Sampling Quantum Nonlocal Correlations with High Probability

It is well known that quantum correlations for bipartite dichotomic measurements are those of the form (Formula presented.), where the vectors ui and vj are in the unit ball of a real Hilbert space. In this work we study the probability of the nonlocal nature of these correlations as a function of (Formula presented.), where the previous vectors are sampled according to the Haar measure in the unit sphere of (Formula presented.). In particular, we prove the existence of an (Formula presented.) such that if (Formula presented.), (Formula presented.) is nonlocal with probability tending to 1 as (Formula presented.), while for (Formula presented.), (Formula presented.) is local with probability tending to 1 as (Formula presented.).

Tear Secretion Induced by Selective Stimulation of Corneal and Conjunctival Sensory Nerve Fibers

Purpose. To measure the increase in tear secretion evoked by selective stimulation of the different populations of sensory receptors of the cornea and conjunctiva by using moderate and intense mechanical, chemical, and cold stimuli. Methods. Six healthy subjects participated in the study. Tear secretion was measured in both eyes by the Schirmer’s test conducted under control conditions and after stimulation of the center of the cornea and the temporal conjunctiva with a gas esthesiometer. Mechanical stimulation consisted in three pulses of 3 seconds’ duration of warmed air (at 34°C on the eye surface) applied at moderate (170 mL/min) and high (260 mL/min) flow rates. Cold thermal stimulation was made with cooled air that produced a corneal temperature drop of −1°C or −4.5°C. Chemical (acidic) stimulation was performed with a jet of gas containing a mixture of 80% CO2 in air. Results. The basal volume of tear secretion increased significantly (P < 0.05, paired t-test) after stimulation of the cornea with high-flow mechanical stimuli (260 mL/min), intense cooling pulses (−4.5°C), and chemical stimulation (80% CO2). The same stimuli were ineffective when applied to the conjunctiva. Moderate mechanical (170 mL/min) and cold (−1°C) stimulation of the cornea or the conjunctiva did not change significantly the volume of tear secretion. Conclusions. Reflex tear secretion caused by corneal stimulation seems to be chiefly due to activation of corneal polymodal nociceptors, whereas selective excitation of corneal mechanonociceptors or cold receptors appears to be less effective in evoking an augmented lacrimal secretion. Conjunctival receptors stimulated at equivalent levels do not evoke an increased tear secretion.