Papers

We consider the quickest change detection from 1-bit quantized observations, where the post-change distribution is a parametric model with unknown parameters and the quantization thresholds are jointly chosen with the detection statistic. We propose an Adaptive-Quantization-Threshold CUSUM (AQuTeCUSUM) algorithm, which estimates the post-change parameter online and adaptively selects the quantization threshold to maximize the induced Kullback-Leibler divergence. Under suitable regularity conditions, we characterize the average run length and worst-case average detection delay of the AQuTe-CUSUM procedure, and show that it is asymptotically optimal in first-order as the average run length goes to infinity. Finally, we assess the performance of AQuTe-CUSUM for two distributions, namely the Gaussian and Poisson.

We establish exact second-order coding rate regions at the two corner points of the capacity region of the two-user Gaussian multiple-access channel. For any average error probability $\varepsilon\in(0,1)$, we characterize the $n^{-1/2}$-scale fluctuations of achievable rates around each corner point, proving a converse that matches the previously known achievability bound. The proof first extracts a rectangular subcode that preserves the independence of the two transmitted codewords. The Polyanskiy–Verdú good-code output distribution theorem then yields log-determinant constraints that induce a spectral decomposition of a trimmed codebook into diffuse and exceptional subspaces. An entropic Brascamp–Lieb projection inequality controls the codeword inner product on the diffuse subspace, while variance-inflated Gaussian output distributions handle the low-dimensional exceptional subspace. Combining these two treatments yields the joint Gaussian limit required for the matching second-order converse.

Near maximum distance separable (NMDS) codes of dimension 3 and length n over the finite field with q elements are equivalent to (n,3)-arcs in PG(2,q). For every odd prime power q we construct, by adding five suitable points to a conic of PG(2,q), a family of [q+6,3,q+3] NMDS codes and determine their weight distributions completely; three distinct weight enumerators occur, governed by two explicit quadratic-character conditions on the parameters. For every odd prime power q, no code of our family is monomially equivalent to a code of the recent [q+6,3,q+3] NMDS family of Fan, Wang and Xu, even where the weight enumerators of the two families coincide: the separating invariant is a triple of geometric data attached to the underlying arc. Extending the configuration by a sixth point on a distinguished external line, we further obtain [q+7,3,q+4] NMDS codes, together with their weight distributions, for every odd prime power q >= 11 (admissible parameters exist for no q <= 9); the existence proof combines exact and Weil-type character sum estimates with a finite computer verification. Our proofs are purely geometric and rest on a simple counting identity for the trisecant lines of a point set obtained by extending a conic. All the codes constructed are optimal locally recoverable codes with locality 2.

In this paper, we provide estimators for quantum Rényi and Tsallis entropies with nearly optimal sample complexity. Specifically, for order $\alpha$, dimension $d$, and additive error $\varepsilon$, 1. For $0 < \alpha < 1$, the sample complexity is $O(d^{1+1/\alpha}/\varepsilon^{1/\alpha} + d^{1/\alpha-1}/\varepsilon^{2})$ for Rényi entropy and $O(d^{1+1/\alpha}/\varepsilon^{1/\alpha} + d^{2-2\alpha}/\varepsilon^2)$ for Tsallis entropy. In particular, for $0 < \alpha \leq 1/2$, the sample complexity for both entropies is $O(d^{1+1/\alpha}/\varepsilon^{1/\alpha})$. 2. For non-integer $\alpha > 1$, the sample complexity is $O(d^2/\varepsilon^{1/\alpha} + d^{1-1/\alpha}/\varepsilon^2)$ for Rényi entropy. Our upper bounds improve the quantum Rényi entropy estimators due to Acharya, Issa, Shende, and Wagner (2017) and the quantum Tsallis entropy estimators due to Chen, Liu, and Wang (2026), and match the lower bounds recently established by Wang (2026).

We study $n$-party fault-tolerant consensus against general (non-threshold) adversaries. We describe an infinite family $Z_\mathsf{proj}^{n,d}$ of $Q^d$-satisfying $n$-party adversary structures based on finite projective geometry which cause error-free $R$-round protocols for interactive consistency on $L$-bit inputs to require $\Omega(Ln^{2+1/d})$ bits of expected communication. Likewise, $Z_\mathsf{proj}^{n,d}$ causes error-free byzantine agreement and broadcast to cost $\Omega(Ln^{1+1/d})$ bits. In every case, the lower bound is $\Omega(L_{\mathsf{out}} \cdot n^{1+1/d})$ bits, where $L_{\mathsf{out}}$ is the output length. The family $Z_\mathsf{proj}^{n,d}$ also causes reliable broadcast and byzantine agreement to cost $\Omega(Ln^{1+1/d})$ bits of expected communication in asynchronous networks. Moreover, there exists a related family $Z_\mathsf{2\textsf-proj}^{n,d}$ of $Q^d$-satisfying adversary structures that make core set agreement cost $\Omega(Ln^{2+1/d})$ bits. These asynchronous lower bounds hold against send-omission adversaries, even if the protocol uses cryptography. Their basis is that if a quorum of non-faulty parties agree on an output and terminate, then the messages they sent before terminating must suffice for the parties outside the quorum to also terminate with the same output. Surprisingly, if we do not require the parties to terminate (stop sending messages) after they output, then these bounds no longer hold. We show this by designing a non-terminating omission-tolerant reliable broadcast protocol that can for any parameter $\delta > 1$ be tuned to cost $(1 + \frac{1}{\delta - 1})Ln + O(\delta n^2\log(\delta n))$ bits, which is of independent interest. Lastly, we show how to get termination with $O(Ln^{1+1/d} + n^2\log n)$ bits (assuming the $Q^d$ condition), and thus prove our asynchronous lower bounds tight.

Let $W_N$ be an exact length-$N$ block from a strictly positive i.i.d. source $\mathbf p$ on a fixed finite alphabet. We prove that the canonical T-complexity $c_T$ satisfies \[ \frac{c_T(W_N)}{e^{-\gamma}h(\mathbf p) N/\log N}\longrightarrow1 \] in probability and in $L^r$ for every fixed $1\le r<\infty$, where $h(\mathbf p)$ is the source entropy in nats and $\gamma$ is the Euler-Mascheroni constant. The proof combines an exact length budget for canonical recovery, a critical-scale $E_1$ estimate for an ideal backward chain, and an exact finite-block boundary representation. An exact Doob-transform identity expresses the finite-boundary law relative to the ideal law conditioned at each step to avoid the current history-dependent successor codeword. A history-uniform renewal estimate then makes the telescoping endpoint density uniformly asymptotic to one, so no one-step approximation errors accumulate.

We study the problem of guessing a realization of an i.i.d. random sequence given element-wise correlated side-information. We use type-counting to provide estimates of the tail probabilities of the number of guesses for the case without side-information, which was shown earlier through large-deviation techniques. We then extend the same counting argument to the conditional setting, obtaining new explicit expressions for the corresponding guesswork exponents as divergences involving conditional tilted distributions. Finally, we provide an application of these exponents to brute-force password guessing with side-information.

Chernoff information is a fundamental divergence measure characterizing the optimal error exponent in Bayesian binary hypothesis testing, with applications in information fusion, time-series analysis, and statistical learning theory. However, closed-form expressions exist only for simple parametric families, and nonparametric estimation remains difficult because the quantity is defined as an optimization of the unnormalized Rényi divergence over its order. We reformulate this optimization via a derivative condition, whose zero locates the optimal mixture parameter, and estimate the derivative directly using a $k$-nearest-neighbor method. We prove the $L_2$-consistency of the derivative estimator under mild regularity conditions on the densities and their domain. Coupled with a bisection procedure that locates the optimal parameter up to arbitrary precision, this yields an estimator for Chernoff information.

Intelligent channel state information (CSI) feedback is essential for realizing the high capacity and spectral efficiency goals of future 6G systems, yet existing deep learning solutions face a trade-off between model generalization and scenario-specific performance. Large neural networks generalize well but incur high computational and tuning costs, while small models excel in particular environments but require repetitive costly end-to-end training for each base station (BS). To address these challenges, we introduce a model repository-based deployment framework in which a centralized AI data center maintains a catalog of scene-specific CSI models. The repository is enhanced with a Learnware-based framework, where each model is associated with a specification including semantic part (network architecture parameters) and statistical part (codeboo-fingerprint embeddings of training-data distributions). A BS submits only its local statistical specifications to retrieve the most relevant pre-trained model, enhancing data privacy by avoiding raw CSI transmission and drastically reducing retrieval latency and communication overhead. We further develop a data-driven search strategy that matches codebook fingerprints to model performance, achieving over 90% selection accuracy. In simulations, our scheme yields 18.8% and 57.7% performance improvements over the General Model in LOS and NLOS scenarios, respectively while reducing local fine-tuning by up to 1000 samples and 100 epochs. This Learnware-based approach minimizes redundant training, maximizes model reuse, and supports rapid,privacy-enhancing deployment of CSI feedback models.

The quantum approximate optimization algorithm (QAOA) targets NP-hard maximum-likelihood (ML) detection in multiple-input multiple-output (MIMO) systems. Existing $M$-ary quadrature amplitude modulation (M-QAM) detectors design angles by expected Ising energy: online per instance, warm-started, or ramped, while train-once designs remain B/QPSK-only or block-local, leaving M-QAM without a size-scalable benchmark. Their infinite-size spin-glass theory assumes independent disorder, matching the retained covariances at B/QPSK but not M-QAM's correlated couplings and fields. We develop a correlated infinite-size multi-species spin-glass framework whose covariance-matched evaluators make that energy an offline objective with a size-scalable benchmark. In addition, the ML rate, the exponential rate of sampling the ML string, is for the first time exploited for QAOA angle design in MIMO detection. The energy evaluator is $q$-free at $O(p\,4^p)$ cost while the ML rate transfers angles from a fixed $q_{\rm ref}$-qubit reference. Tests reach 4096-QAM, 128 antennas, $p=30$ and per-symbol SNR 0-45 dB. In simulations, ML rates fall as a power law $r_0\,p^{-\alpha}$, with larger exponents for the sampling design, which tracks exact ML at $5\times5$ 16-QAM (0-20 dB) and $3\times3$ 64-QAM (8-28 dB) while its bit-error rate (BER) advantage widens with SNR to two orders of magnitude. The approach points toward near-optimum decoding on deeper noiseless fault-tolerant quantum (FTQ) circuits.

Impulsive noise (IN), characterized by its high power and non-Gaussian distribution, poses a critical challenge in modern orthogonal frequency-division multiplexing (OFDM) systems, driven by the proliferation of electronic devices. Current IN mitigation techniques rely heavily on time-domain processing. These methods are applied before the discrete Fourier transform (DFT), introducing additional complexity, failing to align with OFDM's inherent frequency-domain processing flow, and risking the destruction of subcarrier orthogonality due to imperfect IN subtraction. To address these limitations, we propose a frequency-domain, block-based framework for mitigating IN. The statistical representation of IN in the frequency domain is first derived using a transformed Gaussian mixture model. Based on this model, we develop an optimal receiver that leverages perfect noise state information (NSI), thereby identifying scenarios in which NSI is critical. We then propose an unsupervised block-based expectation-maximization (EM) framework for NSI estimation and develop three variants for evaluation. These include a simple symbol-by-symbol variance-updated EM, a sequence-based transition-updated EM, and a MAP-based EM that exploits a sparsity-promoting prior to automatically prune the number of states. Our frequency-domain design operates after the DFT, seamlessly integrates with the OFDM processing chain, preserves subcarrier orthogonality, and leverages the known IN block structure to achieve substantial performance gains without the immense complexity of time-domain impulse reconstruction.

This paper addresses the problem of efficiently estimating aggregate human preferences by dynamically adapting questions based on respondents'answers. To this end, we formulate and address two sub-problems: preference estimation and question design. First, regarding preference estimation, we model respondents' preferences and estimate them using Bayesian estimation, employing a particle filter as a computationally efficient approximation. The main theoretical contribution to this sub-problem is to analyze the preference estimation error using an information-theoretic approach, deriving a theoretical lower bound for the error. Second, regarding question design, we formulate the design problem as an Expected Information Gain maximization problem and employ an epsilon-greedy strategy to solve the problem in a computationally efficient way. We theoretically analyze the search efficiency of the approach, demonstrating that it achieves higher efficiency than a random search. Finally, we verify the effectiveness of the proposed method through numerical simulations.

Channel knowledge map (CKM) is a promising technology for environment-aware sixth-generation (6G) wireless networks. However, existing CKMs are tightly coupled with wireless devices and downstream tasks, which limit their scalability and reusability in wireless networks. To address these limitations, this article proposes the concept of universal CKM (uCKM) as a foundational wireless environment prior, which aims to enable cross-device and cross-task channel knowledge transfer for environment-aware wireless networks. We first revisit the representative CKMs and discuss their limitations. Then, the uCKM-enabled new paradigm for environment-aware wireless networks is introduced, and its benefits are highlighted from the perspectives of uCKM construction and utilization phases, for which we propose the visions of “All for uCKM” and “uCKM for All”, i.e., the data acquired by all devices and tasks should contribute to the construction of uCKM, while the constructed uCKM, in turn, can be utilized to support all devices and tasks. Subsequently, we discuss the main challenges of uCKM and propose potential solutions. Last, we provide simulation results to demonstrate the feasibility and performance gains brought by uCKM and outline future research directions.

We develop a column-wise chi-squared geometry for discrete memoryless channels (DMCs) yielding tight, logarithm-free bounds on mutual information, channel dispersion, and finite-blocklength coding rates without evaluating logarithms of the channel matrix. The key parameter is~\(\eta\)—the worst-case relative deviation of a transition probability from its output marginal, which is small precisely when the channel is close to the fully noisy channel $t_{ij}=s_j$. We prove three main results: (1) a third-order ratio expansion showing \(I(X;Y)/\chi^2(X;Y)\to 1/2\) as \(\eta\to 0\) with an \(O(\eta)\) skewness correction; (2) a two-sided dispersion equivalence bounding \(V(X;Y)\) above and below by \(\chi^2(X;Y)\) with explicit constants \(c_{\pm}(\eta)\to 1\); and (3) a certified robust design rate \(R_{\mathrm{cert}}(n,\varepsilon)\) with total certification gap \(O(\eta)+O(\eta/\sqrt{n})+O(\log n/n)\). The certified bounds on \(I\) and \(V\) require only addition, multiplication, division, and square roots; the final rate also uses \(Q^{-1}(\varepsilon)\).

We study finite-sample parameter estimation in logistic regression with Gaussian design, where the goal is to estimate $\mathbf{\theta}^*\in \mathbb{R}^d$ with $R=\|\mathbf{\theta}^*\|_2\ge 1$ from i.i.d. samples $\{(\mathbf{x}_i,y_i)\}_{i=1}^n,$ $\mathbf{x}_i \sim N(0,\mathbf{I}_d)$, $y_i\mid \mathbf{x}_i \sim \mathrm{Bernoulli}((1+\exp(-\mathbf{x}_i^\top \mathbf{\theta}^*))^{-1})$. In this paper, we provide the first minimax optimal estimator, and improve on the best known finite-sample error rate for the maximum likelihood estimator (MLE). These two accomplishments are due to a minimax optimal estimator for the parameter norm $R$. First, we establish the minimax lower bound $\Omega(\sqrt{R^3/n})$ for norm estimation. We then improve the best known norm estimation error rate of the MLE, i.e., $O(\sqrt{R^3d/n})$ from Chardon, Lerasle and Mourtada (2024), to $\tilde{O}(\sqrt{R^3/n}+R^2d/n)$. The additional term, $R^2d/n$, appears to be the intrinsic bias of the MLE, as evidenced by the high-dimensional asymptotic theory of Zhao, Sur and Candes (2022) and numerical examples. We show that, however, this additional term is not information-theoretically necessary. To this end, we construct an efficient debiased norm estimator that achieves the error rate $O(\sqrt{R^3/n})$ and is therefore minimax optimal. Combining this with the optimal direction estimator given by the MLE, we establish the minimax optimal rate $\Theta(\sqrt{Rd/n}+\sqrt{R^3/n})$ for estimating $\mathbf{\theta}^*$, as well as the improved finite-sample error rate $\tilde{O}(\sqrt{Rd/n}+\sqrt{R^3/n}+R^2d/n)$ for the MLE. Numerical experiments demonstrate that the proposed minimax optimal estimators outperform the MLE.

It is a major challenge in quantum fault-tolerance to obtain low-overhead protocols for performing non-Clifford gates. In this vein, we construct quantum codes with low-weight stabilizers that support transversal (i.e. low-depth) implementations of the non-Clifford $C^{r-1}Z$ gate, for every constant $r\geq 3$. In particular, we obtain length-$n$ quantum LDPC codes (with constant-weight stabilizers) of polynomial distance $d\geq n^{(1-\epsilon)/r}$ supporting transversal $C^{r-1}Z$ gates on a close-to-linear number $k\geq n^{1-\epsilon}$ of disjoint tuples of logical qubits, for arbitrarily small $\epsilon>0$. Our construction is the first with constant-weight stabilizers that obtains $dk\gg n$, and as a consequence achieves arbitrarily small magic state overhead exponent $\gamma=\log(n/k)/\log(d)>0$. Comparable prior constructions instead required at least polylogarithmic stabilizer weight. We also show how to obtain linearly many $k=\Omega(n)$ logical $C^{r-1}Z$ gates, though with stabilizer weight and physical circuit depth $n^\epsilon$. We show that our transversal gates also support addressing (i.e. targeting) of specific logical qubits. To obtain our codes, we develop a general transformation based on cup products that maps classical codes satisfying a multiplication property to quantum codes with transversal $C^{r-1}Z$. We apply this transformation to a new family of classical Tanner codes that we construct from punctured tensor products of algebraic codes.

Adaptive coders are commonly primed with training data, turned into context tables or shipped dictionaries. The training data generally do not match the source being encoded, and the coder must decide how much to trust them. We make that trust a design variable: a Krichevsky–Trofimov (KT) estimator over an $m$-ary alphabet whose training counts are scaled by $\xi\in[0,1]$. For a training sequence of length $\ell$ at Kullback–Leibler divergence $D$ nats per symbol from the message source, the redundancy-minimizing weight is $\xi^*=d/(2\ell D+d)$, $d=m-1$. The effective training length $\xi^*\ell$ follows a harmonic law: any mismatch caps the usable training information at $d/(2D)$ symbols, however much was collected. Three implementable selectors supply the unknown $D$: offline, from the spread of the training set; by a plug-in loop, from the decoded prefix; and by a twice-universal mixture, with no estimation at all. On the ten English texts of the Calgary and Canterbury corpora, weighting removes up to $22.7\%$ of the redundancy of the classical KT code, the $\xi=0$ endpoint, and beats both endpoints on every file. An open-source implementation is provided.

Multipartite entanglement remains a challenging and not fully understood aspect of quantum information. Monogamy-of-Entanglement (MoE) games have been highly effective for studying limitations on the usefulness of entanglement imposed by monogamy constraints. To better reveal the extent to which multipartite entanglement can be useful, we introduce a class of quantum guessing games, termed One-at-a-Time Guessing (OTG) games. In these games, quantum players individually guess the outcomes of random measurements performed by a referee on a pre-shared entangled state. Unlike MoE games, OTG games select players individually at random according to a specified probability distribution, thereby probing each player's correlation with the referee. We show that, despite monogamy constraints, players sharing certain entangled states can moderately outperform those relying only on classical uncertainty. This advantage arises even in simple OTG games involving only Pauli measurements on qubits, where optimal entanglement increases the winning probability by at least 4%. This contrasts with MoE games, where shared entanglement has been shown in several settings to provide only limited (if any) advantage over classical strategies. We further establish a majorization property: the value of an OTG game respects the majorization ordering of the player-selection probability distribution. We also analyze in detail a two-player OTG game in which the referee measures one of the three Pauli observables on a qubit, and show that it is optimally played using a specific parameterized family of three-qubit $W$-like states. These results suggest that OTG games provide a useful framework for investigating the usefulness of multipartite entanglement in multiparty quantum correlations.

Active inference selects actions by minimising an expected free energy functional over predicted futures. However, adding an expectation over yet-unobserved outcomes means the free energy functional no longer has a Kullback-Leibler structure, which hinders message passing treatments of inference procedures. We propose an alternative formulation based on a Bethe free energy functional, fully supporting inference by message passing. The epistemic drive is maintained by imposing an information constraint, next to normalisation, marginalisation and form constraints, insisting that the mutual information between future observations, states and parameters given actions must be at least as large as the entropy of the goal prior. For a specific value of the corresponding Karush-Kuhn-Tucker multiplier, the stationary point of this constrained Bethe Lagrangian recovers the expected free energy solution. We show that, as the information demand is varied, the solved multiplier moves through its inactive, interior, and saturated regimes. In the inactive regime the agent's epistemic drive switches off entirely, while in the saturated regime it is maximal. We compare the performance of the constrained Bethe agent on three tasks against EFE and Q-MDP.

Quantum $(r,\delta)$-locally recoverable codes are quantum error-correcting codes capable of correcting $\delta-1$ qudit erasures within one subset of qudits of cardinality at most $r+\delta-1$. In this paper, we introduce the more general framework of entanglement-assisted quantum $(r,\delta)$-locally recoverable codes, assuming that the local recovery operation is assisted by receiver-held qudits that remain unaffected by erasures. We establish necessary and sufficient conditions for these codes to satisfy this property. For codes derived from Hermitian or Euclidean constructions, we establish connections between entanglement-assisted quantum and classical notions of $(r,\delta)$-local recoverability, and derive a Singleton-like bound. Furthermore, we construct optimal pure entan\-gle\-ment-assisted quantum $(r,\delta)$-locally recoverable codes from several families of classical codes, including bivariate $J$-affine variety codes, BCH codes, and homothetic-BCH codes.

A bounded agent may obtain information for a decision from its own past, from peers, or from both sources. Retaining task-relevant history can reduce later communication, while a peer message can supply what memory lacks. Under limits on both resources, how should an agent allocate its information budget? Given a fixed task and decision rule, the memory and message rate pairs attaining a performance threshold form an achievable region under specified rules for using history and peer observations. We call its efficient boundary the remembering–signaling frontier. Across conditions where history permits the same maximum reduction in task loss, we hypothesize that a bounded agent will need less peer communication when it obtains a larger loss reduction from history. In preliminary referential games, target repetition coincided with shorter successful messages, while predictability from a hidden cyclic rule did not shorten them. Experiments varying memory and message rates can estimate the frontier and test this prediction across cooperative tasks.

We show how to compile an arbitrary classical circuit into a fault-tolerant circuit, which performs the desired computation even when an almost-linear number of bits are adversarially chosen and corrupted in each timestep. Using a variant of this fault-tolerance scheme that only detects (rather than corrects) corruptions, we give a new construction of probabilistically checkable proofs (PCPs) for NP with polylogarithmic query complexity. This PCP construction from fault-tolerance presents a promising candidate for quantization by the work of Anshu, Breuckmann, and Nguyen (STOC'24), who provided a roadmap for constructing quantum PCPs via fault-tolerance.

Time-critical interactive systems increasingly require ultra-low-latency device identification for multiple users, yet prevailing approaches such as passwords, QR codes, and RFID/NFC are constrained by human input, frame-based sensing, or near-contact range. This paper presents ECO-ID, an event-camera-based optical system for multi-user, ultra-low-latency identification over visible light communication (VLC). Leveraging microsecond-resolution, asynchronous observations of brightness transitions, ECO-ID employs a spatiotemporal coding design: disjoint LED subsets provide spatial separation among users, while user-specific timing delays encode identities without inter-user synchronization. The optical channel and event-driven sensing reduce full-scene capture relative to frame cameras and limit the RF attack surface, while enabling rapid token verification with freshness and replay protection. We implement a prototype and demonstrate that ECO-ID can practically achieve approximately 99.8% localization and 98.7% identification with 0.64 ms mean latency, while theoretically supporting identification at the scale of tens of concurrent users. Overall, ECO-ID provides a fast, privacy-conscious, and security-aware alternative for scalable multi-user identification in time-critical interactive environments.

We prove a fault-tolerance theorem for quantum computation against adversarial noise. For every quantum circuit on $\bar{N}$ logical qudits of depth $\bar{T}$, we construct a fault-tolerant circuit on $N=\text{poly}(\bar{N})$ physical qudits of depth $\bar{T}\cdot\bar{N}^{o(1)}$, which is robust against an adversary who may arbitrarily choose and corrupt an almost-linear number $N^{1-o(1)}$ of physical qudits at each time step. This robustness significantly improves upon prior fault-tolerance theorems, which assumed corruptions were either local and stochastic, or else only act on a polynomially vanishing fraction of qudits. Our fault-tolerance scheme addresses a key bottleneck towards constructing quantum PCPs via the circuit-to-Hamiltonian mapping of Anshu, Breuckmann, and Nguyen (STOC'24). More fundamentally, our result demonstrates that fault-tolerant quantum computation remains possible under noise models that are global, worst-case, and non-Markovian over the full duration of the computation, directly countering concerns that correlated noise could fundamentally undermine quantum fault tolerance. Our construction is based on a new family of subsystem product codes we develop, which have large dimension and distance along with low-weight parity-checks, and which support transversal non-Clifford gates. We show how to perform single-shot fault-tolerant error correction on these codes using a Floquet-like procedure based on the local testability of classical tensor codes. We then obtain a universal fault-tolerance scheme using repeated code switching in a hypercubic qudit architecture. Finally, we recursively compose our scheme with itself to reduce an initially exponential qudit dimension down to a constant.

Peer prediction seeks to incentivize agents to truthfully report an observed signal by rewarding joint sets of reports without observing a ground truth. Following the generalization of information-theoretic mutual information introduced in Kong and Schoenebeck (2019), we call a function of a joint distribution over signals a mutual information when it is non-negative and disincentivizes garbling reports for all information structures. An unbiased estimator for a mutual information takes some number of samples from the distribution and returns rewards for both agents, such that the expected reward is equal to the mutual information. We seek to characterize the set of mutual informations with unbiased estimators for a given number of samples. We show that for three or fewer sampled report pairs, the only mutual information with an unbiased estimator is trivially zero, and for four or five samples with a binary report space, the Determinant Mutual Information (DMI) of Kong (2024) is the unique mutual information (up to a scalar multiple). We further show that DMI ceases to be unique at six samples. We provide an improved estimator of DMI for any given number of samples and characterize its convergence rate. We also examine mutual information estimators that accept a randomized number of samples. First, we show that mutual information estimators on an ex-ante bounded number of samples (termed "stop-short estimators") can achieve a lower variance than an equivalent fixed-sample estimator (for DMI). Second, we introduce the class of scoring-rule-based mutual informations and identify in this family a mutual information that can be estimated with under three samples in expectation.

This paper develops fluid antenna array (FAA)-inspired subarray sizing and transmit-power design for a two-hop amplify-and-forward (AF) unmanned aerial vehicle (UAV) relay using progressively contracting user-location posteriors. A contiguous reconfigurable subarray is shared by first-hop reception and second-hop forwarding, such that its active size jointly determines the receive gain, forwarding gain, and beamwidth. By adaptively controlling the effective aperture, the proposed design exploits geometric reconfigurability to balance array gain against pointing robustness under location uncertainty. Projecting the position covariance onto the array direction yields a closed-form direction-limited size inversely proportional to directional uncertainty. Posterior samples are propagated through the two-hop rate model, and the subarray size and transmit power are then selected to minimize UAV power subject to a worst-user lower-tail rate requirement and hardware power limits. The planned configuration is further audited over instantaneous two-hop Rician channels at the true user positions. At t = 8 s, the proposed design saves 3.17 dB over full-array narrow-beam transmission on paired feasible geometries and achieves 60.0% service success at a 0.15-W budget, compared with 43.2% for a fixed eight-element subarray.

We construct two families of non-binary entanglement assisted (EA) quasi-cyclic (QC) quantum low-density parity-check (QLDPC) codes over arbitrary finite fields, each possessing a precisely determined code rate. The first family is derived from a pair of non-binary classical QC-LDPC codes, designed such that the unassisted portion of the overall Tanner graph of the resulting EA-QC-QLDPC code is free of 4-cycles. The second family, on the other hand, is constructed from a single non-binary classical QC-LDPC code whose Tanner graph itself is 4-cycle-free. In developing the codes belonging to the first family, we employ a single Bell pair to establish entanglement between the transmitter and the receiver, thereby minimizing the required entanglement resources. Furthermore, these constructions demonstrate that careful graph-based design can effectively balance error-correction performance with entanglement consumption, providing a practical approach for realizing efficient non-binary EA-QC-QLDPC codes.

Lossy compression is conventionally driven by a task-agnostic distortion (e.g., MSE or MS-SSIM), yet in many emerging applications the receiver cares not about uniform fidelity but about a downstream task whose relevant content varies across the signal and evolves over time. We formulate task-aware compression as a weighted rate-distortion problem, in which a single codec is driven by a separable, per-component weighted distortion whose weights encode task importance and may depend on the source. We introduce task consistency, i.e., that minimizing the weighted distortion also minimizes the true task loss, and characterize when it holds: for linear tasks, the task loss admits a weighted-MSE form with signal-independent weights under suitable cross-term conditions, while for nonlinear tasks, an integrated-gradients analysis motivates separable task-aware weights. We show how task symmetry and irrelevance further constrain the admissible weights. Guided by this theory, we realize the weight-conditioned code in a single learned Vision Transformer (ViT) codec whose token-level attention natively consumes a per-component importance vector, so one fixed backbone is re-targeted at runtime, from universal (task-agnostic) to task-specialized operation, purely by swapping the injected weights, without retraining, while producing a single human-viewable reconstruction steered to the active task. On downstream face-analysis tasks, a single model reaches 91.4% accuracy at 0.034 bpp on a localized task, within 1.9% of a task-specific codec (93.3%) and well above a universal codec (76.9%). Such task-adaptive compression suits bandwidth-constrained perception systems, e.g., in Physical AI, where the active task drifts and per-task retraining is infeasible.

We propose two-level decorrelated coding (TLDC), a novel coded modulation scheme for the $D_4$ lattice that combines Voronoi shaping with a two-stage decoding process to achieve lattice shaping and coding gains at low complexity. In TLDC, the decoded values of the first level allow the several random variables in the second level to become approximately uncorrelated. The resulting independence of the variables in level two permits decoding in parallel or consolidation into a larger codeword, enhancing performance. TLDC supports flexible choice of FEC within each level. Using bit-interleaved or multi-level polar codes at each level, the resulting coded modulation scheme exhibits a gain of up to 0.5 dB over analogous state-of-the-art coded modulation schemes on a 16-QAM under AWGN at block sizes of 64 and 1024 bits.

Fluid intelligent metasurface (FIM) is an emerging antenna architecture that continuously reshapes its physical geometry to optimize wireless performance. While existing studies on FIM-aided integrated sensing and communication (ISAC) rely on co-located single-base-station (BS) deployments, they fundamentally underutilize FIM's morphological flexibility due to restricted observation angles. In this paper, we investigate a FIM-augmented cell-free ISAC architecture, where distributed access points (APs) collaboratively observe a target from diverse angles. We derive the complete Fisher information matrix for target angle estimation and obtain a closed-form localization CRB that explicitly quantifies the angular diversity gain. By analyzing the block structure of the Fisher information matrix, we uncover three cell-free-specific phenomena: (i) cross-AP information coupling, (ii) multiplicative Tx–Rx FIM coupling, and (iii) angular diversity amplification. Under a 28\,GHz configuration with four APs and eight FIM elements per AP, our analysis shows that distributed angular diversity amplifies the FIM morphing gain to 15.8\,dB, compared to only 0.4\,dB in a single-AP pair deployment with the same total antenna count. We further propose an alternating optimization algorithm for joint beamforming and FIM shape design via semidefinite relaxation whose tightness is formally proved. Numerical results confirm that the proposed cell-free FIM-ISAC architecture achieves a 4.5\,dB localization CRB reduction over the single-AP fixed-array baseline at 10\,dB sensing SNR while maintaining communication quality-of-service constraints across the entire Pareto frontier.