Quantum entropy and central limit theorem.

We introduce a framework to study discrete-variable (DV) quantum systems based on qudits. It relies on notions of a mean state (MS), a minimal stabilizer-projection state (MSPS), and a new convolution. Some interesting consequences are: The MS is the closest MSPS to a given state with respect to the relative entropy; the MS is extremal with respect to the von Neumann entropy, demonstrating a "maximal entropy principle in DV systems." We obtain a series of inequalities for quantum entropies and for Fisher information based on convolution, giving a "second law of thermodynamics for quantum convolutions." We show that the convolution of two stabilizer states is a stabilizer state. We establish a central limit theorem, based on iterating the convolution of a zero-mean quantum state, and show this converges to its MS. The rate of convergence is characterized by the "magic gap," which we define in terms of the support of the characteristic function of the state. We elaborate on two examples: the DV beam splitter and the DV amplifier.

Resource theory of quantum scrambling.

Quantum chaos has become a cornerstone of physics through its many applications. One trademark of quantum chaotic systems is the spread of local quantum information, which physicists call scrambling. In this work, we introduce a mathematical definition of scrambling and a resource theory to measure it. We also describe two applications of this theory. First, we use our resource theory to provide a bound on magic, a potential source of quantum computational advantage, which can be efficiently measured in experiment. Second, we also show that scrambling resources bound the success of Yoshida's black hole decoding protocol.

Quantum Fourier analysis.

Quantum Fourier analysis is a subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum symmetry. We establish bounds on the quantum Fourier transform F, as a map between suitably defined [Formula: see text] spaces, leading to an uncertainty principle for relative entropy. We cite several applications of quantum Fourier analysis in subfactor theory, in category theory, and in quantum information. We suggest a topological inequality, and we outline several open problems.

Mathematical picture language program.

We give an overview of our philosophy of pictures in mathematics. We emphasize a bidirectional process between picture language and mathematical concepts: abstraction and simulation. This motivates a program to understand different subjects, using virtual and real mathematical concepts simulated by pictures.

Quon 3D language for quantum information.

We present a 3D topological picture-language for quantum information. Our approach combines charged excitations carried by strings, with topological properties that arise from embedding the strings in the interior of a 3D manifold with boundary. A quon is a composite that acts as a particle. Specifically, a quon is a hemisphere containing a neutral pair of open strings with opposite charge. We interpret multiquons and their transformations in a natural way. We obtain a type of relation, a string-genus "joint relation," involving both a string and the 3D manifold. We use the joint relation to obtain a topological interpretation of the C∗-Hopf algebra relations, which are widely used in tensor networks. We obtain a 3D representation of the controlled NOT (CNOT) gate that is considerably simpler than earlier work, and a 3D topological protocol for teleportation.

Pacifier restriction and exclusive breastfeeding.

OBJECTIVE: We tested the hypothesis that removing pacifiers from routine distribution in our mother-baby unit (MBU) would be associated with greater breastfeeding initiation or exclusivity during the birth hospitalization. METHODS: We retrospectively compared exclusive breastfeeding, breastfeeding plus supplemental formula feeding, and exclusive formula feeding rates for 2249 infants admitted to the MBU at our university teaching hospital during the 5 months before and 8 months after restriction of routine pacifier distribution. Formula supplementation, if not medically indicated, was discouraged per standard practice, but access to formula was not restricted. RESULTS: Of the 2249 infants, 79% were exclusively breastfed from July through November 2010, when pacifiers were routinely distributed. During the 8-month period after pacifier restriction, this proportion decreased significantly to 68% (P < .001). A corresponding increase from 18% to 28% was observed in the number of breastfed infants receiving supplemental formula feeds in the same period (P < .001). During the study period, the proportion of exclusively formula-fed infants increased from 1.8% to 3.4% (P < .05). CONCLUSIONS: Restricting pacifier distribution during the newborn hospitalization without also restricting access to formula was associated with decreased exclusive breastfeeding, increased supplemental formula feeding, and increased exclusive formula feeding. Because high-quality, prospective medical literature addressing pacifier use and breastfeeding does not conclusively show an adverse relationship in women who are motivated to breastfeed, more studies are needed to help determine what effect, if any, pacifiers have on breastfeeding initiation and exclusivity in the immediate newborn period.

Defining the medical home: the Oregon experience.

OBJECTIVE: The patient-centered medical home (PCMH) is emerging as a key strategy to improve health outcomes, reduce total costs, and strengthen primary care, but a myriad of operational measures of the PCMH have emerged. In 2009, the state of Oregon convened a public, legislatively mandated committee charged with developing PCMH measures. We report on the process of, outcomes of, and lessons learned by this committee. METHODS: The Oregon PCMH advisory committee was appointed by the director of the Oregon Department of Human Services and held 7 public meetings between October 2009 and February 2010. The committee engaged a diverse group of Oregon stakeholders, including a variety of practicing primary care physicians. RESULTS: The committee developed a PCMH measurement framework, including 6 core attributes, 15 standards, and 27 individual measures. Key successes of the committee's work were to describe PCMH core attributes and functions in patient-centered language and to achieve consensus among a diverse group of stakeholders. CONCLUSIONS: Oregon's PCMH advisory committee engaged local stakeholders in a process that resulted in a shared PCMH measurement framework and addressed stakeholders' concerns. The state of Oregon now has implemented a PCMH program using the framework developed by the PCMH advisory committee. The Oregon experience demonstrates that a brief public process can be successful in producing meaningful consensus on PCMH roles and functions and advancing PCMH policy.

Carotenemia in Normal-weight Bulimia: A Finding Unrelated to Other Physical Manifestations of the Syndrome.

Carotenemia, well described in eating disorders, is considered a marker for one or another pathophysiologic process occurring during the disease. We studied 17 adolescent, normal-weight women with bulimia, 11 of whom were determined clinically to be candidates for outpatient treatment, and 6 of whom were recommended for hospitalization. The outpatient group had an elevated serum carotene level (mean = 309.0 ± 92.0 µg/dl), whereas the inpatient group had a normal level (mean = 164.8 ± 59.2 µg/dl; t = 3.92, p = .002). Our data do not support the relationship of carotenemia to malnutrition, menstrual dysfunction, or any other factor associated with the manifestations of eating disorders. We suggest that carotenemia may be an indicator of some homeostatic mechanism activated in response to the disorder.