Measurement of qubits

We describe in detail the theory underpinning the measurement of density matrices of a pair of quantum two-level systems (qubits). Our particular emphasis is on qubits realized by the two polarization degrees of freedom of a pair of entangled photons generated in a down-conversion experiment; however, the discussion applies in general, regardless of the actual physical realization. Two techniques are discussed, namely, a tomographic reconstruction (in which the density matrix is linearly related to a set of measured quantities) and a maximum likelihood technique which requires numerical optimization (but has the advantage of producing density matrices that are always non-negative definite). In addition, a detailed error analysis is presented, allowing errors in quantities derived from the density matrix, such as the entropy or entanglement of formation, to be estimated. Examples based on down-conversion experiments are used to illustrate our results

Research designs considerations for chronic pain prevention clinical trials: IMMPACT recommendations

Although certain risk factors can identify individuals who aremost likely to develop chronic pain, few interventions to prevent chronic pain have been identified. To facilitate the identification of preventive interventions, an IMMPACTmeeting was convened to discuss research design considerations for clinical trials investigating the prevention of chronic pain. We present general design considerations for prevention trials in populations that are at relatively high risk for developing chronic pain. Specific design considerations included subject identification, timing and duration of treatment, outcomes, timing of assessment, and adjusting for risk factors in the analyses.We provide a detailed examination of 4 models of chronic pain prevention (ie, chronic postsurgical pain, postherpetic neuralgia, chronic low back pain, and painful chemotherapy-induced peripheral neuropathy). The issues discussed can, inmany instances, be extrapolated to other chronic pain conditions. These examples were selected because they are representative models of primary and secondary prevention, reflect persistent pain resulting from multiple insults (ie, surgery, viral infection, injury, and toxic or noxious element exposure), and are chronically painful conditions that are treated with a range of interventions. Improvements in the design of chronic pain prevention trials could improve assay sensitivity and thus accelerate the identification of efficacious interventions. Such interventions would have the potential to reduce the prevalence of chronic pain in the population. Additionally, standardization of outcomes in prevention clinical trials will facilitate meta-analyses and systematic reviews and improve detection of preventive strategies emerging from clinical trials