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It is generally assumed that every process in quantum physics can be described mathematically by a completely positive map. However, experimentally reconstructed processes are not necessarily completely positive due to statistical or systematic errors. In this paper, we introduce a test for discriminating statistical from systematic errors which is necessary to interpret experimentally reconstructed, non-completely positive maps. We demonstrate the significance of the test using several examples given by experiments and simulations. In particular, we demonstrate experimentally how an initial correlation between the system to be measured and its environment leads to an experimentally reconstructed map with negative eigenvalues. These experiments are carried out using atomic 171Yb+ ions confined in a linear Paul trap, addressed and coherently manipulated by radio frequency radiation. [ABSTRACT FROM AUTHOR]

Novel ion traps that provide either a static or a dynamic magnetic gradient field allow for the use of radio-frequency radiation for coupling internal and motional states of ions, which is essential for conditional quantum logic. We show that the Hamiltonian describing this coupling in the presence of a resonant dynamic gradient, is identical, in a dressed state basis, to the Hamiltonian in the case of a static gradient. The coupling strength is in both cases described by the same effective Lamb-Dicke parameter. This insight can be used to overcome demanding experimental requirements when using a dynamic gradient field for state-of-the-art experiments with trapped ions, for example, in quantum information science. At the same time, this insight opens new experimental perspectives by way of using a single resonant or detuned dynamic gradient field, inducing long-range coupling, for conditional multi-qubit dynamics. [ABSTRACT FROM AUTHOR]

The size of controllable quantum systems has grown in recent times. Therefore, the spatial degree of freedom becomes more and more important in experimental quantum systems. However, the investigation of entanglement in many-body systems mainly concentrated on the number of entangled particles and ignored the spatial degree of freedom so far. As a consequence, a general concept together with experimentally realizable criteria has been missing to describe the spatial distribution of entanglement. We close this gap by introducing the concept of entanglement width as measure of the spatial distribution of entanglement in many-body systems. We develop criteria to detect the width of entanglement based solely on global observables. As a result, our entanglement criteria can be applied easily to many-body systems since single-particle addressing is not necessary. [ABSTRACT FROM AUTHOR]

In order to faithfully detect the state of an individual two-state quantum system (qubit) realized using, for example, a trapped ion or atom, state selective scattering of resonance fluorescence is well established. The simplest way to read out this measurement and assign a state is the threshold method. The detection error can be decreased by using more advanced detection methods like the time-resolved method (Myerson et al 2008 Phys. Rev. Lett.100 200502) or the π-pulse detection method (Hemmerling et al 2012 New. J. Phys.14 023043). These methods were introduced to qubits with a single possible state change during the measurement process. However, there exist many qubits like the hyperfine qubit of where several state change are possible. To decrease the detection error for such qubits, we develop generalizations of the time-resolved method and the π-pulse detection method for such qubits. We show the advantages of these generalized detection methods in numerical simulations and experiments using the hyperfine qubit of . The generalized detection methods developed here can be implemented in an efficient way such that experimental real time state discrimination with improved fidelity is possible. [ABSTRACT FROM AUTHOR]