Kochen-Specker theorem for a single qubit using positive operator-valued measures

A proof of the Kochen-Specker theorem for a single two-level system is presented. It employs five eight-element positive operator-valued measures and a simple algebraic reasoning based on the geometry of the dodecahedron.Comment: REVTeX4, 4 pages, 2 figure

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

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

Parity proofs of the Kochen-Specker theorem based on 60 complex rays in four dimensions

It is pointed out that the 60 complex rays in four dimensions associated with a system of two qubits yield over 10^9 critical parity proofs of the Kochen-Specker theorem. The geometrical properties of the rays are described, an overview of the parity proofs contained in them is given, and examples of some of the proofs are exhibited.Comment: 17 pages, 13 tables, 3 figures. Several new references have been adde

Critical noncolorings of the 600-cell proving the Bell-Kochen-Specker theorem

Aravind and Lee-Elkin (1997) gave a proof of the Bell-Kochen-Specker theorem by showing that it is impossible to color the 60 directions from the center of a 600-cell to its vertices in a certain way. This paper refines that result by showing that the 60 directions contain many subsets of 36 and 30 directions that cannot be similarly colored, and so provide more economical demonstrations of the theorem. Further, these subsets are shown to be critical in the sense that deleting even a single direction from any of them causes the proof to fail. The critical sets of size 36 and 30 are shown to belong to orbits of 200 and 240 members, respectively, under the symmetries of the polytope. A comparison is made between these critical sets and other such sets in four dimensions, and the significance of these results is discussed.Comment: 2 new references added, caption to Table 9 correcte

Circulating tumour DNA analysis to direct therapy in advanced breast cancer (plasmaMATCH): a multicentre, multicohort, phase 2a, platform trial.

BACKGROUND: Circulating tumour DNA (ctDNA) testing might provide a current assessment of the genomic profile of advanced cancer, without the need to repeat tumour biopsy. We aimed to assess the accuracy of ctDNA testing in advanced breast cancer and the ability of ctDNA testing to select patients for mutation-directed therapy. METHODS: We did an open-label, multicohort, phase 2a, platform trial of ctDNA testing in 18 UK hospitals. Participants were women (aged ≥18 years) with histologically confirmed advanced breast cancer and an Eastern Cooperative Oncology Group performance status 0-2. Patients had completed at least one previous line of treatment for advanced breast cancer or relapsed within 12 months of neoadjuvant or adjuvant chemotherapy. Patients were recruited into four parallel treatment cohorts matched to mutations identified in ctDNA: cohort A comprised patients with ESR1 mutations (treated with intramuscular extended-dose fulvestrant 500 mg); cohort B comprised patients with HER2 mutations (treated with oral neratinib 240 mg, and if oestrogen receptor-positive with intramuscular standard-dose fulvestrant); cohort C comprised patients with AKT1 mutations and oestrogen receptor-positive cancer (treated with oral capivasertib 400 mg plus intramuscular standard-dose fulvestrant); and cohort D comprised patients with AKT1 mutations and oestrogen receptor-negative cancer or PTEN mutation (treated with oral capivasertib 480 mg). Each cohort had a primary endpoint of confirmed objective response rate. For cohort A, 13 or more responses among 78 evaluable patients were required to infer activity and three or more among 16 were required for cohorts B, C, and D. Recruitment to all cohorts is complete and long-term follow-up is ongoing. This trial is registered with ClinicalTrials.gov, NCT03182634; the European Clinical Trials database, EudraCT2015-003735-36; and the ISRCTN registry, ISRCTN16945804. FINDINGS: Between Dec 21, 2016, and April 26, 2019, 1051 patients registered for the study, with ctDNA results available for 1034 patients. Agreement between ctDNA digital PCR and targeted sequencing was 96-99% (n=800, kappa 0·89-0·93). Sensitivity of digital PCR ctDNA testing for mutations identified in tissue sequencing was 93% (95% CI 83-98) overall and 98% (87-100) with contemporaneous biopsies. In all cohorts, combined median follow-up was 14·4 months (IQR 7·0-23·7). Cohorts B and C met or exceeded the target number of responses, with five (25% [95% CI 9-49]) of 20 patients in cohort B and four (22% [6-48]) of 18 patients in cohort C having a response. Cohorts A and D did not reach the target number of responses, with six (8% [95% CI 3-17]) of 74 in cohort A and two (11% [1-33]) of 19 patients in cohort D having a response. The most common grade 3-4 adverse events were raised gamma-glutamyltransferase (13 [16%] of 80 patients; cohort A); diarrhoea (four [25%] of 20; cohort B); fatigue (four [22%] of 18; cohort C); and rash (five [26%] of 19; cohort D). 17 serious adverse reactions occurred in 11 patients, and there was one treatment-related death caused by grade 4 dyspnoea (in cohort C). INTERPRETATION: ctDNA testing offers accurate, rapid genotyping that enables the selection of mutation-directed therapies for patients with breast cancer, with sufficient clinical validity for adoption into routine clinical practice. Our results demonstrate clinically relevant activity of targeted therapies against rare HER2 and AKT1 mutations, confirming these mutations could be targetable for breast cancer treatment. FUNDING: Cancer Research UK, AstraZeneca, and Puma Biotechnology

Practical guidance for running late-phase platform protocols for clinical trials: lessons from experienced UK clinical trials units

Background Late-phase platform protocols (including basket, umbrella, multi-arm multi-stage (MAMS), and master protocols) are generally agreed to be more efficient than traditional two-arm clinical trial designs but are not extensively used. We have gathered the experience of running a number of successful platform protocols together to present some operational recommendations. Methods Representatives of six UK clinical trials units with experience in running late-phase platform protocols attended a 1-day meeting structured to discuss various practical aspects of running these trials. We report and give guidance on operational aspects which are either harder to implement compared to a traditional late-phase trial or are specific to platform protocols. Results We present a list of practical recommendations for trialists intending to design and conduct late-phase platform protocols. Our recommendations cover the entire life cycle of a platform trial: from protocol development, obtaining funding, and trial set-up, to a wide range of operational and regulatory aspects such as staffing, oversight, data handling, and data management, to the reporting of results, with a particular focus on communication with trial participants and stakeholders as well as public and patient involvement. Discussion Platform protocols enable many questions to be answered efficiently to the benefit of patients. Our practical lessons from running platform trials will support trial teams in learning how to run these trials more effectively and efficiently

Infectious Speciation Revisited: Impact of Symbiont-Depletion on Female Fitness and Mating Behavior of Drosophila paulistorum

The neotropical Drosophila paulistorum superspecies, consisting of at least six geographically overlapping but reproductively isolated semispecies, has been the object of extensive research since at least 1955, when it was initially trapped mid-evolution in flagrant statu nascendi. In this classic system females express strong premating isolation patterns against mates belonging to any other semispecies, and yet uncharacterized microbial reproductive tract symbionts were described triggering hybrid inviability and male sterility. Based on theoretical models and limited experimental data, prime candidates fostering symbiont-driven speciation in arthropods are intracellular bacteria belonging to the genus Wolbachia. They are maternally inherited symbionts of many arthropods capable of manipulating host reproductive biology for their own benefits. However, it is an ongoing debate as to whether or not reproductive symbionts are capable of driving host speciation in nature and if so, to what extent. Here we have reevaluated this classic case of infectious speciation by means of present day molecular approaches and artificial symbiont depletion experiments. We have isolated the α-proteobacteria Wolbachia as the maternally transmitted core endosymbionts of all D. paulistorum semispecies that have coevolved towards obligate mutualism with their respective native hosts. In hybrids, however, these mutualists transform into pathogens by overreplication causing embryonic inviability and male sterility. We show that experimental reduction in native Wolbachia titer causes alterations in sex ratio, fecundity, and mate discrimination. Our results indicate that formerly designated Mycoplasma-like organisms are most likely Wolbachia that have evolved by becoming essential mutualistic symbionts in their respective natural hosts; they have the potential to trigger pre- and postmating isolation. Furthermore, in light of our new findings, we revisit the concept of infectious speciation and discuss potential mechanisms that can restrict or promote symbiont-induced speciation at post- and prezygotic levels in nature and under artificial laboratory conditions