Shaping frequency entangled qudits

We demonstrate the creation, characterization, and manipulation of frequency-entangled qudits by shaping the energy spectrum of entangled photons. The generation of maximally entangled qudit states is verified up to dimension d=4 through tomographic quantum-state reconstruction. Subsequently, we measure Bell parameters for qubits and qutrits as a function of their degree of entanglement. In agreement with theoretical predictions, we observe that for qutrits the Bell parameter is less sensitive to a varying degree of entanglement than for qubits. For frequency-entangled photons, the dimensionality of a qudit is ultimately limited by the bandwidth of the pump laser and can be on the order of a few millions.

Factor analysis of the North American Spine Society outcome assessment instrument: a study based on a spine registry of patients treated with lumbar and cervical disc arthroplasty.

Background context Studies involving factor analysis (FA) of the items in the North American Spine Society (NASS) outcome assessment instrument have revealed inconsistent factor structures for the individual items. Purpose This study examined whether the factor structure of the NASS varied in relation to the severity of the back/neck problem and differed from that originally recommended by the developers of the questionnaire, by analyzing data before and after surgery in a large series of patients undergoing lumbar or cervical disc arthroplasty. Study design/setting Prospective multicenter observational case series. Patient sample Three hundred ninety-one patients with low back pain and 553 patients with neck pain completed questionnaires preoperatively and again at 3 to 6 and 12 months follow-ups (FUs), in connection with the SWISSspine disc arthroplasty registry. Outcome measures North American Spine Society outcome assessment instrument. Methods First, an exploratory FA without a priori assumptions and subsequently a confirmatory FA were performed on the 17 items of the NASS-lumbar and 19 items of the NASS-cervical collected at each assessment time point. The item-loading invariance was tested in the German version of the questionnaire for baseline and FU. Results Both NASS-lumbar and NASS-cervical factor structures differed between baseline and postoperative data sets. The confirmatory analysis and item-loading invariance showed better fit for a three-factor (3F) structure for NASS-lumbar, containing items on “disability,” “back pain,” and “radiating pain, numbness, and weakness (leg/foot)” and for a 5F structure for NASS-cervical including disability, “neck pain,” “radiating pain and numbness (arm/hand),” “weakness (arm/hand),” and “motor deficit (legs).” Conclusions The best-fitting factor structure at both baseline and FU was selected for both the lumbar- and cervical-NASS questionnaires. It differed from that proposed by the originators of the NASS instruments. Although the NASS questionnaire represents a valid outcome measure for degenerative spine diseases, it is able to distinguish among all major symptom domains (factors) in patients undergoing lumbar and cervical disc arthroplasty; overall, the item structure could be improved. Any potential revision of the NASS should consider its factorial structure; factorial invariance over time should be aimed for, to allow for more precise interpretations of treatment success.

Nucleon and pion structure with lattice QCD simulations at physical value of the pion mass

We present results on the nucleon scalar, axial, and tensor charges as well as on the momentum fraction, and the helicity and transversity moments. The pion momentum fraction is also presented. The computation of these key observables is carried out using lattice QCD simulations at a physical value of the pion mass. The evaluation is based on gauge configurations generated with two degenerate sea quarks of twisted mass fermions with a clover term. We investigate excited states contributions with the nucleon quantum numbers by analyzing three sink-source time separations. We find that, for the scalar charge, excited states contribute significantly and to a less degree to the nucleon momentum fraction and helicity moment. Our result for the nucleon axial charge agrees with the experimental value. Furthermore, we predict a value of 1.027(62) in the MS¯¯¯¯¯ scheme at 2 GeV for the isovector nucleon tensor charge directly at the physical point. The pion momentum fraction is found to be ⟨x⟩π±u−d=0.214(15)(+12−9) in the MS¯¯¯¯¯ at 2 GeV.