An Entropic Lens on Stabilizer States

The $n$-qubit stabilizer states are those left invariant by a $2^n$-element subset of the Pauli group. The Clifford group is the group of unitaries which take stabilizer states to stabilizer states; a physically--motivated generating set, the Hadamard, phase, and CNOT gates which comprise the Clifford gates, imposes a graph structure on the set of stabilizers. We explicitly construct these structures, the "reachability graphs," at $n\le5$. When we consider only a subset of the Clifford gates, the reachability graphs separate into multiple, often complicated, connected components. Seeking an understanding of the entropic structure of the stabilizer states, which is ultimately built up by CNOT gate applications on two qubits, we are motivated to consider the restricted subgraphs built from the Hadamard and CNOT gates acting on only two of the $n$ qubits. We show how the two subgraphs already present at two qubits are embedded into more complicated subgraphs at three and four qubits. We argue that no additional types of subgraph appear beyond four qubits, but that the entropic structures within the subgraphs can grow progressively more complicated as the qubit number increases. Starting at four qubits, some of the stabilizer states have entropy vectors which are not allowed by holographic entropy inequalities. We comment on the nature of the transition between holographic and non-holographic states within the stabilizer reachability graphs.Comment: 53 pages, 18 figures, 7 tables. Data files, Mathematica notebook, and Mathematica package available at (https://github.com/WMunizzi/StabilizerStateData

Bounding Entanglement Entropy with Contracted Graphs

Following on our previous work arXiv:2204.07593 and arXiv:2306.01043 studying the orbits of quantum states under Clifford circuits via `reachability graphs', we introduce `contracted graphs' whose vertices represent classes of quantum states with the same entropy vector. These contracted graphs represent the double cosets of the Clifford group, where the left cosets are built from the stabilizer subgroup of the starting state and the right cosets are built from the entropy-preserving operators. We study contracted graphs for stabilizer states, as well as W states and Dicke states, discussing how the diameter of a state's contracted graph constrains the `entropic diversity' of its $2$-qubit Clifford orbit. We derive an upper bound on the number of entropy vectors that can be generated using any $n$-qubit Clifford circuit, for any quantum state. We speculate on the holographic implications for the relative proximity of gravitational duals of states within the same Clifford orbit. Although we concentrate on how entropy evolves under the Clifford group, our double-coset formalism, and thus the contracted graph picture, is extendable to generic gate sets and generic state properties.Comment: 45 pages, 17 figures, 8 table

Clifford Orbits from Cayley Graph Quotients

We describe the structure of the $n$-qubit Clifford group $\mathcal{C}_n$ via Cayley graphs, whose vertices represent group elements and edges represent generators. In order to obtain the action of Clifford gates on a given quantum state, we introduce a quotient procedure. Quotienting the Cayley graph by the stabilizer subgroup of a state gives a reduced graph which depicts the state's Clifford orbit. Using this protocol for $\mathcal{C}_2$, we reproduce and generalize the reachability graphs introduced in arXiv:2204.07593. Since the procedure is state-independent, we extend our study to non-stabilizer states, including the W and Dicke states. Our new construction provides a more precise understanding of state evolution under Clifford circuit action.Comment: 42 pages, 22 figures, 1 Mathematica packag

You\u27re So Gay! : Do Different Forms of Bullying Matter for Adolescent Males?

This study examined effects of adolescent males\u27 perceptions of being bullied because of verbal taunts related to gender nonconformity (i.e., They say I\u27m gay ). Participants included 251 ninth- (n = 77), tenth- (n = 96), and eleventh- (n = 78) grade students in a private, all-male college preparatory school. Participants were divided into two groups based on whether they were bullied by being called gay. Out of the 251 participants, 121 (48%) reported having been bullied and 127 (50%) stated that they had not been bullied during the past year (2% did not report). Of the 121 participants who had been bullied, 32 (26%) reported that they had been bullied because others called them gay (Group 1) and 89 (74%) reported that they had been bullied for other reasons, exclusive of being called gay (Group 2). Consistent with predictions, the boys who were bullied because they were called gay experienced greater psychological distress, greater verbal and physical bullying, and more negative perceptions of their school experiences than boys who were bullied for other reasons. Implications for school-based intervention services for bullying are discussed

Fight Navigator: Exploring the Feasibility of a Retaliatory Violence Prevention Program to Help Youth Manage the Code of the Street

Violence remains the leading cause of injury and death for people between the ages of 15 and 24 and presents a challenge for communities of color. Better understanding of the context surrounding violence is critical in order to develop effective prevention interventions. We conducted a two-phase, qualitative, feasibility study to develop and initially evaluate a retaliatory violence program, Fight Navigator. Focus groups (n=20) and semi-structured case vignette interviews (n=20) were conducted with the target population that were analyzed using a consensual qualitative research approach. Findings suggest that participants were more likely to believe that conflicts could be resolved without violence and were better able to identify specific face-saving techniques to respond to threats after participating in the intervention. Our results demonstrate the value of incorporating youth perspectives into violence prevention efforts and pave the pathway for future research and practice

New Constraints on the Composition of Jupiter from Galileo Measurements and Interior Models

Using the helium abundance measured by Galileo in the atmosphere of Jupiter and interior models reproducing the observed external gravitational field, we derive new constraints on the composition and structure of the planet. We conclude that, except for helium which must be more abundant in the metallic interior than in the molecular envelope, Jupiter could be homogeneous (no core) or could have a central dense core up to 12 Earth masses. The mass fraction of heavy elements is less than 7.5 times the solar value in the metallic envelope and between 1 and 7.2 times solar in the molecular envelope. The total amount of elements other than hydrogen and helium in the planet is between 11 and 45 Earth masses.Comment: 15 pages, 2 figures (1 color

Functionalized Carbon Nanotube Adsorption Interfaces for Electron Transfer Studies of Galactose Oxidase

Modified electrodes featuring specific adsorption platforms able to access the electrochemistry of the copper containing enzyme galactose oxidase (GaOx) were explored, including interfaces featuring nanomaterials such as nanoparticles and carbon nanotubes (CNTs). Electrodes modified with various self-assembled monolayers (SAMs) including those with attached nanoparticles or amide-coupled functionalized CNTs were examined for their ability to effectively immobilize GaOx and study the redox activity related to its copper core. While stable GaOx electrochemistry has been notoriously difficult to achieve at modified electrodes, strategically designed functionalized CNT-based interfaces, cysteamine SAM-modified electrode subsequently amide-coupled to carboxylic acid functionalized single wall CNTs, were significantly more effective with high GaOx surface adsorption along with well-defined, more reversible, stable (≥ 8 days) voltammetry and an average ET rate constant of 0.74 s-1 in spite of increased ET distance - a result attributed to effective electronic coupling at the GaOx active site. Both amperometric and fluorescence assay results suggest embedded GaOx remains active. Fundamental ET properties of GaOx may be relevant to biosensor development targeting galactosemia while the use functionalized CNT platforms for adsorption/electrochemistry of electroactive enzymes/proteins may present an approach for fundamental protein electrochemistry and their future use in both direct and indirect biosensor schemes

Detection of Human Influence on a New, Validated 1500-Year Temperature Reconstruction

Climate records over the last millennium place the twentieth-century warming in a longer historical context. Reconstructions of millennial temperatures show a wide range of variability, raising questions about the reliability of currently available reconstruction techniques and the uniqueness of late-twentieth-century warming. A calibration method is suggested that avoids the loss of low-frequency variance. A new reconstruction using this method shows substantial variability over the last 1500 yr. This record is consistent with independent temperature change estimates from borehole geothermal records, compared over the same spatial and temporal domain. The record is also broadly consistent with other recent reconstructions that attempt to fully recover low-frequency climate variability in their central estimate. High variability in reconstructions does not hamper the detection of greenhouse gas-induced climate change, since a substantial fraction of the variance in these reconstructions from the beginning of the analysis in the late thirteenth century to the end of the records can be attributed to external forcing. Results from a detection and attribution analysis show that greenhouse warming is detectable in all analyzed high-variance reconstructions (with the possible exception of one ending in 1925), and that about a third of the warming in the first half of the twentieth century can be attributed to anthropogenic greenhouse gas emissions. The estimated magnitude of the anthropogenic signal is consistent with most of the warming in the second half of the twentieth century being anthropogenic