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Localization of quantum Bernoulli noises (LQBNs) are the family of local annihilation and local creation operators acting on Bernoulli functionals. In this paper, we construct a density operator ρk represented by LQBNs, and define a new quantum entropy S (ρ k) based on LQBNs. Furthermore, we demonstrate that this quantum entropy S (ρ k) also has the basic properties of von Neumann entropy, such as concavity, subadditivity, and nonnegativity. In particular, we obtain the necessary and sufficient condition for S (ρ k) = k. [ABSTRACT FROM AUTHOR]

Background: The mental health and quality of life in children with asthma have attracted widespread attention. This study focused on the evaluation of mental health conditions and their clinical characteristics in Chinese children with asthma.Methods: A total of 261 children with asthma aged 6 to 16 years old and 261 age- and gender-matched children from the general population were recruited to participate in this study from Guizhou Provincial People's Hospital. The parents of all subjects were interviewed using the MINI Kid and were required to finish a clinical characteristics questionnaire. Logistic regression analysis was performed to evaluate risk factors.Results: The prevalence of mental health conditions in the asthma group was significantly higher than that in the control group (26.4% vs 14.6%, P < 0.001). A total of 10 mental health conditions was identified in the asthma group, the most common of which was ADHD (11.5%; 30/261), followed by oppositional defiant disorder (ODD) (10.7%; 28/261), separation anxiety disorder (6.1%; 16/261), social anxiety disorder (3.8%; 10/261), specific phobias (2.3%; 6/261), agoraphobia without panic (1.5%; 4/261), (mild) manic episodes (1.1%; 3/261), major depressive episodes (MDEs) (0.8%; 2/261), movement (tic) disorder (0.8%; 2/261), and dysthymia (0.4%; 1/261). A total of 6 neuropsychiatric conditions was detected in the control group, including ODD (5.7%; 15/261), ADHD (4.6%; 12/261), social anxiety disorder (3.1%; 8/261), seasonal anxiety disorder (SAD) (2.3%; 6/261), specific phobias (1.1%; 3/261), and agoraphobia without panic (0.4%; 1/261). The prevalence rates of ODD, ADHD, and SAD differed significantly between the two groups (P < 0.05). Multiple regression analysis revealed that severe persistent asthma (OR = 3.077, 95% CI 1.286-7.361), poor asthma control (OR = 2.005, 95% CI 1.111-3.619), and having asthma for > 3 years (OR = 2.948, 95% CI 1.580-5.502) were independent risk factors for the presence of mental health conditions in asthmatic children.Conclusions: Children with asthma have a higher rate of mental health conditions than non-asthmatic children. Standardized diagnosis and treatment may help reduce the risk of neuropsychiatric conditions. [ABSTRACT FROM AUTHOR]