Two-Qubit Separabilities as Piecewise Continuous Functions of Maximal Concurrence

The generic real (b=1) and complex (b=2) two-qubit states are 9-dimensional and 15-dimensional in nature, respectively. The total volumes of the spaces they occupy with respect to the Hilbert-Schmidt and Bures metrics are obtainable as special cases of formulas of Zyczkowski and Sommers. We claim that if one could determine certain metric-independent 3-dimensional "eigenvalue-parameterized separability functions" (EPSFs), then these formulas could be readily modified so as to yield the Hilbert-Schmidt and Bures volumes occupied by only the separable two-qubit states (and hence associated separability probabilities). Motivated by analogous earlier analyses of "diagonal-entry-parameterized separability functions", we further explore the possibility that such 3-dimensional EPSFs might, in turn, be expressible as univariate functions of some special relevant variable--which we hypothesize to be the maximal concurrence (0 < C <1) over spectral orbits. Extensive numerical results we obtain are rather closely supportive of this hypothesis. Both the real and complex estimated EPSFs exhibit clearly pronounced jumps of magnitude roughly 50% at C=1/2, as well as a number of additional matching discontinuities.Comment: 12 pages, 7 figures, new abstract, revised for J. Phys.

Two-Qubit Separability Probabilities and Beta Functions

Due to recent important work of Zyczkowski and Sommers (quant-ph/0302197 and quant-ph/0304041), exact formulas are available (both in terms of the Hilbert-Schmidt and Bures metrics) for the (n^2-1)-dimensional and (n(n-1)/2-1)-dimensional volumes of the complex and real n x n density matrices. However, no comparable formulas are available for the volumes (and, hence, probabilities) of various separable subsets of them. We seek to clarify this situation for the Hilbert-Schmidt metric for the simplest possible case of n=4, that is, the two-qubit systems. Making use of the density matrix (rho) parameterization of Bloore (J. Phys. A 9, 2059 [1976]), we are able to reduce each of the real and complex volume problems to the calculation of a one-dimensional integral, the single relevant variable being a certain ratio of diagonal entries, nu = (rho_{11} rho_{44})/{rho_{22} rho_{33})$. The associated integrand in each case is the product of a known (highly oscillatory near nu=1) jacobian and a certain unknown univariate function, which our extensive numerical (quasi-Monte Carlo) computations indicate is very closely proportional to an (incomplete) beta function B_{nu}(a,b), with a=1/2, b=sqrt{3}in the real case, and a=2 sqrt{6}/5, b =3/sqrt{2} in the complex case. Assuming the full applicability of these specific incomplete beta functions, we undertake separable volume calculations.Comment: 17 pages, 4 figures, paper is substantially rewritten and reorganized, with the quasi-Monte Carlo integration sample size being greatly increase

Qubit-Qutrit Separability-Probability Ratios

Paralleling our recent computationally-intensive (quasi-Monte Carlo) work for the case N=4 (quant-ph/0308037), we undertake the task for N=6 of computing to high numerical accuracy, the formulas of Sommers and Zyczkowski (quant-ph/0304041) for the (N^2-1)-dimensional volume and (N^2-2)-dimensional hyperarea of the (separable and nonseparable) N x N density matrices, based on the Bures (minimal monotone) metric -- and also their analogous formulas (quant-ph/0302197) for the (non-monotone) Hilbert-Schmidt metric. With the same seven billion well-distributed (``low-discrepancy'') sample points, we estimate the unknown volumes and hyperareas based on five additional (monotone) metrics of interest, including the Kubo-Mori and Wigner-Yanase. Further, we estimate all of these seven volume and seven hyperarea (unknown) quantities when restricted to the separable density matrices. The ratios of separable volumes (hyperareas) to separable plus nonseparable volumes (hyperareas) yield estimates of the separability probabilities of generically rank-six (rank-five) density matrices. The (rank-six) separability probabilities obtained based on the 35-dimensional volumes appear to be -- independently of the metric (each of the seven inducing Haar measure) employed -- twice as large as those (rank-five ones) based on the 34-dimensional hyperareas. Accepting such a relationship, we fit exact formulas to the estimates of the Bures and Hilbert-Schmidt separable volumes and hyperareas.(An additional estimate -- 33.9982 -- of the ratio of the rank-6 Hilbert-Schmidt separability probability to the rank-4 one is quite clearly close to integral too.) The doubling relationship also appears to hold for the N=4 case for the Hilbert-Schmidt metric, but not the others. We fit exact formulas for the Hilbert-Schmidt separable volumes and hyperareas.Comment: 36 pages, 15 figures, 11 tables, final PRA version, new last paragraph presenting qubit-qutrit probability ratios disaggregated by the two distinct forms of partial transpositio

Advances in delimiting the Hilbert-Schmidt separability probability of real two-qubit systems

We seek to derive the probability--expressed in terms of the Hilbert-Schmidt (Euclidean or flat) metric--that a generic (nine-dimensional) real two-qubit system is separable, by implementing the well-known Peres-Horodecki test on the partial transposes (PT's) of the associated 4 x 4 density matrices). But the full implementation of the test--requiring that the determinant of the PT be nonnegative for separability to hold--appears to be, at least presently, computationally intractable. So, we have previously implemented--using the auxiliary concept of a diagonal-entry-parameterized separability function (DESF)--the weaker implied test of nonnegativity of the six 2 x 2 principal minors of the PT. This yielded an exact upper bound on the separability probability of 1024/{135 pi^2} =0.76854$. Here, we piece together (reflection-symmetric) results obtained by requiring that each of the four 3 x 3 principal minors of the PT, in turn, be nonnegative, giving an improved/reduced upper bound of 22/35 = 0.628571. Then, we conclude that a still further improved upper bound of 1129/2100 = 0.537619 can be found by similarly piecing together the (reflection-symmetric) results of enforcing the simultaneous nonnegativity of certain pairs of the four 3 x 3 principal minors. In deriving our improved upper bounds, we rely repeatedly upon the use of certain integrals over cubes that arise. Finally, we apply an independence assumption to a pair of DESF's that comes close to reproducing our numerical estimate of the true separability function.Comment: 16 pages, 9 figures, a few inadvertent misstatements made near the end are correcte

A priori probability that a qubit-qutrit pair is separable

We extend to arbitrarily coupled pairs of qubits (two-state quantum systems) and qutrits (three-state quantum systems) our earlier study (quant-ph/0207181), which was concerned with the simplest instance of entangled quantum systems, pairs of qubits. As in that analysis -- again on the basis of numerical (quasi-Monte Carlo) integration results, but now in a still higher-dimensional space (35-d vs. 15-d) -- we examine a conjecture that the Bures/SD (statistical distinguishability) probability that arbitrarily paired qubits and qutrits are separable (unentangled) has a simple exact value, u/(v Pi^3)= >.00124706, where u = 2^20 3^3 5 7 and v = 19 23 29 31 37 41 43 (the product of consecutive primes). This is considerably less than the conjectured value of the Bures/SD probability, 8/(11 Pi^2) = 0736881, in the qubit-qubit case. Both of these conjectures, in turn, rely upon ones to the effect that the SD volumes of separable states assume certain remarkable forms, involving "primorial" numbers. We also estimate the SD area of the boundary of separable qubit-qutrit states, and provide preliminary calculations of the Bures/SD probability of separability in the general qubit-qubit-qubit and qutrit-qutrit cases.Comment: 9 pages, 3 figures, 2 tables, LaTeX, we utilize recent exact computations of Sommers and Zyczkowski (quant-ph/0304041) of "the Bures volume of mixed quantum states" to refine our conjecture

Turner syndrome and associated problems in turkish children: A multicenter study

Objective: Turner syndrome (TS) is a chromosomal disorder caused by complete or partial X chromosome monosomy that manifests various clinical features depending on the karyotype and on the genetic background of affected girls. This study aimed to systematically investigate the key clinical features of TS in relationship to karyotype in a large pediatric Turkish patient population. Methods: Our retrospective study included 842 karyotype-proven TS patients aged 0-18 years who were evaluated in 35 different centers in Turkey in the years 2013-2014. Results: The most common karyotype was 45,X (50.7%), followed by 45,X/46,XX (10.8%), 46,X,i(Xq) (10.1%) and 45,X/46,X,i(Xq) (9.5%). Mean age at diagnosis was 10.2±4.4 years. The most common presenting complaints were short stature and delayed puberty. Among patients diagnosed before age one year, the ratio of karyotype 45,X was significantly higher than that of other karyotype groups. Cardiac defects (bicuspid aortic valve, coarctation of the aorta and aortic stenosi) were the most common congenital anomalies, occurring in 25% of the TS cases. This was followed by urinary system anomalies (horseshoe kidney, double collector duct system and renal rotation) detected in 16.3%. Hashimoto’s thyroiditis was found in 11.1% of patients, gastrointestinal abnormalities in 8.9%, ear nose and throat problems in 22.6%, dermatologic problems in 21.8% and osteoporosis in 15.3%. Learning difficulties and/or psychosocial problems were encountered in 39.1%. Insulin resistance and impaired fasting glucose were detected in 3.4% and 2.2%, respectively. Dyslipidemia prevalence was 11.4%. Conclusion: This comprehensive study systematically evaluated the largest group of karyotype-proven TS girls to date. The karyotype distribution, congenital anomaly and comorbidity profile closely parallel that from other countries and support the need for close medical surveillance of these complex patients throughout their lifespan. © Journal of Clinical Research in Pediatric Endocrinology

Diffusion of Myosin V on Microtubules: A Fine-Tuned Interaction for Which E-Hooks Are Dispensable

Organelle transport in eukaryotes employs both microtubule and actin tracks to deliver cargo effectively to their destinations, but the question of how the two systems cooperate is still largely unanswered. Recently, in vitro studies revealed that the actin-based processive motor myosin V also binds to, and diffuses along microtubules. This biophysical trick enables cells to exploit both tracks for the same transport process without switching motors. The detailed mechanisms underlying this behavior remain to be solved. By means of single molecule Total Internal Reflection Microscopy (TIRFM), we show here that electrostatic tethering between the positively charged loop 2 and the negatively charged C-terminal E-hooks of microtubules is dispensable. Furthermore, our data indicate that in addition to charge-charge interactions, other interaction forces such as non-ionic attraction might account for myosin V diffusion. These findings provide evidence for a novel way of myosin tethering to microtubules that does not interfere with other E-hook-dependent processes

Synthesis of aryl-substituted quinolines and tetrahydroquinolines through Suzuki–Miyaura coupling reactions

Okten, Salih/0000-0001-9656-1803WOS: 000484663600009The synthesis and characterization of substituted (trifluoromethoxy, thiomethyl, and methoxy) phenyl quinolines is described. Dichlorobis(triphenylphosphine)palladiunn(II)-catalyzed Suzuki-Miyaura cross-coupling of 6-bromo- and 6,8-dibronno-1,2,3,4-tetrahydroquinolines, 5-bromo-8-methoxyquinoline, and 5,7-dibromo-8-methoxyquinoline with substituted phenylboronic acids affords the corresponding 6-aryl- (13a-d), 6,8-diaryl- (14a-c), 5-aryl- (15), and 5,7-diaryl- (16b, c) tetrahydroquinolines and quinolines in high yields (68%-82%). The structures of all the products are characterized by H-1 NMR, C-13 NMR, F-1(9) NMR, and Fourier transform infrared spectroscopy and by elemental analysis.Scientific and Technological Research Council of Turkey (TUBITAK)Turkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [112T394]The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was supported by grants from the Scientific and Technological Research Council of Turkey (TUBITAK; project number: 112T394)

De novo balanced (X;14) translocation in a patient with recurrent miscarriages: Case report [Tekrarlayan düşükler yapan bir hastada doǧumsal dengeli (X;14) translokasyonu]

We report a 23-year-old phenotypically normal female patient who had previously suffered from recurrent spontaneous abortion (RSA) who found to have an X;14 trans location and a Methylene- Tetrahdrofolate-Reductase (MTHFR) C677T heterozygote mutation. G-banding cytogenetic analysis was cultured from the peripheral blood lymphocy tes. MTHFR, factor V Leiden and prothrombin gene mutations were studied from DNA obtained from peripheral blood lym- phocytes with stripassay. DNA for X inactivation pattern study was also obtained with the method described above. G-banding cytogentic analysis from cultured peripheral blood lymphocytes of the patient revealed 46,XderX,t(X;14)(q13;q32) and found to be heterozygous for C677T MTHFR mutation. An X inactivation pattern study revealed a complete inactivated nor mal X chromosome, asexpected. The possible causes of recurrent miscarriages in our patient were unbalanced gametes, skewed X inactivation and MTHFR C677T heterozygote mutation. © 2011 by Türkiye Klinikleri