processing, based on the notion of entangled quantum states as computational resources. The most prominent application is the one-way quantum computer, with the cluster state as its universal resource. Here we demonstrate the principles of MBQC using deterministically generated graph states of up to 7 qubits, in a system of trapped atomic ions. Firstly we implement a universal set of operations for quantum computing. Secondly we demonstrate a family of measurement-based quantum error correction codes, and show their improved performance as the code length is increased. We show that all our graph states violate a multipartite Bell inequality and are therefore capable of information processing tasks that cannot be described by a local hidden variable model. The methods presented can directly be scaled up to generate graph states of several tens of qubits.