Search

We prove a lower bound on the number of copies needed to test the property of a multipartite quantum state being product across some bipartition (i.e. not genuinely multipartite entangled), given the promise that the input state either has this property or is $\epsilon$-far in trace distance from any state with this property. We show that $\Omega(n / \log n)$ copies are required (for fixed $\epsilon \leq \frac{1}{2}$), complementing a previous result that $O(n / \epsilon^2)$ copies are sufficient. Our proof technique proceeds by considering uniformly random ensembles over such states, and showing that the trace distance between these ensembles becomes arbitrarily small for sufficiently large $n$ unless the number of copies is at least $\Omega (n / \log n)$. We discuss implications for testing graph states and computing the generalised geometric measure of entanglement., Comment: 19 pages, 2 figures

Storage, organizing, and decorating are an important part of home design. While one can buy commercial items for many of these tasks, this can be costly, and re-use is more sustainable. An alternative is a "home hack", a functional assembly that can be constructed from existing household items. However, coming up with such hacks requires combining objects to make a physically valid design, which might be difficult to test if they are large, require nailing or screwing something to the wall, or the designer has mobility limitations. In this work, we present a design and visualization system for creating workable functional assemblies, FabHacks, which is based on a solver-aided domain-specific language (S-DSL) FabHaL. By analyzing existing home hacks shared online, we create a design abstraction for connecting household items using predefined types of connections. We provide a UI for FabHaL that can be used to design assemblies that fulfill a given specification. Our system leverages a physics-based solver that takes an assembly design and finds its expected physical configuration. Our validation includes a user study showing that users can create assemblies successfully using our UI and explore a range of designs.

We consider models of quantum computation that involve operations performed on some fixed resourceful quantum state. Examples that fit this paradigm include magic state injection and measurement-based approaches. We introduce a framework that incorporates both of these cases and focus on the role of coherence (or superposition) in this context, as exemplified through the Hadamard gate. We prove that given access to incoherent unitaries (those that are unable to generate superposition from computational basis states, e.g. CNOT, diagonal gates), classical control, computational basis measurements, and any resourceful ancillary state (of arbitrary dimension), it is not possible to implement any coherent unitary (e.g. Hadamard) exactly with non-zero probability. We also consider the approximate case by providing lower bounds for the induced trace distance between the above operations and $n$ Hadamard gates. To demonstrate the stability of this result, this is then extended to a similar no-go result for the case of using $k$ Hadamard gates to exactly implement $n>k$ Hadamard gates., Comment: 31 pages, 3 figures. Latest version includes an improved bound for Lemma 19, added references, and data access statement. Accepted in Quantum

Topological data analysis (TDA) has had enormous success in science and engineering in the past decade. Persistent topological Laplacians (PTLs) overcome some limitations of persistent homology, a key technique in TDA, and provide substantial insight to the behavior of various geometric and topological objects. This work extends PTLs to directed flag complexes, which are an exciting generalization to flag complexes, also known as clique complexes, that arise naturally in many situations. We introduce the directed flag Laplacian and show that the proposed persistent directed flag Laplacian (PDFL) is a distinct way of analyzing these flag complexes. Example calculations are provided to demonstrate the potential of the proposed PDFL in real world applications.

We present a conceptual design of a high-performance camera system with applications to neutrino detectors, deep sea exploration, and glaciology. The design combines ultra-sensitive cameras with a number of well-calibrated light sources enclosed in a pressure vessel. The instrument will be capable of withstanding extreme environments such as those encountered in Antarctica or the deep ocean, and be deployable as a standalone system that can be retrieved for deep-sea exploration or glaciology. The camera system is designed to be replicated and deployed in multiple detectors, requiring only modest modifications from one detector to another. The instrument combines a number of capabilities essential for neutrino detector calibrations, including characterization of the scattering and absorption properties of the optical medium, measurement of geometries via photogrammetry, and detector surveillance. The ability to deploy the instrument at different detector sites also offers opportunities for cross-calibration efforts. We present the conceptual design of the instrument and describe plans to produce a prototype., Comment: 8 pages, 3 figures, Presented at the 38th International Cosmic Ray Conference (ICRC2023)

Parametric CAD models encode entire families of shapes that should, in principle, be easy for designers to explore. However, in practice, parametric CAD models can be difficult to manipulate due to implicit semantic constraints among parameter values. Finding and enforcing these semantic constraints solely from geometry or programmatic shape representations is not possible because these constraints ultimately reflect design intent. They are informed by the designer's experience and semantics in the real world. To address this challenge, we introduce a zero-shot pipeline that leverages pre-trained large language and image model to infer meaningful space of variations for a shape. We then re-parameterize a new constrained parametric CAD program that captures these variations, enabling effortless exploration of the design space along meaningful design axes.

Large Computer-Aided Design (CAD) projects usually require collaboration across many different CAD systems as well as applications that interoperate with them for manufacturing, visualization, or simulation. A fundamental barrier to such collaborations is the ability to refer to parts of the geometry (such as a specific face) robustly under geometric and/or topological changes to the model. Persistent referencing schemes are a fundamental aspect of most CAD tools, but models that are shared across systems cannot generally make use of these internal referencing mechanisms, creating a challenge for collaboration. In this work, we address this issue by developing a novel learning-based algorithm that can automatically find correspondences between two CAD models using the standard representation used for sharing models across CAD systems: the Boundary-Representation (B-rep). Because our method works directly on B-reps it can be generalized across different CAD applications enabling collaboration.

This report summarizes the current status of neutrino physics and the broad and exciting future prospects identified for the Neutrino Frontier as part of the 2021 Snowmass Process., Comment: 49 pages, contribution to: 2021 Snowmass Summer Study. Minor updates

The design of man-made objects is dominated by computer aided design (CAD) tools. Assisting design with data-driven machine learning methods is hampered by lack of labeled data in CAD's native format; the parametric boundary representation (B-Rep). Several data sets of mechanical parts in B-Rep format have recently been released for machine learning research. However, large scale databases are largely unlabeled, and labeled datasets are small. Additionally, task specific label sets are rare, and costly to annotate. This work proposes to leverage unlabeled CAD geometry on supervised learning tasks. We learn a novel, hybrid implicit/explicit surface representation for B-Rep geometry, and show that this pre-training significantly improves few-shot learning performance and also achieves state-of-the-art performance on several existing B-Rep benchmarks.

Neutrinos are the most elusive among the known elementary particles, because of their feeble interactions with ordinary matter. They are also the most mysterious, because of their tiny masses that suggest a novel mass generating mechanism, their unknown Dirac or Majorana nature, and their big quantum mixing leading to large-amplitude flavor oscillations. This Topical Group focuses on neutrino properties that are not directly investigated in other Topical Groups of the Neutrino Frontier: in particular, the absolute value of the neutrino masses, the Dirac or Majorana nature of neutrinos, their electromagnetic properties, their lifetime, and hypothetical exotic properties., Comment: Topical Group Report for NF05 (Neutrino Frontier Topical Group on Neutrino Properties) for Snowmass 2021. 51 pages excluding references

We describe our work on inferring the degrees of freedom between mated parts in mechanical assemblies using deep learning on CAD representations. We train our model using a large dataset of real-world mechanical assemblies consisting of CAD parts and mates joining them together. We present methods for re-defining these mates to make them better reflect the motion of the assembly, as well as narrowing down the possible axes of motion. We also conduct a user study to create a motion-annotated test set with more reliable labels., Comment: Contains 5 pages, 2 figures. Presented at the ICML 2022 Workshop on Machine Learning in Computational Design

The effect of quantum steering arises from the judicious combination of an entangled state with a set of incompatible measurements. Recently, it was shown that this form of quantum correlations can be quantified in terms of a dimension, leading to the notion of genuine high-dimensional steering. While this naturally connects to the dimensionality of entanglement (Schmidt number), we show that this effect also directly connects to a notion of dimension for measurement incompatibility. More generally, we present a general connection between the concepts of steering and measurement incompatibility, when quantified in terms of dimension. From this connection, we propose a novel twist on the problem of simulating quantum correlations. Specifically, we show how the correlations of certain high-dimensional entangled states can be exactly recovered using only shared randomness and lower-dimensional entanglement. Finally, we derive criteria for testing the dimension of measurement incompatibility, and discuss the extension of these ideas to quantum channels., Comment: 10 pages, 2 figures

We investigate the compression of quantum information with respect to a given set $\mathcal{M}$ of high-dimensional measurements. This leads to a notion of simulability, where we demand that the statistics obtained from $\mathcal{M}$ and an arbitrary quantum state $\rho$ are recovered exactly by first compressing $\rho$ into a lower dimensional space, followed by some quantum measurements. A full quantum compression is possible, i.e., leaving only classical information, if and only if the set $\mathcal{M}$ is jointly measurable. Our notion of simulability can thus be seen as a quantification of measurement incompatibility in terms of dimension. After defining these concepts, we provide an illustrative examples involving mutually unbiased basis, and develop a method based on semi-definite programming for constructing simulation models. In turn we analytically construct optimal simulation models for all projective measurements subjected to white noise or losses. Finally, we discuss how our approach connects with other concepts introduced in the context of quantum channels and quantum correlations.

Neutrino telescopes provide strong sensitivity to sterile neutrino oscillations through matter-enhanced oscillation, occurring in the few TeV energy range for eV$^{2}$-scale neutrino mass-squared splittings. Prior searches have focused on $\nu_\mu$ disappearance, which has a particularly strong sensitivity to the mixing angle $\theta_{24}$ via $\nu_\mu\rightarrow\nu_s$ transitions. Nowadays, the $\nu_\mu\rightarrow\nu_e$ and $\nu_\mu\rightarrow\nu_\tau$ appearance channels have been considered less promising at neutrino telescopes, due in part to the much smaller target volume for cascades relative to tracks. This work explores the detectability of these signatures at neutrino telescopes given present constraints on sterile neutrino mixing, and as an example, forecasts the sensitivity of the IceCube Neutrino Observatory to the mixing angles $\theta_{14}$, $\theta_{24}$, and $\theta_{34}$ in the 3+1 sterile neutrino model using the cascade channel with ten years of data. We find that $\nu_\tau$ appearance signatures consistent with the existing IceCube $\nu_\mu$ disappearance best-fit point are discoverable for values of $\theta_{34}$ consistent with world constraints, and that the sterile neutrino parameters favored by the BEST and gallium anomalies are expected to be testable at the 95\% confidence level., Comment: Implemented reviewer comments. Updated format of references, added a new reference, fixed several typos, made several clarifications, updated axis labels on a few plots, added some new discussion, and changed the color of a contour