Optimal state for keeping reference frames aligned and the Platonic solids

The optimal N qubit states featuring highest sensitivity to small misalignment of cartesian reference frames are found using the Quantum Cramer-Rao bound. It is shown that the optimal states are supported on the symmetric subspace and hence are mathematically equivalent to a single spin J=N/2. Majorana representation of spin states is used to reveal a beautiful connection between the states optimal for aligning reference frames and the platonic solids

Observables have no value: a no-go theorem for position and momentum observables

A very simple illustration of the Bell-Kochen-Specker contradiction is presented using continuous observables in infinite dimensional Hilbert space. It is shown that the assumption of the \emph{existence} of putative values for position and momentum observables for one single particle is incompatible with quantum mechanics.Comment: 6 pages, 1 Latex figure small corrections, refference and comments adde

Kochen-Specker Theorem for Finite Precision Spin One Measurements

Unsharp spin 1 observables arise from the fact that a residual uncertainty about the actual orientation of the measurement device remains. If the uncertainty is below a certain level, and if the distribution of measurement errors is covariant under rotations, a Kochen-Specker theorem for the unsharp spin observables follows: There are finite sets of directions such that not all the unsharp spin observables in these directions can consistently be assigned approximate truth-values in a non-contextual way.Comment: 4 page

Multiqubit symmetric states with high geometric entanglement

We propose a detailed study of the geometric entanglement properties of pure symmetric N-qubit states, focusing more particularly on the identification of symmetric states with a high geometric entanglement and how their entanglement behaves asymptotically for large N. We show that much higher geometric entanglement with improved asymptotical behavior can be obtained in comparison with the highly entangled balanced Dicke states studied previously. We also derive an upper bound for the geometric measure of entanglement of symmetric states. The connection with the quantumness of a state is discussed

The generalized Kochen-Specker theorem

A proof of the generalized Kochen-Specker theorem in two dimensions due to Cabello and Nakamura is extended to all higher dimensions. A set of 18 states in four dimensions is used to give closely related proofs of the generalized Kochen-Specker, Kochen-Specker and Bell theorems that shed some light on the relationship between these three theorems.Comment: 5 pages, 1 Table. A new third paragraph and an additional reference have been adde

The Projective Line Over the Finite Quotient Ring GF(2)[xx]/<x3−x>< x^{3} - x> and Quantum Entanglement II. The Mermin "Magic" Square/Pentagram

In 1993, Mermin (Rev. Mod. Phys. 65, 803--815) gave lucid and strikingly simple proofs of the Bell-Kochen-Specker (BKS) theorem in Hilbert spaces of dimensions four and eight by making use of what has since been referred to as the Mermin(-Peres) "magic square" and the Mermin pentagram, respectively. The former is a $3 \times 3$ array of nine observables commuting pairwise in each row and column and arranged so that their product properties contradict those of the assigned eigenvalues. The latter is a set of ten observables arranged in five groups of four lying along five edges of the pentagram and characterized by similar contradiction. An interesting one-to-one correspondence between the operators of the Mermin-Peres square and the points of the projective line over the product ring ${\rm GF}(2) \otimes \rm{GF}(2)$ is established. Under this mapping, the concept "mutually commuting" translates into "mutually distant" and the distinguishing character of the third column's observables has its counterpart in the distinguished properties of the coordinates of the corresponding points, whose entries are both either zero-divisors, or units. The ten operators of the Mermin pentagram answer to a specific subset of points of the line over GF(2)[$x$]/$$. The situation here is, however, more intricate as there are two different configurations that seem to serve equally well our purpose. The first one comprises the three distinguished points of the (sub)line over GF(2), their three "Jacobson" counterparts and the four points whose both coordinates are zero-divisors; the other features the neighbourhood of the point ($1, 0$) (or, equivalently, that of ($0, 1$)). Some other ring lines that might be relevant for BKS proofs in higher dimensions are also mentioned.Comment: 6 pages, 5 figure

HAART as a Strategy for Reduction of HIV-1 Transmission in Sub-Saharan Africa: Survival and Virus Load Parameters from the Drug Resource Enhancement against AIDS and Malnutrition Program

Background: The concept of universal antiretroviral use as a strategy for reduction of new cases of HIV infection has been evaluated in mathematical models as a potential approach to curtailing the Sub-Saharan African epidemic. In order to further substantiate such models, additional strategic parameters based on robust patient data should be considered, including survival of HIV-infected populations under HAART and subject infectivity as determined by HIV RNA levels. Methods: A retrospective cohort study was conducted in a population of patients enrolled in DREAMcenters throughout sub-Saharan Africa in order to determine survival under HAART. Cox regression analysis was performed evaluating parameters associated with survival such as CD4 cell count, viral load, body mass index (BMI) and hemoglobin (HB) levels. DREAM criteria for HAART initiation included (1) WHO stage 3-4 regardless of CD4 cell value (2) 100,000 copies in any subject. Virus load response to HAART was assessed in a subset of patients. Results: Adult non-pregnant patients who accessed DREAM centers from 1/2002 to 7/2009 were evaluated. A total of 34,295 patients (22,249 females/12,041 males) were included. Median age was 34 years (IQR:29-42) and median observation time 476 days (IQR:206 –950). Baseline median viral load, CD4 cell counts, HB and BMI values were 4.4 (IQR:3.6-5.0), 243 (IQR:109-416), 10.8 (IQR:9.2-12.4), and 20.3 (IQR:18.3-22.7).Over time 23,795 patients initiated HAART. Cox survival analysis (adjusted for Viral Load and HB) according to CD4 cell strata was performed. The relative risk of death in the lowest CD4 stratum (500) was 3.3 [2.7 –4.1]. Survival estimates at >7 years of HAART ranged from 50% to 95% according to baseline CD4 cell count and HB levels. In a subset of 13,405 subjects who received HAART for >6 months with at least 2 virus load measures available, 55.9% achieved < 50 copies/ml and an additional 19.7% achieved levels < 400 copies/ml (75.6% total). Final median virus load value was 58 (IQ: 0 –2000). Conclusions: Contrary to more conservative estimates used in mathematical modeling studies, patients in our cohort demonstrated a significant survival benefit even within the lowest CD4 cell stratum. Patients on HAART had low potential infectivity as measured by plasma virus load. Cohort data from African patients can contribute to the further refinement of predictive models

Isomorphism between the Peres and Penrose proofs of the BKS theorem in three dimensions

It is shown that the 33 complex rays in three dimensions used by Penrose to prove the Bell-Kochen-Specker theorem have the same orthogonality relations as the 33 real rays of Peres, and therefore provide an isomorphic proof of the theorem. It is further shown that the Peres and Penrose rays are just two members of a continuous three-parameter family of unitarily inequivalent rays that prove the theorem.Comment: 7 pages, 2 Tables. A concluding para and 9 new references have been added to the second versio

Clinical and ultrasonographic features of abdominal tuberculosis in HIV positive adults in Zambia

Background: The diagnosis of abdominal tuberculosis (TB) is difficult, especially so in health care facilities in developing countries where laparoscopy and colonoscopy are rarely available. There is little information on abdominal TB in HIV infection. We estimated the prevalence and clinical features of abdominal (excluding genitourinary) TB in HIV infected adults attending the University Teaching Hospital, Zambia. Methods: We screened 5,609 medical inpatients, and those with fever, weight loss, and clinical features suggestive of abdominal pathology were evaluated further. A clinical algorithm was used to specify definitive investigations including laparoscopy or colonoscopy, with culture of biopsies and other samples. Results: Of 140 HIV seropositive patients with these features, 31 patients underwent full evaluation and 22 (71%) had definite or probable abdominal TB. The commonest presenting abdominal features were ascites and persistent tenderness. The commonest ultrasound findings were ascites, para-aortic lymphadenopathy (over 1 cm in size), and hepatomegaly. Abdominal TB was associated with CD4 cell counts over a wide range though 76% had CD4 counts <100 cells/μL. Conclusion: The clinical manifestations of abdominal TB in our HIV-infected patients resembled the well-established pattern in HIV-uninfected adults. Patients with fever, weight loss, abdominal tenderness, abdominal lymphadenopathy, ascites and/or hepatomegaly in Zambia have a high probability of abdominal TB, irrespective of CD4 cell count. © 2009 Sinkala et al; licensee BioMed Central Ltd

Evaluating adherence to highly active antiretroviral therapy with use of pill counts and viral load measurement in the drug resources enhancement against AIDS and malnutrition program in Mozambique

Background. Maintaining treatment adherence among the growing number of patients receiving antiretroviral treatment in Africa is a dramatic challenge. The objective of our study was to explore the results of a computerized pill count method and to test the validity, sensitivity, and specificity of this method with respect to viral load measurement in an African setting. Methods. We performed a prospective, observational study involving patients who received first-line highly active antiretroviral therapy in Mozambique from 1 April 2005 through 31 March 2006. Enrolled patients had received treatment for at least 3 months before the study. For defining treatment adherence levels, pill counts were used, and the results were analyzed with viral load measurements at the end of the observation period. Results. The study involved 531 participants. During the 12 months of observation, 137 patients left the program or discontinued first-line therapy. Of the remaining 394 patients, 284 (72.1%) had >95% treatment adherence; of those 284 patients, 274 (96.5%) had a final viral load <1000 copies/mL. A Cox proportional hazards analysis revealed that the relationship between >95% treatment adherence and the final viral load was closer than that between >90% treatment adherence and viral load. Conclusions. Treatment adherence >95% maximizes the results of the nonnucleoside reverse-transcriptase inhibitor-based regimen. The pill count method appears to be a reliable and economic tool for monitoring treatment adherence in resource-limited settings