Transformations among Pure Multipartite Entangled States via Local Operations Are Almost Never Possible

Local operations assisted by classical communication (LOCC) constitute the free operations in entanglement theory. Hence, the determination of LOCC transformations is crucial for the understanding of entanglement. We characterize here almost all LOCC transformations among pure multipartite multilevel states. Combined with the analogous results for qubit states shown by Gour \emph{et al.} [J. Math. Phys. 58, 092204 (2017)], this gives a characterization of almost all local transformations among multipartite pure states. We show that nontrivial LOCC transformations among generic, fully entangled, pure states are almost never possible. Thus, almost all multipartite states are isolated. They can neither be deterministically obtained from local-unitary-inequivalent (LU-inequivalent) states via local operations, nor can they be deterministically transformed to pure, fully entangled LU-inequivalent states. In order to derive this result, we prove a more general statement, namely, that, generically, a state possesses no nontrivial local symmetry. We discuss further consequences of this result for the characterization of optimal, probabilistic single copy and probabilistic multi-copy LOCC transformations and the characterization of LU-equivalence classes of multipartite pure states.Comment: 13 pages main text + 10 pages appendix, 1 figure; close to published versio

Least squares approximations of measures via geometric condition numbers

For a probability measure on a real separable Hilbert space, we are interested in "volume-based" approximations of the d-dimensional least squares error of it, i.e., least squares error with respect to a best fit d-dimensional affine subspace. Such approximations are given by averaging real-valued multivariate functions which are typically scalings of squared (d+1)-volumes of (d+1)-simplices. Specifically, we show that such averages are comparable to the square of the d-dimensional least squares error of that measure, where the comparison depends on a simple quantitative geometric property of it. This result is a higher dimensional generalization of the elementary fact that the double integral of the squared distances between points is proportional to the variance of measure. We relate our work to two recent algorithms, one for clustering affine subspaces and the other for Monte-Carlo SVD based on volume sampling

Gender Moderation in Gamification: Does One Size Fit All?

Organizations actively seek methods for increasing employee engagement by incorporating game elements in core systems and processes, in an effort to increase their perceived playfulness. However, little is known about the actual impact of these elements on perceived playfulness. This study includes results from three repeated experiments performed during a gamified academic course. The relationships between enjoyment of specific game elements, the way they increase perceived playfulness, and gender moderations of these relations were examined. All three experiments show that badges had a positive relation with perceived playfulness and were more enjoyable to women. Surprisingly, the results showed that when men were the majority of subjects in the group, the relations between the game elements and perceived playfulness were different from when men were a minority. These results provide important insight into what possibly influences perceived playfulness in gamified solutions

Three-Prong Distribution of Massive Narrow QCD Jets

We study the planar-flow distributions of narrow, highly boosted, massive QCD jets. Using the factorization properties of QCD in the collinear limit, we compute the planar-flow jet function from the one-to-three splitting function at tree-level. We derive the leading-log behavior of the jet function analytically. We also compare our semi-analytic jet function with parton-shower predictions using various generators.Comment: 59 pages, 9 figure

PreFair: Privately Generating Justifiably Fair Synthetic Data

When a database is protected by Differential Privacy (DP), its usability is limited in scope. In this scenario, generating a synthetic version of the data that mimics the properties of the private data allows users to perform any operation on the synthetic data, while maintaining the privacy of the original data. Therefore, multiple works have been devoted to devising systems for DP synthetic data generation. However, such systems may preserve or even magnify properties of the data that make it unfair, endering the synthetic data unfit for use. In this work, we present PreFair, a system that allows for DP fair synthetic data generation. PreFair extends the state-of-the-art DP data generation mechanisms by incorporating a causal fairness criterion that ensures fair synthetic data. We adapt the notion of justifiable fairness to fit the synthetic data generation scenario. We further study the problem of generating DP fair synthetic data, showing its intractability and designing algorithms that are optimal under certain assumptions. We also provide an extensive experimental evaluation, showing that PreFair generates synthetic data that is significantly fairer than the data generated by leading DP data generation mechanisms, while remaining faithful to the private data.Comment: 15 pages, 11 figure

Deterministic Entanglement of Assistance and Monogamy Constraints

Certain quantum information tasks require entanglement of assistance, namely a reduction of a tripartite entangled state to a bipartite entangled state via local measurements. We establish that 'concurrence of assistance' (CoA) identifies capabilities and limitations to producing pure bipartite entangled states from pure tripartite entangled states and prove that CoA is an entanglement monotone for $(2\times2\times n)$-dimensional pure states. Moreover, if the CoA for the pure tripartite state is at least as large as the concurrence of the desired pure bipartite state, then the former may be transformed to the latter via local operations and classical communication, and we calculate the maximum probability for this transformation when this condition is not met.Comment: 5 pages, no figure