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Register a new userEntanglement in Cognition violating Bell Inequalities Beyond Cirelsons Bound
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We present the results of two tests where a sample of human participants were asked to make judgements about the conceptual combinations {it The Animal Acts} and {it The Animal eats the Food}. Both tests significantly violate the Clauser-Horne-Shimony-Holt version of Bell inequalities (`CHSH inequality), thus exhibiting manifestly non-classical behaviour due to the meaning connection between the individual concepts that are combined. We then apply a quantum-theoretic framework which we developed for any Bell-type situation and represent empirical data in complex Hilbert space. We show that the observed violations of the CHSH inequality can be explained as a consequence of a strong form of `quantum entanglement between the component conceptual entities in which both the state and measurements are entangled. We finally observe that a quantum model in Hilbert space can be elaborated in these Bell-type situations even when the CHSH violation exceeds the known `Cirelson bound, in contrast to a widespread belief. These findings confirm and strengthen the results we recently obtained in a variety of cognitive tests and document and image retrieval operations on the same conceptual combinations.
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D{u}r [Phys. Rev. Lett. {bf 87}, 230402 (2001)] constructed $N$-qubit bound entangled states which violate a Bell inequality for $Nge 8$, and his result was recently improved by showing that there exists an $N$-qubit bound entangled state violating the Bell inequality if and only if $Nge 6$ [Phys. Rev. A {bf 79}, 032309 (2009)]. On the other hand, it has been also shown that the states which D{u}r considered violate Bell inequalities different from the inequality for $Nge 6$. In this paper, by employing different forms of Bell inequalities, in particular, a specific form of Bell inequalities with $M$ settings of the measuring apparatus for sufficiently large $M$, we prove that there exists an $N$-qubit bound entangled state violating the $M$-setting Bell inequality if and only if $Nge 4$.
We demonstrate a novel approach of violating position dependent Bell inequalities by photons emitted via independent photon sources in free space. We trace this violation back to path entanglement created a posteriori by the selection of modes due to the process of detection.
We review in this paper the research status on testing the completeness of Quantum mechanics in High Energy Physics, especially on the Bell Inequalities. We briefly introduce the basic idea of Einstein, Podolsky, and Rosen paradox and the results obtained in photon experiments. In the tests of Bell inequalities in high energy physics, the early attempts of using spin correlations in particle decays and later on the mixing of neutral mesons used to form the quasi-spin entangled states are covered. The related experimental results in K^0 and B^0 systems are presented and discussed. We introduce the new scheme, which is based on the non-maximally entangled state and proposed to implement in phi factory, in testing the Local Hidden Variable Theory. And, we also discuss the possibility in generalizing it to the tau charm factory.
We experimentally demonstrate, using qubits encoded in photon polarization, that if two parties share a single reference direction and use locally orthogonal measurements they will always violate a Bell inequality, up to experimental deficiencies. This contrasts with the standard view of Bell inequalities in which the parties need to share a complete reference frame for their measurements. Furthermore, we experimentally demonstrate that as the reference direction degrades the probability of violating a Bell inequality decreases smoothly to (39.7 +/- 0.1) % in the limiting case that the observers do not share a reference direction. This result promises simplified distribution of entanglement between separated parties, with applications in fundamental investigations of quantum physics and tasks such as quantum communication.
The machinery of the human brain -- analog, probabilistic, embodied -- can be characterized computationally, but what machinery confers what computational powers? Any such system can be abstractly cast in terms of two computational components: a finite state machine carrying out computational steps, whether via currents, chemistry, or mechanics; plus a set of allowable memory operations, typically formulated in terms of an information store that can be read from and written to, whether via synaptic change, state transition, or recurrent activity. Probing these mechanisms for their information content, we can capture the difference in computational power that various systems are capable of. Most human cognitive abilities, from perception to action to memory, are shared with other species; we seek to characterize those (few) capabilities that are ubiquitously present among humans and absent from other species. Three realms of formidable constraints -- a) measurable human cognitive abilities, b) measurable allometric anatomic brain characteristics, and c) measurable features of specific automata and formal grammars -- illustrate remarkably sharp restrictions on human abilities, unexpectedly confining human cognition to a specific class of automata (nested stack), which are markedly below Turing machines.
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