A Simple Proof of the Kochen-Specker Theorem on the Problem of Hidden Variables

In this talk I present a simple derivation of an old result of Kochen and Specker, which is apparently unrelated to the famous work of Bell on hidden variables, but is presumably equally important. Kochen and Specker showed in 1967 that quantum mechanics cannot be embedded into a classical stochastic theory, provided the quantum theoretical probability distributions are reproduced and one additional highly desirable property is satisfied. This showed in a striking manner what were the difficulties in implementing the Einstein programme of a `complete' version of quantum mechanics.Comment: 9 pages, invited talk (birthday contribution for Ruth Durrer, Geneva, January 25, 2008

Kochen-Specker theorem and experimental test on hidden variables

A recent proposal to experimentally test quantum mechanics against noncontextual hidden-variable theories [Phys. Rev. Lett. 80, 1797 (1998)] is shown to be related with the smallest proof of the Kochen-Specker theorem currently known [Phys. Lett. A 212, 183 (1996)]. This proof contains eighteen yes-no questions about a four-dimensional physical system, combined in nine mutually incompatible tests. When these tests are considered as tests about a two-part two-state system, then quantum mechanics and non-contextual hidden variables make the same predictions for eight of them, but make different predictions for the ninth. Therefore, this ninth test would allow us to discriminate between quantum mechanics and noncontextual hidden-variable theories in a (gedanken) single run experiment.Comment: 4 pages, 1 figure. To appear in Int. J. Mod. Phys.

Alice and Bob get away with it: A playlet

Alice and Bob use Aravind's version of the Bell-Kochen-Specker theorem to fend off awkward questions about what exactly they were doing in Amsterdam last week

Proposed test of macroscopic quantum contextuality

We show that, for any system with a number of levels which can be identified with n qubits, there is an inequality for the correlations between three compatible dichotomic measurements which must be satisfied by any noncontextual theory, but is violated by any quantum state. Remarkably, the violation grows exponentially with n, and the tolerated error per correlation also increases with n, showing that state-independent quantum contextuality is experimentally observable in complex systems.Comment: REVTeX4, 5 pages, 1 figur

A priori Knowledge and the Kochen-Specker Theorem

We introduce and formalize a notion of "a priori knowledge" about a quantum system, and show some properties about this form of knowledge. Finally, we show that the Kochen-Specker theorem follows directly from this study. This version is a draft version, the bibliography in particular is extremely scarce. Comments welcome

Quantum contextuality for rational vectors

The Kochen-Specker theorem states that noncontextual hidden variable models are inconsistent with the quantum predictions for every yes-no question on a qutrit, corresponding to every projector in three dimensions. It has been suggested [D. A. Meyer, Phys. Rev. Lett. 83, 3751 (1999)] that the inconsistency would disappear when we are restricted to projectors on unit vectors with rational components; that noncontextual hidden variables could reproduce the quantum predictions for rational vectors. Here we show that a qutrit state with rational components violates an inequality valid for noncontextual hidden-variable models [A. A. Klyachko et al., Phys. Rev. Lett. 101, 020403 (2008)] using rational projectors. This shows that the inconsistency remains even when using only rational vectors.Comment: REVTeX4-1, 1 pag

Gender, Psychiatric and Cognitive Status Related to Experiential Auras in Patients with Temporal Lobe Epilepsy

Objective: To determine whether the experiential auras in patients with temporal lobe epilepsy (TLE) are related to gender, psychiatric comorbidity, material-specific memory impairment, lateralization by video-EEG and structural neuroimaging abnormalities.Material and methods: Retrospective review (1998-2015) of clinical charts and video-EEG of patients with TLE and experiential auras followed at the JM Ramos Mejía and El Cruce Hospitals Results: We included 35 patients, 51.4% were male, mean age 35 years, mean epilepsy duration 20.3 years. Laterality of the epileptogenic zone was right (57.1%) and left (37.1%) temporal. An epileptogenic lesion was detected in most of cases and hippocampal sclerosis was the most common finding. Seventy-four percent of patients underwent epilepsy surgery (Engel I-II: 65.4%). The most frequent neuropsychological finding was visual memory deficit, and most patients had executive dysfunction. Almost half patients had a psychiatric comorbidity. Déjà vu was the most frequent experiential aura (60%), followed by jamais vu (20%), strangeness (20%), depersonalization (14.3%), dreaminess (11.4%), autobiographical memory recall (8.6%) and time perception alteration (5.7%). Most patients (62.9%) had a single experiential aura (déjà vu 54.5%, jamais vu 18.2%, strangeness 13.6%, depersonalization 9.1%, prescience 4.5%) associated with non-experiential auras in the majority of cases (81%).Conclusion: Most of patients presented a single experiential aura, most frequently déjà vu, associated with non-experiential auras, mainly fear. A right temporal lobe seizure focus was the most frequent, including for patients with déjà vu. In relation to gender, déjà vu was more common in male patients. A high prevalence of psychiatric comorbidity was observed and despite of the reduced number of cases, the 3 patients with psychosis presented déjà vu. Most of patients presented visual memory deficit associated with executive dysfunction.Fil: Vanessa Benjumea-Cuartas. Provincia de Buenos Aires. Ministerio de Salud. Hospital Alta Complejidad en Red El Cruce Dr. Néstor Carlos Kirchner Samic; Argentina. Gobierno de la Ciudad de Buenos Aires. Hospital General de Agudos "Ramos Mejía"; ArgentinaFil: Brenda Giagante. Provincia de Buenos Aires. Ministerio de Salud. Hospital Alta Complejidad en Red El Cruce Dr. Néstor Carlos Kirchner Samic; Argentina. Universidad Nacional Arturo Jauretche. Unidad Ejecutora de Estudios en Neurociencias y Sistemas Complejos. Provincia de Buenos Aires. Ministerio de Salud. Hospital Alta Complejidad en Red El Cruce Dr. Néstor Carlos Kirchner Samic. Unidad Ejecutora de Estudios en Neurociencias y Sistemas Complejos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Unidad Ejecutora de Estudios en Neurociencias y Sistemas Complejos; ArgentinaFil: Kochen, Sara Silvia. Gobierno de la Ciudad de Buenos Aires. Hospital General de Agudos "Ramos Mejía"; Argentina. Universidad Nacional Arturo Jauretche. Unidad Ejecutora de Estudios en Neurociencias y Sistemas Complejos. Provincia de Buenos Aires. Ministerio de Salud. Hospital Alta Complejidad en Red El Cruce Dr. Néstor Carlos Kirchner Samic. Unidad Ejecutora de Estudios en Neurociencias y Sistemas Complejos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Unidad Ejecutora de Estudios en Neurociencias y Sistemas Complejos; Argentina. Provincia de Buenos Aires. Ministerio de Salud. Hospital Alta Complejidad en Red El Cruce Dr. Néstor Carlos Kirchner Samic; Argentin