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01.
arXiv (CS.AI) 2026-06-15

COGNITION: From Evaluation to Defense against Multimodal LLM CAPTCHA Solvers

arXiv:2512.02318v4 Announce Type: replace-cross Abstract: This paper studies how multimodal large language models (MLLMs) undermine the security guarantees of visual CAPTCHA. We identify the attack surface where an adversary can cheaply automate CAPTCHA solving using off-the-shelf models. We evaluate 7 representative MLLMs on 18 real-world CAPTCHA task types, measuring single-shot accuracy, success under limited retries, end-to-end latency, and per-solve cost. We further validate our findings through a supplemental external dataset and an adaptive-attacker setting with session memory, while also analyzing the impact of task-specific prompt engineering and few-shot demonstrations on solver effectiveness. We reveal that MLLMs can reliably solve recognition-oriented and low-interaction CAPTCHA tasks at human-like cost and latency, whereas tasks requiring fine-grained localization, multi-step spatial reasoning, or cross-frame consistency remain significantly harder for current models. By examining the reasoning traces of such MLLMs, we investigate the underlying mechanisms of why models succeed/fail on specific CAPTCHA puzzles and use these insights to derive defense-oriented guidelines for selecting and strengthening CAPTCHA tasks. To validate these principles, we present a proof-of-concept by hardening a vulnerable CAPTCHA type using our guidelines. We demonstrate that incorporating fine-grained localization and implicit counting reduces the success rate of state-of-the-art MLLMs from over 95\% to 0\%, confirming that structural changes can effectively mitigate the threat. We conclude by emphasizing the urgent need for CAPTCHA redesign as MLLM capabilities increasingly threaten existing defenses. Code Availability (https://doi.org/10.5281/zenodo.20406852).

02.
PLOS Medicine 2026-05-26

Requiring code sharing to strengthen transparency and trust in research

Authors:

by Helen Lumbard, Lauren Cadwallader, Devin Soper, on behalf of the PLOS Medicine Staff Editors PLOS Medicine has always championed open science and data transparency. Now, recognizing that code is as essential a research artifact as the data it analyzes, we are strengthening our code sharing policy to further ensure reproducibility and trust in the scientific record. Recognizing that code is as essential a research artifact as the data it analyzes, this Editorial outlines how PLOS Medicine is strengthening its code sharing policy to further ensure reproducibility and trust in the scientific record.

03.
arXiv (CS.AI) 2026-06-17

Decidable By Construction: Design-Time Verification for Trustworthy AI

arXiv:2603.25414v4 Announce Type: replace-cross Abstract: A prevailing assumption in machine learning is that model correctness must be enforced after the fact. We observe that the properties determining whether an AI model is numerically stable, computationally correct, or consistent with a physical domain do not necessarily demand post hoc enforcement. They can be verified at design time, before training begins, at marginal computational cost, with particular relevance to models deployed in high-leverage decision support and scientifically constrained settings. These properties share a specific algebraic structure: they are expressible as constraints over finitely generated abelian groups $\mathbb{Z}^n$, where inference is decidable in polynomial time and the principal type is unique. A framework built on this observation composes three prior results (arXiv:2603.16437, arXiv:2603.17627, arXiv:2603.18104): a dimensional type system carrying arbitrary annotations as persistent codata through model elaboration; a program hypergraph that infers Clifford algebra grade and derives geometric product sparsity from type signatures alone; and an adaptive domain model architecture preserving both invariants through training via forward-mode coeffect analysis and exact posit accumulation. We believe this composition yields a novel information-theoretic result: Hindley-Milner unification over abelian groups computes the maximum a posteriori hypothesis under a computable restriction of Solomonoff's universal prior, placing the framework's type inference on the same formal ground as universal induction. We compare four contemporary approaches to AI reliability and show that each imposes overhead that can compound across deployments, layers, and inference requests. This framework eliminates that overhead by construction.

04.
arXiv (CS.AI) 2026-06-17

ANEForge: Python for direct computation on the Apple Neural Engine

arXiv:2606.17090v1 Announce Type: cross Abstract: ANEForge is a Python package that programs the Apple Neural Engine (ANE), the fixed-function neural accelerator on every recent Apple device, directly and without CoreML. In production the engine is reachable only through CoreML, which treats it as a scheduling option: no configuration requires the ANE, and a model can silently run on the CPU or GPU instead. ANEForge compiles a lazy tensor graph, built from 58 fused operators and 19 native bridge operators, into a single ANE program. The program is dispatched through the same ANE daemon and kernel-driver stack as Apple's internal framework. Beyond inference, the package reaches the engine's native fused attention, streams int8, int4, and sparse weights, keeps decoder and optimizer state resident across steps, and runs the forward pass, backward pass, and optimizer update of training on the engine. A small fused program completes a call in about 90us, near the engine's 70us per-program dispatch floor, and a pretrained ResNet-18 forward runs end-to-end in 0.33ms. ResNet-18, a sentence encoder, and a Vision Transformer run end-to-end against framework references, and a Stable Diffusion U-Net validates its forward pass. ANEForge targets Apple Silicon under macOS 14 and later. Each release is verified against a recorded macOS and ANE-compiler version.

05.
arXiv (CS.LG) 2026-06-19

DF-ExpEnse: Diffusion Filtered Exploration for Sample Efficient Finetuning

arXiv:2606.19656v1 Announce Type: cross Abstract: A natural recipe for intelligent robotic decision-making is initializing from pretrained generative control policies, which have summarized offline experience, and adapting them to self-collected online experience. We present DF-ExpEnse, an exploration technique that improves the quality of online experience collection, thus increasing finetuning sample-efficiency. DF-ExpEnse leverages the multimodal modeling capabilities of the generative control policy to create an expressive and tractably evaluatable candidate set. It then utilizes an ensemble of critics to identify the action that best balances quality with high exploration interest. In fleet settings, DF-ExpEnse further enables cross-agent communication to facilitate collaborative exploration as a group. DF-ExpEnse can be seamlessly integrated with existing strategies that finetune pretrained generative control policies via reinforcement learning. We experimentally validate consistent sample-efficiency benefits through DF-ExpEnse across a variety of manipulation and locomotion tasks, compared to default finetuning and alternative action selection schemes. Project can be found at https://df-expense.github.io.

06.
arXiv (CS.AI) 2026-06-16

FragFuse: Bypassing Access Control of Large Language Model Agents via Memory-Based Query Fragmentation and Fusion

arXiv:2606.15609v1 Announce Type: cross Abstract: Large language model (LLM) agents increasingly rely on long-term memory to support complex task execution, user personalization, and domain adaptation. Meanwhile, emerging access-control mechanisms for LLM agents are being explored to block policy-violating requests and prevent misuse. We reveal a novel attack surface arising from agent memory operations: prohibited content that would trigger access control can be fragmented across interactions, stored in long-term memory in benign-appearing form, and later reconstructed through memory retrieval without appearing explicitly in the final user query. We propose FragFuse, the first attack that enables unprivileged users to bypass agent access control by exploiting this temporal channel introduced by long-term memory. FragFuse operates in three stages: (1) identifying rejection-responsive fragments via black-box adaptive querying with fragment masking; (2) injecting these fragments into memory using marker carrier queries; and (3) retrieving and fusing the stored fragments through a follow-up attack query. Although FragFuse can be instantiated manually for individual agents, we further develop a surrogate-based optimization scheme that tunes fusion instructions and marker designs, enabling automated attack generation without violating the attacker's threat-model assumptions. We evaluate FragFuse across four representative agent settings and task domains, covering three state-of-the-art agent access-control mechanisms. FragFuse achieves an average bypass success rate of 86.3% and an average end-to-end harmful task success rate of 41.1% across all settings, with only 4.4% average task-success degradation compared with configurations without access control. We also show that alternative defenses, including state-of-the-art prompt-injection detectors and perplexity detectors, do not effectively address this attack.

07.
arXiv (CS.AI) 2026-06-16

SMEPilot: Characterizing and Optimizing LLM Inference with Scalable Matrix Extensions

arXiv:2606.16332v1 Announce Type: cross Abstract: Modern CPUs increasingly integrate matrix extensions, such as Arm Scalable Matrix Extension (SME), that provide high-throughput matrix execution within the CPU. For LLM inference, however, these units are not a universal replacement for conventional CPU cores: prefill, decode, attention, and KV-cache operations expose different arithmetic intensities, vector behavior, and layout requirements, while SME units and CPU cores still compete for shared memory bandwidth. This paper studies this mismatch through a roofline-based characterization of SME-enabled CPUs and uses the resulting model to guide operator-level execution choices. We present SMEPilot, an LLM inference engine that selects CPU-only, SME-only, or cooperative SME+CPU execution for each operator shape. SMEPilot partitions matrix work across SME and CPU cores at tile granularity, overlaps SME-suitable matrix stages with CPU-suitable vector stages in attention, and maintains layout state so packed tensor representations are reused rather than repeatedly rebuilt on critical paths. Across Llama-3.2-3B, Qwen3-4B, and Qwen3-30BA3B on phone, PC, and server platforms, SMEPilot improves end-to-end inference performance by up to 3.94$\times$.

08.
arXiv (quant-ph) 2026-06-11

Rolling Stock Planning Using the Quantum Approximate Optimization Algorithm

arXiv:2606.11383v1 Announce Type: new Abstract: Rolling stock planning is a complex optimization problem in railway management that involves assigning physical trains to scheduled trips while minimizing operational costs. In this work, we address a specific instance of this problem featuring 190 trips over two days, subject to constraints such as mandatory maintenance stops. We reformulate the problem as a Maximum-Weight Independent Set (MWIS) problem on a graph where nodes represent feasible train cycles. To handle the computational complexity of the large search space, we propose a hybrid divide-and-conquer algorithm. This approach iteratively selects subgraphs and solves the MWIS problem using various solvers, including exact classical methods and the Quantum Approximate Optimization Algorithm (QAOA). We evaluate the algorithm's performance by comparing these methods and analyzing the scaling with respect to subgraph size, with QAOA assessed through both classical simulation and execution on a quantum device (IQM Emerald). Our results indicate that increasing the subgraph size generally improves solution quality, demonstrating that the hybrid framework can effectively bridge the gap between polynomial-time approximate solvers and exponential-time exact methods.

09.
arXiv (CS.CL) 2026-06-16

Follow the Latent Roadmap: Navigating Revocable Decoding for Diffusion LLMs with Anchor Tokens

Diffusion Large Language Models (dLLMs) offer a promising avenue for parallel generation but face a trade-off between decoding speed and quality. While revocable decoding strategies attempt to mitigate errors by verifying and remasking tokens, they typically operate within a mixed-quality context. This leads to two critical failures: Error Propagation, where new tokens absorb toxic information from erroneous context, and Local Error Reinforcement, where errors mutually reinforce each other to evade detection. To alleviate these challenges, we propose ASRD (Anchor Supervised Revocable Decoding), a training-free framework that operates within the embedding space. ASRD explicitly decouples the decoding context into trusted Anchor Tokens, which are identified via temporal consistency, and uncertain candidates. Leveraging a dynamic Anchor Tokens Cache, we introduce two complementary mechanisms: (1) Anchor-Guided Generation, which injects entropy-weighted anchor signals into masked positions to implicitly rectify attention toward the reliable global skeleton; and (2) Anchor-Perturbed Verification, which applies orthogonal perturbations to uncertain candidate tokens, destabilizing and remasking errors driven by fragile local consensus. Extensive experiments on math and coding benchmarks demonstrate that ASRD outperforms recent remasking baselines, achieving accuracy improvements of up to 6.4\% while accelerating inference throughput by up to 7.2$\times$.

10.
arXiv (quant-ph) 2026-06-24

Topological entanglement and number theory

arXiv:2410.01492v3 Announce Type: replace-cross Abstract: The recent developments in the study of topological multi-boundary entanglement in the context of 3d Chern-Simons theory (with gauge group $G$ and level $k$) suggest a strong interplay between entanglement measures and number theory. The purpose of this note is twofold. First, we introduce a $q$-deformed version of the Witten zeta function using the Chern-Simons theory at level $k$. We analyze the large $k$ limit of this function and show that it converges to an integer multiple of the classical Witten zeta function of $G$, where the integer multiple is precisely the order of the center of the group. This analysis provides an alternative way to compute the classical zeta functions, and we present some examples. Next, we study the quantum state associated with the $S^3$ complement of torus links of type $T_{p,p}$ and show that we can write the Rényi entropies at finite $k$ in terms of $q$-deformed Witten zeta functions. Using our first result, we obtain the $k \to \infty$ limit of the Rényi entropies and find that the entropies converge to finite values, which can be written in terms of the classical Witten zeta functions evaluated at positive integers. Since Witten zeta functions naturally appear in the symplectic volumes of moduli spaces of flat connections on Riemann surfaces, we give a geometric interpretation of the $k \to \infty$ limit of the Rényi and entanglement entropies in terms of these volumes. The results of this paper reveal an intriguing connection between topological entanglement, number-theoretic structures arising from Witten zeta functions, and the geometry of moduli spaces.

11.
arXiv (math.PR) 2026-06-16

Probabilities

arXiv:2601.18853v4 Announce Type: replace-cross Abstract: Probabilities is the English translation of the book Probabilités Tome 1 and Tome 2. The mathematic content is authored by Prof. Jean-Yves Ouvrard. The English version has been done by his eldest son Dr. Xavier Ouvrard. This probability theory book covers not only an introduction to this field, but also advanced concepts based on measure theory. The first part introduces the fundamentals of probability theory across 7 chapters, targeting bachelor level, including event algebras, random variables, independence, conditional probabilities, moments of discrete and continuous random variables, generating functions, and limit theorems. The second part contains 10 chapters and corresponds to master level. Following a brief introduction to measure theory, this part develops more advanced topics: probability measures and their complements, distributions and moments of random variables, modes of convergence, laws of large numbers, conditional expectation, Fourier transforms and characteristic functions, Gaussian random variables, convergence of measures, convergence in distribution, discrete-time stochastic processes, martingales, and Markov chains. The reader's work is greatly facilitated by the inclusion, in every chapter, of numerous exercises, all accompanied by detailed solutions that often provide substantial extensions to the theoretical material.

12.
arXiv (CS.CL) 2026-06-16

MedSynth: Realistic, Synthetic Medical Dialogue-Note Pairs

Physicians spend significant time documenting clinical encounters, a burden that contributes to professional burnout. To address this, robust automation tools for medical documentation are crucial. We introduce MedSynth – a novel dataset of synthetic medical dialogues and notes designed to advance the Dialogue-to-Note (Dial-2-Note) and Note-to-Dialogue (Note-2-Dial) tasks. Informed by an extensive analysis of disease distributions, this dataset includes over 10,000 dialogue-note pairs covering over 2000 ICD-10 codes. We demonstrate that our dataset markedly enhances the performance of models in generating medical notes from dialogues, and dialogues from medical notes. The dataset provides a valuable resource in a field where open-access, privacy-compliant, and diverse training data are scarce. Code is available at https://github.com/ahmadrezarm/MedSynth/tree/main and the dataset is available at https://huggingface.co/datasets/Ahmad0067/MedSynth.

13.
arXiv (CS.CL) 2026-06-24

One Year Later...The Harms Persist, But So Do We!

General-purpose large language models (LLMs) are increasingly used for mental health-related conversations, yet safety safeguards remain inadequate and inconsistent across clinical conditions. This study evaluates six proprietary LLMs across 16 DSM-5 conditions using four adversarial attack variants, introducing an eight-dimension harm taxonomy and a multi-dimensional evaluation framework. Results show that safeguards hold reliably only for suicide and self-harm, while conditions such as eating disorders, substance use disorder, and major depressive disorder exhibit failure rates of up to 100%. We argue that ethical design and deployment of these LLMs demand clearly defined harm categories across clinical conditions and implementation of safeguards accordingly. Until such safeguards are in place, these models pose significant risks to vulnerable populations, making their growing integration into educational settings a particularly concerning.

14.
arXiv (CS.AI) 2026-06-12

Decentralized Autoregressive Generation

arXiv:2601.03184v3 Announce Type: replace-cross Abstract: The decentralization of autoregressive generation has attracted considerable attention in recent years as a solution to scaling bottlenecks. However, despite promising empirical results, this paradigm currently lacks rigorous theoretical justification. In this work, we formally establish the theoretical equivalence between decentralized and centralized training. To achieve this, we adapt the Discrete Flow Matching framework for autoregressive generation, leveraging its inherent properties to demonstrate that global models naturally decompose into independent experts. Finally, we conduct extensive experiments across diverse multimodal benchmarks, empirically validating that decentralized training maintains competitive parity with standard centralized architectures.

15.
bioRxiv (Bioinfo) 2026-06-16

PhenoBIC: operator-free single-cell spatial phenotyping in multiplex imaging data using deep learning of cell staining patterns

Multiplex imaging is a valuable tool for spatially examining tissue microenvironments at the single-cell level to uncover biological and clinical insights. However, most multiplex image analysis workflows currently require manual intervention for cell phenotyping, which slows progress, demands human effort, and yields operator-dependent outputs. Here, we developed PhenoBIC, a pre-trained deep learning model for image classification of the multiplexed biomarker signals in a cell (Biomarker Imprint of a Cell) to classify cell phenotypes. We show that PhenoBIC (F1-score ~0.88) outperforms manual gating (widely used) and other machine learning-based computational approaches for cell marker expression classification. We validated this across multiple biomarkers, tissue sampling strategies (whole biopsies and tissue microarrays), multiplex panels, imaging platforms, and tissue types. We have released our in-house training and validation datasets of ~1.4 million manually curated cell expression ground truth labels. We have also open-sourced PhenoBIC and enabled its community-wide deployment via the QuPath interface.

16.
arXiv (CS.AI) 2026-06-11

Market Design for AI: Beyond the Copyright Binary

arXiv:2606.12260v1 Announce Type: cross Abstract: How can we design a market of human-generated content for use in training AI models that both enables technological progress and preserves individual incentives for high-quality content creation? Existing approaches take polar positions: a "free-for-all" model based on fair use and a "strong intellectual property rights" model. We show that both fail: Free-for-all does not compensate creators, and – by modeling as a static Stackelberg game – strong intellectual property rights also underpower creative incentives. We find this especially true for more innovative creators, a phenomenon we term the "originality penalty." Extending this insight to a dynamic model, we find another market failure undermining AI model performance, even for an initially good model: Such a model induces greater reliance by humans on AI-assisted creation, resulting in homogenized content feeding back into training, which degrades the model performance – a "curse of precision." We further propose a market design with a data intermediary internalizing cross-creator externalities and subsidizing innovative contributions, thereby restoring efficiency.

17.
arXiv (CS.CV) 2026-06-18

Seeing Through Occlusion: Deterministic Arm Kinematic Correction for Robot Teleoperation

Markerless, single-RGB-D-camera motion capture provides a low-cost and non-invasive alternative to conventional marker-based systems for robot teleoperation; however, depth estimation often degrades in the presence of self-occlusion, particularly during upper-limb motion. This paper presents an Arm Kinematic Correction (AKC) method that improves depth estimation by enforcing geometric constraints based on constant arm lengths. The proposed approach reconstructs occluded joint depths by leveraging wrist positions and predefined arm lengths via a deterministic formulation based on the Pythagorean theorem, thereby avoiding the need for complex probabilistic modeling or parameter tuning. Experimental validation against a Vicon reference system demonstrates reliable performance for both static and dynamic joint motions, evaluated using root-mean-square error (RMSE) and Pearson correlation. Furthermore, motion-mapping teleoperation is successfully demonstrated in both simulated and physical robot environments. The results show that AKC enhances robustness and preserves anatomical consistency under long-duration, severe self-occlusion, even when paired with less reliable temporal filters, highlighting its practicality for real-time applications such as robot teleoperation and human-robot interaction.

18.
medRxiv (Medicine) 2026-06-18

Antimicrobial-resistant E. coli in human, animal and environmental reservoirs in rural Bangladeshi households with young children

In low-income countries, ESBL-producing Escherichia coli (ESBL-EC) is frequently detected in humans, animals and household environments, indicating widespread exposure to antimicrobial resistance (AMR). Established risk factors such as antibiotic use do not explain the high community carriage of AMR in all settings; identifying the dominant exposure pathways can inform interventions against AMR. We aimed to investigate (i) animal-human-environment sharing of AMR by assessing associations between the abundance of ESBL-EC in the household environment, domestic animal feces and young children's stool and (ii) household factors associated with ESBL-EC abundance in these reservoirs. We enrolled 112 households from the CRADLE trial in rural Bangladesh. We enumerated ESBL-EC in drinking water, food, child hand rinses, outdoor soil, indoor floor swabs, chicken and cow feces, and stool from children aged 6 months. We recorded indicators of sanitation, animal ownership/management, human and animal antibiotic use, and child exposure behaviors using structured questionnaires and spot checks. The highest prevalence of ESBL-EC was in child stool (95.6%) and animal feces (82.3-96.9%), followed by soil (48.2%) and floors (36.6%); < 10% of food, child hands and drinking water harbored ESBL-EC. The abundance of ESBL-EC in child stool was not associated with its abundance in any sampled matrix; the abundance in chicken but not cow feces showed positive correlations with soil, floors, child hands, and drinking water (correlation coefficients: 0.19-0.39, p-values < 0.05). Higher-quality latrines (improved, pour-flush, with slab) were associated with lower ESBL-EC abundance across matrices; unsafe animal management (animals roaming or spending the night inside the home) was associated with higher abundance. Child antibiotic use and exposure behaviors (soil ingestion, time spent on floor) were not associated with ESBL-EC abundance in child stool. We observed high AMR colonization among young children and domestic animals in rural Bangladesh not explained by traditional fecal-oral exposure pathways. Future studies should explore additional pathways and assess whether sanitation and animal management improvements can reduce AMR.

19.
Nature (Science) 2026-06-10

‘Hidden hero’ peptides guard crops against sudden cold

Authors: Unknown Author

A protein signal remains silent under normal conditions but is activated under cold stress to protect developing pollen. This ‘on-demand’ resilience mechanism could enable the development of ‘climate smart’ crops that maintain high yields in good years and food security under climate stress. A peptide signal ensures that, in cold conditions, developing pollen receives nutrients at the right time.

20.
arXiv (CS.CL) 2026-06-18

VISUALSKILL: Multimodal Skills for Computer-Use Agents

Computer-use agents (CUAs) approach human-level performance on standardised benchmarks but still struggle on long-horizon tasks and unseen software. Existing skill libraries address this with reusable skills, but represent the skill artifact as text only, despite the visual nature of GUI interaction. We propose VISUALSKILL: a hierarchical multimodal skill, tailored to each target application and organised as a central index over per-topic files, which the agent consumes through a load_topic MCP tool that fetches the relevant topic's text and figures on demand. We construct each skill with a two-stage pipeline that combines authored documentation with live-application UI exploration. On two CUA benchmarks, CUA-World and OSExpert-Eval, a Claude Code CLI agent backed by Claude Opus 4.6 reaches an average score of 0.456 with VISUALSKILL, a +15.3 point absolute lift over the no-skill baseline (0.303). Against a matched text-only skill that is generated from the same source content and differs from VISUALSKILL only in modality, VISUALSKILL yields a further +8.3 point absolute gain over the matched text-only skill (0.373 vs. 0.456), providing direct evidence that retaining visual figures in the skill artifact, rather than verbalizing them away, helps the agent both identify UI elements and verify workflow state after each action. Our code is available at https://github.com/XMHZZ2018/VisualSkills.

21.
arXiv (quant-ph) 2026-06-24

Preparing multi-qudit states in a definite-weight subspace

arXiv:2606.24659v1 Announce Type: new Abstract: We formulate a deterministic algorithm for preparing arbitrary multi-qudit states in a definite-weight subspace. By ordering the corresponding computational basis states according to a Gray code for multiset permutations, the state-preparation task is reduced to performing a sequence of controlled 2-qudit Gray rotations. We use this algorithm to prepare exact eigenstates of the SU(3)-invariant Heisenberg Hamiltonian, whose Bethe ansatz is nested. In particular, we describe the preparation of the Bethe states, which are SU(3) highest-weight states, as well as their lower-weight descendants. We also consider the preparation of $SU(d)$ Dicke states and their q-deformations.

22.
arXiv (quant-ph) 2026-06-15

Fourier analysis of quantum neural network with non-linear data embedding

arXiv:2606.14206v1 Announce Type: new Abstract: Fourier analysis has become a crucial tool for understanding the expressivity of Variational Quantum Circuit (VQC) models, as well as an important indicator of barren plateaus (BP). While existing literature has only studied angle-embedded VQCs in a noiseless environment, here we develop the Fourier analysis of VQCs with non-linear data embedding, with particular focus on amplitude embedding, which provides a naturally compact encoding scheme. We first investigate a subtle difference in the domain of input features within amplitude embedding that leads to a distinct expressivity of the zero-frequency Fourier coefficient. By assuming that the ensemble of unitaries generated from the parameter space forms at least a 2-design with respect to the unitary group, we derive, via Weingarten calculus, that the mean of the Fourier coefficients is concentrated at zero, and the variance scales at an exponentially decaying order with respect to the multi-dimensional frequency magnitude. When a noise channel with unitary Kraus operators and probabilities $\{p_k\}$ is taken into account, the variance is further suppressed by a factor $\left(\sum_k p_k^2\right)^{Q}

23.
arXiv (quant-ph) 2026-06-11

Fermions are fundamentally more nonlocal than Bosons

arXiv:2606.12363v1 Announce Type: new Abstract: Bell's theorem shows that entangled quantum particles can exhibit correlations that classical particles cannot reproduce without an additional nonlocal resource, such as communication. In this sense, quantum particles are fundamentally more nonlocal than classical ones, and entanglement becomes unavoidable in physics. Here we prove the analogous result within quantum theory itself: indistinguishable fermions transmitted through a quantum network can generate correlations that distinguishable particles or indistinguishable bosons cannot reproduce without additional communication. In the same sense, fermions are fundamentally more nonlocal than bosons or distinguishable particles, motivating fermionic anticommutation and indistinguishability as unavoidable operational resources. Our result further implies that fermions can strictly surpass all qubit-based protocols for certain distributed computing tasks, demonstrating that a complete understanding of information processing requires going beyond qubits to fermionic information carriers - febits.

24.
arXiv (math.PR) 2026-06-18

Finite free perpetuities

arXiv:2606.19115v1 Announce Type: new Abstract: We introduce and study finite free perpetuities, defined as monic polynomial solutions of degree $n$ to the affine fixed-point equation \[ p(z) = \mathbb{E}\!\left[ A^{n}\,p\!\left(\frac{z-B}{A}\right)\mathbf{1}_{\{A\neq0\}} \right] + \mathbb{E}\!\left[ (z-B)^n\mathbf{1}_{\{A=0\}} \right], \] where $A$ and $B$ are complex-valued random variables with finite moments up to order $n$. Equivalently, if $p(z)=\mathbb{E}[(z-X)^n]$, then $p$ encodes a truncated moment version of the classical perpetuity equation $X\stackrel{d}{=}AX+B$ with $X$ and $(A,B)$ independent. This places finite free perpetuities between classical perpetuities and free-probabilistic fixed-point laws. We prove existence and uniqueness under weak conditions, and we identify a broad class of admissible pairs $(A,B)$ for which the resulting polynomial has only real, nonnegative zeros. Our approach uses finite free additive and multiplicative convolutions together with a probabilistic representation via the $U$-transform. As a motivating example, we exhibit an explicit family of finite free perpetuities expressed in terms of Jacobi polynomials and show that their empirical root distributions converge to a free-beta-prime law. More generally, for admissible sequences of parameters, we prove weak convergence of the empirical root distributions of finite free perpetuities to the law of a free perpetuity characterized by the corresponding free fixed-point equation. This yields a finite-degree polynomial model approximating free perpetuities and clarifies the connection between classical affine recursions, finite free convolutions, and free probability.

25.
arXiv (quant-ph) 2026-06-16

How Many Shots Are Enough for a Quantum Circuit?

arXiv:2606.16965v1 Announce Type: new Abstract: Quantum algorithms require repeated circuit executions, known as shots, to estimate output distributions accurately. Determining the minimal number of shots needed to meet a target accuracy is crucial to reduce costs and resource usage, especially on today's noisy and expensive quantum hardware. In this paper, we address the shot optimisation problem in a black-box setting, where no assumptions are made about the structure of the quantum circuit or the noise model of the backend. We introduce IncrementalExecution, a novel online framework that dynamically determines when to stop executing shots based on the principle of point of diminishing returns: the point at which additional shots no longer significantly alter the empirical distribution of a fixed circuit. The framework supports customisable policies for shot management, enabling flexible trade-offs between execution cost and result fidelity within static execution scenarios. We assess our proposal through an extensive experimental evaluation spanning 33,750 framework configurations across 180 unique static quantum circuit-backend combinations, for a total of 7.3M independent experiments. Unlike prior work that relies on problem-specific knowledge or algorithm-dependent assumptions (e.g., variational or adaptive workflows), our approach is applicable to a large set of static circuits and immediately deployable on current quantum cloud platforms.