QUROPE Quantum Information Processing and Communication in Europe

We construct minimax optimal non-asymptotic confidence sets for low rank matrix recovery algorithms such as the Matrix Lasso or Dantzig selector.

I investigate the extent to which the description of quantum systems by Gibbs states can be justified purely on the basis of tomographic data, without recourse to theoretical concepts such as infinite ensembles, environments, or information or to the systems' dynamics. I show that the use of Gibbs states amounts to a relevance hypothesis, which I spell out in detail. This hypothesis can be subjected to statistical hypothesis testing and hence assessed on the basis of the experimental data.

Recent contributions in the field of quantum state tomography have shown that, despite the exponential growth of Hilbert space with the number of subsystems, tomography of one-dimensional quantum systems may still be performed efficiently by tailored reconstruction schemes. Here, we discuss a scalable method to reconstruct mixed states that are well approximated by matrix product operators. The reconstruction scheme only requires local information about the state, giving rise to a reconstruction technique that is scalable in the system size.

The principle of maximum likelihood reconstruction has proven to yield satisfactory results in the context of quantum state tomography for many-body systems of moderate system sizes. Until recently, however, quantum state tomography has been considered to be infeasible for systems consisting of a large number of subsystems due to the exponential growth of the Hilbert space dimension with the number of constituents. Several reconstruction schemes have been proposed since then to overcome the two main obstacles in quantum many-body tomography: experiment time and post-processing resources.

We report on the implementation of a quantum process tomography technique known as direct characterization of quantum dynamics applied on coherent and incoherent single-qubit processes in a system of trapped 

We present a filtered backprojection algorithm for reconstructing the Wigner function of a system of large angular momentum j from Stern–Gerlach-type measurements. Our method is advantageous over the full determination of the density matrix in that it is insensitive to experimental fluctuations in j, and allows for a natural elimination of high-frequency noise in the Wigner function by taking into account the experimental uncertainties in the determination of j, its projection m and the quantization axis orientation.

Controlling the interaction of a single quantum system with its environment is a fundamental challenge in quantum science and technology. We strongly suppressed the coupling of a single spin in diamond with the surrounding spin bath by using double-axis dynamical decoupling. The coherence was preserved for arbitrary quantum states, as verified by quantum process tomography. The resulting coherence time enhancement followed a general scaling with the number of decoupling pulses.

A number of superconducting qubits, such as the transmon or the phase qubit, have an energy level structure with small anharmonicity. This allows for convenient access of higher excited states with similar frequencies. However, special care has to be taken to avoid unwanted higher-level populations when using short control pulses. Here we demonstrate the preparation of arbitrary three level superposition states using optimal control techniques in a transmon.