The Role of Topology in Quantum Tomography

We investigate quantum tomography in scenarios where prior information restricts the state space to a smooth manifold of lower dimensionality. By considering stability we provide a general framework that relates the topology of the manifold to the minimal number of binary measurement settings that is necessary to discriminate any two states on the manifold. We apply these findings to cases where the subset of states under consideration is given by states with bounded rank, fixed spectrum, given unitary symmetry or taken from a unitary orbit. For all these cases we provide both upper and lower bounds on the minimal number of binary measurement settings necessary to discriminate any two states of these subsets

Efficient Pure State Quantum Tomography from Five Orthonormal Bases

For any finite dimensional Hilbert space, we construct explicitly five orthonormal bases such that the corresponding measurements allow for efficient tomography of an arbitrary pure quantum state. This means that such measurements can be used to distinguish an arbitrary pure state from any other state, pure or mixed, and the pure state can be reconstructed from the outcome distribution in a feasible way. The set of measurements we construct is independent of the unknown state, and therefore our results provide a fixed scheme for pure state tomography, as opposed to the adaptive (state dependent) scheme proposed by Goyeneche et al. in [Phys. Rev. Lett. 115, 090401 (2015)]. We show that our scheme is robust with respect to noise in the sense that any measurement scheme which approximates these measurements well enough is equally suitable for pure state tomography. Finally, we present two convex programs which can be used to reconstruct the unknown pure state from the measurement outcome distributions.Comment: 5 pages, 2 figures, 1 page of supplemental materia

Comparison between computed and measured fibre orientation in injection moulded parts

International audienceShort fibre reinforced thermoplastic materials play an important role in automotive industries due to their excellent processing behaviour, reasonable good mechanical performance, high design freedom and cheap prices. Although the thermo-mechanical requirements for the materials used increase the development cycles decrease. Numerical simulation, FEA, analysis can be a strong assistant when judging designs and reducing cost and time consuming experimental tests. The mechanical properties for short fibre reinforced thermoplastics are mainly dominated by fibre orientation which results from injection moulding process. Several commercial tools offering 3D flow simulation are on the market, each of them with strengths and weaknesses and a lot of opportunities for future application in part design. In cooperation with Ecole Nationale Superieure des Mines de Paris a study was carried out in order to compare two different injection moulding simulation tools (MOLDFLOW MPI® and REM-3D®) with experimental data concerning fibre orientation prediction. The study contains investigations on the accuracy and sources of measurement errors on the well-established surface ellipse method on polished surfaces and gives an overview on the state-of-the art in this field. On the other hand simulation results compared with measurements on a sample geometry taken at different locations indicate that the accuracy of the simulation needs some improvement, too. Areas of fairly good agreement and those of significant differences are discussed. The importance of accurate fibre orientation on subsequent thermo-mechanical analysis is stressed out by comparing experimental data with simulated deformation behaviour. As a conclusion, alternatives both for experimental setup and algorithms used for the numerical prediction of fibre orientation so far based on the well-known Folgar-Tucker model are proposed. The limitations of this model for real parts will be discussed for this purpose