Proposed experimental tests of the Bell-Kochen-Specker theorem

For a two-particle two-state system, sets of compatible propositions exist for which quantum mechanics and noncontextual hidden-variable theories make conflicting predictions for every individual system whatever its quantum state. This permits a simple all-or-nothing state-independent experimental verification of the Bell-Kochen-Specker theorem.Comment: LaTeX, 8 page

Parity proofs of the Kochen-Specker theorem based on the 24 rays of Peres

A diagrammatic representation is given of the 24 rays of Peres that makes it easy to pick out all the 512 parity proofs of the Kochen-Specker theorem contained in them. The origin of this representation in the four-dimensional geometry of the rays is pointed out.Comment: 14 pages, 6 figures and 3 tables. Three references have been added. Minor typos have been correcte

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

Parity proofs of the Bell-Kochen-Specker theorem based on the 600-cell

The set of 60 real rays in four dimensions derived from the vertices of a 600-cell is shown to possess numerous subsets of rays and bases that provide basis-critical parity proofs of the Bell-Kochen-Specker (BKS) theorem (a basis-critical proof is one that fails if even a single basis is deleted from it). The proofs vary considerably in size, with the smallest having 26 rays and 13 bases and the largest 60 rays and 41 bases. There are at least 90 basic types of proofs, with each coming in a number of geometrically distinct varieties. The replicas of all the proofs under the symmetries of the 600-cell yield a total of almost a hundred million parity proofs of the BKS theorem. The proofs are all very transparent and take no more than simple counting to verify. A few of the proofs are exhibited, both in tabular form as well as in the form of MMP hypergraphs that assist in their visualization. A survey of the proofs is given, simple procedures for generating some of them are described and their applications are discussed. It is shown that all four-dimensional parity proofs of the BKS theorem can be turned into experimental disproofs of noncontextuality.Comment: 19 pages, 11 tables, 3 figures. Email address of first author has been corrected. Ref.[5] has been corrected, as has an error in Fig.3. Formatting error in Sec.4 has been corrected and the placement of tables and figures has been improved. A new paragraph has been added to Sec.4 and another new paragraph to the end of the Appendi

Quantum codewords contradict local realism

Quantum codewords are highly entangled combinations of two-state systems. The standard assumptions of local realism lead to logical contradictions similar to those found by Bell, Kochen and Specker, Greenberger, Horne and Zeilinger, and Mermin. The new contradictions have some noteworthy features that did not appear in the older ones.Comment: 9 pages LaTeX, 1 figur

State-independent quantum violation of noncontextuality in four dimensional space using five observables and two settings

Recently, a striking experimental demonstration [G. Kirchmair \emph{et al.}, Nature, \textbf{460}, 494(2009)] of the state-independent quantum mechanical violation of non-contextual realist models has been reported for any two-qubit state using suitable choices of \emph{nine} product observables and \emph{six} different measurement setups. In this report, a considerable simplification of such a demonstration is achieved by formulating a scheme that requires only \emph{five} product observables and \emph{two} different measurement setups. It is also pointed out that the relevant empirical data already available in the experiment by Kirchmair \emph{et al.} corroborate the violation of the NCR models in accordance with our proof

Quantum mechanical effect of path-polarization contextuality for a single photon

Using measurements pertaining to a suitable Mach-Zehnder(MZ) type setup, a curious quantum mechanical effect of contextuality between the path and the polarization degrees of freedom of a polarized photon is demonstrated, without using any notion of realism or hidden variables - an effect that holds good for the product as well as the entangled states. This form of experimental context-dependence is manifested in a way such that at \emph{either} of the two exit channels of the MZ setup used, the empirically verifiable \emph{subensemble} statistical properties obtained by an arbitrary polarization measurement depend upon the choice of a commuting(comeasurable) path observable, while this effect disappears for the \emph{whole ensemble} of photons emerging from the two exit channels of the MZ setup.Comment: To be published in IJT

Kochen-Specker Vectors

We give a constructive and exhaustive definition of Kochen-Specker (KS) vectors in a Hilbert space of any dimension as well as of all the remaining vectors of the space. KS vectors are elements of any set of orthonormal states, i.e., vectors in n-dim Hilbert space, H^n, n>3 to which it is impossible to assign 1s and 0s in such a way that no two mutually orthogonal vectors from the set are both assigned 1 and that not all mutually orthogonal vectors are assigned 0. Our constructive definition of such KS vectors is based on algorithms that generate MMP diagrams corresponding to blocks of orthogonal vectors in R^n, on algorithms that single out those diagrams on which algebraic 0-1 states cannot be defined, and on algorithms that solve nonlinear equations describing the orthogonalities of the vectors by means of statistically polynomially complex interval analysis and self-teaching programs. The algorithms are limited neither by the number of dimensions nor by the number of vectors. To demonstrate the power of the algorithms, all 4-dim KS vector systems containing up to 24 vectors were generated and described, all 3-dim vector systems containing up to 30 vectors were scanned, and several general properties of KS vectors were found.Comment: 19 pages, 6 figures, title changed, introduction thoroughly rewritten, n-dim rotation of KS vectors defined, original Kochen-Specker 192 (117) vector system translated into MMP diagram notation with a new graphical representation, results on Tkadlec's dual diagrams added, several other new results added, journal version: to be published in J. Phys. A, 38 (2005). Web page: http://m3k.grad.hr/pavici

Diabetes and pregnancy:national trends over a 15 year period

Aims/hypothesis: We aimed to examine time trends in national perinatal outcomes in pregnancies complicated by pre-existing type 1 or type 2 diabetes. Methods: We analysed episode-level data on all obstetric inpatient delivery events (live or stillbirth) between 1 April 1998 and 31 March 2013 (n = 813,921) using the Scottish Morbidity Record (SMR02). Pregnancies to mothers with type 1 (n = 3229) and type 2 (n = 1452) diabetes were identified from the national diabetes database (Scottish Care Information-Diabetes), and perinatal outcomes were compared among women with type 1 diabetes, type 2 diabetes and those without diabetes. Results: The number of pregnancies complicated by diabetes increased significantly, by 44% in type 1 diabetes and 90% in type 2 diabetes, across the 15 years examined, to rates of 1 in 210 and 1 in 504 deliveries, respectively. Compared with women without diabetes, delivery occurred 2.6 weeks earlier (type 1 diabetes 36.7 ± 2.3 weeks) and 2 weeks earlier (type 2 diabetes 37.3 ± 2.4 weeks), respectively, showing significant reductions for both type 1 (from 36.7 weeks to 36.4 weeks, p = 0.03) and type 2 (from 38.0 weeks to 37.2 weeks, p < 0.001) diabetes across the time period. The proportions of preterm delivery were markedly increased in women with diabetes (35.3% type 1 diabetes, 21.8% type 2 diabetes, 6.1% without diabetes; p < 0.0001), and these proportions increased with time for both groups (p < 0.005). Proportions of elective Caesarean sections (29.4% type 1 diabetes, 30.5% type 2 diabetes, 9.6% without diabetes) and emergency Caesarean sections (38.3% type 1 diabetes, 29.1% type 2 diabetes, 14.6% without diabetes) were greatly increased in women with diabetes and increased over time except for stable rates of emergency Caesarean section in type 1 diabetes. Gestational age-, sex- and parity-adjusted z score for birthweight (1.33 ± 1.34; p < 0.001) were higher in type 1 diabetes and increased over time from 1.22 to 1.47 (p < 0.001). Birthweight was also increased in type 2 diabetes (0.94 ± 1.34; p < 0.001) but did not alter with time. There were 65 perinatal deaths in offspring of mothers with type 1 diabetes and 39 to mothers with type 2 diabetes, representing perinatal mortality rates of 20.1 (95% CI 14.7, 24.3) and 26.9 (16.7, 32.9) per 1000 births, respectively, and rates 3.1 and 4.2 times, respectively, those observed in the non-diabetic population (p < 0.001). Stillbirth rates in type 1 and type 2 diabetes were 4.0-fold and 5.1-fold that in the non-diabetic population (p < 0.001). Perinatal mortality and stillbirth rates showed no significant fall over time despite small falls in the rates for the non-diabetic population. Conclusions/interpretation: Women with diabetes are receiving increased intervention in pregnancy (earlier delivery, increased Caesarean section rates), but despite this, higher birthweights are being recorded. Improvements in rates of stillbirth seen in the general population are not being reflected in changes in stillbirth or perinatal mortality in our population with diabetes