Papers

Sulfur is the tenth most abundant element in space, yet it is strongly depleted in the gas phase of dense interstellar regions, suggesting sequestration in dust grain components that are difficult to detect. We study whether UV irradiation and thermal processing of H2S-containing interstellar-ice analogues can produce refractory sulfur species, and whether water-dominated ice enhances their formation. We performed UV irradiation and warm-up experiments on H2S-containing ice analogues with and without water, and the resulting refractory residues were analysed ex situ. Refractory sulfur species, including the sulfur allotropes S6-S8, are formed during UV irradiation and thermal processing of H2S-containing interstellar-ice analogues. Water enhances the formation of these sulfur allotropes by two orders of magnitude. We propose a formation mechanism in which ionic intermediates stabilised by the water-ice matrix promote chain growth and cyclisation, yielding predominantly S8. The combined detection in our residues of sulfur allotropes and polythionic species, also reported in meteorites and samples returned from asteroids, supports their formation in pre-cometary ice mantles covering dust grains. Because these species can incorporate multiple sulfur atoms per molecule, they constitute an efficient solid-phase reservoir for the missing sulfur in dense cloud environments where young stars are born. Refractory sulfur can therefore serve as a tracer of water-ice environments in space.

Parity superselection forbids direct measurement of odd Majorana observables. We learn time-independent, parity-covariant, $k$-mode-local Lindbladians on $m$ modes using even preparations and measurements with uninterrupted short-time evolution. Internal markers turn odd probes into even observables, and pair measurements among three separated markers calibrate their dynamical contributions. Signed Fierz inversion recovers canonical coefficients, while semidefinite fitting yields a valid generator. For finite-range models on known bounded-degree graphs with suitable marker access and a supplied weighted-strength bound $\bar\alpha$, entrywise error $\varepsilon$ is achieved using $\widetilde{\mathcal{O}}(\bar\alpha^2\varepsilon^{-2}\log(m/\delta))$ samples, without external modes or known nonzero coefficient locations. Recovery to diamond-norm error $\varepsilon$ costs an additional factor $m^2$, matching lower bounds for short-time experiments on fresh systems up to logarithmic and fixed geometric factors. Without a supplied graph, one idle ancillary mode per system mode and potentially nonlocal pair operations give total absolute coefficient error at most $\varepsilon$ per mode using $\widetilde{\mathcal{O}}_k(\bar\alpha^2\mathsf d^2m^{\lfloor k/2\rfloor}\varepsilon^{-2}\log(m/\delta))$ samples, under a supplied approximate coefficient-degree bound $\mathsf d$ and controlled weak-coefficient tails. All guarantees hold with probability at least $1-\delta$. For geometric models, fixed-support even observables can be predicted with logarithmic system-size sample complexity at fixed time and accuracy. We also give finite-volume and exponential-tail extensions.

We give a generic compiler for turning a wide class of device-dependent protocols with trusted state preparation into sequential device-independent protocols. In order for our compiler to apply, the trusted-preparation protocol needs to satisfy certain minimal conditions: having an entanglement-based realization in the first place, and the entanglement-based realization corresponding to the optimal strategy of any non-local game that satisfies a fairly weak rigidity condition. We apply our generic compiler to give sequential device-independent protocols for uncloneable encryption, copy-protection of point functions, and blind randomness expansion. Our technical contribution is a new class of rigidity theorems based on Rényi divergences, with flexible cryptographic applications. They allow our compiler to achieve a constant rate (i.e., the ratio of trusted states prepared to device uses), while tolerating a constant level of noise per device usage. This overcomes a fundamental scaling obstacle faced by previous rigidity theorems for trace distance or fidelity. For the generic sequential case, our proof is based on the sharp-divergence chain rule by Fawzi and Fawzi (2021), which suffices for a constant but fairly low rate. In the special case when the devices retain no memory, we improve the rates by deriving a novel subadditivity property for a modified channel sandwiched divergence, which may be of independent interest. Finally, as a prospect for future improvements, we also prove a chain rule for the iterated-mean divergences from Brown, Fawzi and Fawzi (2021).

The independent and identically distributed (iid) paradigm for asymptotic communication through quantum channels describes $n$ uses of a channel $\Phi$ by $\Phi^{\otimes n}$. Since exact tensor-power behaviour is an idealization, we ask whether the asymptotic capacities of $\Phi$ remain achievable for channel sequences that are almost-iid along $\Phi$. We consider sequences of Choi-almost-iid channels whose normalized Choi states are Mazzola-Sutter-Renner (MSR) almost-iid along the normalized Choi state of $\Phi$, with defect parameters $r_n=o(n)$. In Renner's exponential de Finetti theorem for quantum states, almost-iid states appear in the approximating mixture and motivate the MSR almost-iid class. Choi-almost-iid channels play the corresponding role in an exponential de Finetti theorem for quantum channels established in a companion paper. In this paper, we prove that the universal unassisted classical and quantum capacities of the class of Choi-almost-iid channels along $\Phi$ equal those of the channel $\Phi$. Here universality is within this class: for each rate below the relevant capacity, a code sequence depending on $\Phi$ and the rate, but not on the particular channel sequence, achieves vanishing error for every sequence in the class.

Secret sharing is ubiquitous throughout cryptography. All possible access structures are classically feasible, and in the case of threshold access structures, the protocols are even very efficient. However, when moving to the quantum setting, the no-cloning theorem shows that many access structures are impossible. In fact, no-cloning exactly characterizes feasibility: for thresholds, quantum secret sharing is possible if and only if the threshold $t$ is strictly more than $n/2$. In this work, we propose a variant of quantum secret sharing (QSS) where two or more identical copies of the input state are provided, but the output is only required to recover one copy. This notion circumvents the simple one-copy no-cloning obstruction, though the natural $k$-copy generalization still gives much milder obstructions. For thresholds using $k$ copies, no-cloning implies that QSS is impossible whenever $t\leq n/(k+1)$. It is tempting to hypothesize that no-cloning continues to exactly characterize the many-copy case. However, we show that this is not the case. We give positive results showing that multiple copies allow for going slightly beyond the single-copy obstruction: for thresholds, we construct QSS whenever $t>(n-k+1)/2$. On the other hand, we give a novel obstruction we call the Clique Path obstruction, which applies to arbitrary access structures. For thresholds, it shows that QSS is impossible whenever $t\leq (n-1)/k$. Our upper and lower bounds exactly match for $k=2$. Both our results leverage connections to the $k$-colorability of certain graphs derived from the access structure. We leave closing the gap for $k\geq 3$ copies as a fascinating direction for future work. Secret sharing is closely related to error correction, which can also be considered in the many-copy setting. Our results imply similar obstructions for quantum error correction for erasure channels.

We determine the optimal success probability for transmitting a fixed number of classical messages through a finite number of uses of the quantum erasure channel, assisted by noiseless classical feedback and without initial shared entanglement. For an input dimension $d$, an erasure probability $p$, a blocklength $n$, and $M$ equiprobable messages, the optimal success probability is equal to $E[\min\{1,d^K/M\}]$, where $K$ is binomial with parameters $n$ and $1-p$. The converse allows arbitrary adaptive quantum encoders, quantum memories, and receiver instruments. Its main ingredient is an elementary dimension bound for noiseless quantum communication with classical feedback, proved by fixing the classical controls without conditioning the sender's state on the observed transcript. A classical protocol that transmits the base-$d$ digits of an integer representing the message, repeating each digit until the receiver acknowledges its reception or the prescribed blocklength is reached, attains the bound for every integer $M$. We also establish a relative-majorization property of erasure-channel outputs and exactly evaluate a hypothesis-testing converse, recovering the same numerical bound without feedback. That converse need not be achievable without feedback: four uses of the qubit erasure channel and four messages give a strict gap. A product-state code employing tetrahedral qubit states nevertheless outperforms every classical binary erasure code with these parameters. We give an explicit message-size formula and show that the bounded-remainder normal approximation and the average-success strong-converse exponent are unchanged without feedback. We also determine the feedback-assisted error exponent below capacity, prove that it agrees with the no-feedback exponent above a critical rate, and give no-feedback bounds at lower rates.

Macrorealism is a fundamental concept in quantum foundations, capturing basic features of our everyday experience. Among the main tools introduced to test violations of macrorealism are the Leggett-Garg inequalities. These inequalities provide necessary and sufficient conditions for a certain data set including the correlators measured in a number of different experimental runs (weak version of macrorealism). Leggett-Garg inequalities have proved useful for detecting violations of macrorealism in neutrino oscillation experiments. However, it is interesting to investigate a set of necessary and sufficient conditions for strong macrorealism - no-signaling-in-time and arrow-of-time conditions - in order to obtain a more complete characterization of macrorealism in the context of neutrino oscillations. In particular, here we extend previous study of the no-signaling-in-time condition to the case of three-flavor neutrino oscillations, including the CP-violating phase of the Pontecorvo-Maki-Nakagawa-Sakata matrix.

We study how AI agents discover and validate scientific formulas using a controlled case study of the hydrotope, a recently discovered geometric formula that combines the different polynomial pieces of nonlinear surface-wave scattering into one global expression. This problem is deceptively difficult: simple formulas can hold within individual frequency regions, but the global result must identify their boundaries and combine exponentially many potentially active terms. We reconstruct how the formula was originally discovered through human–agent collaboration and analyze 18 single-prompt rediscovery runs under no hint and two forms of human guidance: a false hint representing an incorrect prior and a true hint representing domain-informed insight. Only four recover the formula across all kinematic chambers (i.e., regions in which a single polynomial form applies), while most unsuccessful runs find correct chamber polynomials but fail to combine them or test their full domain. Conventional and LLM-assisted symbolic regression and standard machine-learning regressors likewise fail to recover the global formula in our experiments. Guided by these failure modes, we test a PI$+$two-student workflow in which a coordinating lead agent assigns complementary analytic and numerical tasks to two research agents and independently evaluates their results. The PI$+$two-student team successfully rediscovers the complete hydrotope formula, while the same workflow applied to the harder three negative wavenumber problem discovers a new independent verified analytic expression for the six-point amplitude $A_6$.

Social interactions are shaped by networks that can be highly heterogeneous, with some individuals potentially interacting with many others. However, physical and temporal constraints limit the number of simultaneous interactions, making social contacts inherently intermittent. Here, we investigate how intermittency affects epidemic spreading on complex networks considering two distinct mechanisms: intermittency of connections (links) and individuals themselves (nodes), with periods of activity and inactivity governed by renewal processes with broadly distributed inter-event times. Combining mechanistic theoretical approaches with stochastic simulations, we show that these two forms of intermittency have fundamentally different effects on epidemic spreading. Link intermittency largely preserves the mechanisms responsible for sustaining transmission, and epidemic behavior can be largely explained by the average reduction in contact opportunities. Contrastingly, node intermittency is substantially more effective at containing spreading because the simultaneous interruption of all contacts suppresses transmission while recovery continues independently. The non-Markovian nature of node intermittency plays a key role: shorter and less heterogeneous inter-event times increase epidemic thresholds and enhance epidemic containment. Our results highlight how the temporal organization of individual activity, beyond the average reduction in contacts, can substantially alter epidemic spreading and may help inform interventions that exploit intermittency in social and biological contact networks.

Harnessing active matter to power functional devices has attracted growing interest. We propose a minimal battery model for storing energy extracted from active matter and derive its charging and discharging characteristics analytically. When the energetic cost of sustaining activity is included, the charging power-efficiency trade-off becomes loop-like and the efficiency attains a finite-time maximum, in sharp contrast to passive energy devices.

Machine-learning surrogates accelerate physical simulation, but lower prediction error need not coincide with lower error in physically relevant flow statistics. We examine this question for flow around a NACA4418 airfoil using paired computational-fluid-dynamics simulations and experimental particle-image-velocimetry measurements. A mean-preserving input intervention removes velocity fluctuations from selected regions of observed flow histories. Across four neural operators, removing fluctuations from the most energetic 10% of valid observed cells changes forecasts more than equal-area random removal. Because the masks are not matched for removed fluctuation energy, this contrast measures sensitivity, not independent evidence of physical importance. Separately, a CNO has lower velocity-field error but substantially higher two-component fluctuation-energy error than the reference on both analysis subsets. An output attenuation stress test also demonstrates disagreement between benchmark errors and domain-summed fluctuation energy. These single-benchmark results motivate reporting complementary physical diagnostics alongside aggregate prediction scores; they do not establish counterfactual physical correctness.

We formulate fermionic particle creation in a time-dependent curved spacetime as the exact evolution of a physical Bloch vector. Each Dirac momentum mode reduces to a two-level system, and its instantaneous occupation is obtained by projecting the physical state onto the instantaneous energy basis. This construction is equivalent to the standard Bogoliubov description while retaining the complete finite-time state trajectory in a compact real geometry. It also makes the fermionic occupation bound manifest without attributing its microscopic origin to geometry alone. For a massive Dirac field in de Sitter spacetime, the dynamics reduces to a universal function of the physical momentum in Hubble units and the mass-to-Hubble ratio. We identify a mass-controlled nonadiabatic scale and a singular small-mass boundary layer that resolves the noncommuting massless and late-time limits. Independent Cartesian Bloch, angular Bloch, and Bogoliubov integrations verify the analytical results and recover the standard Gibbons–Hawking Fermi–Dirac plateau.

Starobinsky's original model of inflation, driven by the trace anomaly of conformal fields, and its $R+R^2$ (scalaron) formulation are often treated separately. The original anomaly-driven evolution connects an early de Sitter phase supported by the Euler anomaly to a scalaron regime, where the observable modes leave the horizon. Building on this known background connection, we compute the scalar and tensor spectra on the exact background and find that the anomaly corrections are controlled by $aN_*/(18b)$, where $a$ and $b$ are the Euler-anomaly and $R^2$ coefficients and $N_*$ the number of e-folds after the pivot exits the horizon; scalaron inflation is recovered as this parameter vanishes. The observed tilt at $N_*=60$ then requires only $b/a\simeq35$, rather than the $b/a\gtrsim10^9$ of early realizations. At this benchmark the scalar spectrum is redder than in scalaron inflation at fixed $N_*$, and the tensor-to-scalar ratio is about 17% lower at fixed tilt, a quantitative signature of the anomaly. For minimal gravitational reheating, $N_*\simeq53$, the tilt remains within $1\sigma$ of the Planck value for $b/a\gtrsim35$. In the de Sitter analysis, a finite range of the Weyl coupling excludes an extra real spin-two pole and keeps the causal response decaying. A companion paper gives the full analysis.

We study the monic recurrence coefficients of the generalized Charlier polynomials associated with the discrete weight \[ \rho_\mu(k) = \frac{\mu^k}{(k!)^2}, \qquad k\in\mathbb N_0, \qquad \mu>0. \] We establish complete factorial asymptotics for the deviations $\beta_n-n$ and $\mu-\gamma_n$, proving that they are beyond all algebraic orders and appear at the scale $\mu^{n}/(n!)^2$. The key step is a parametrization $\beta_n-n=\sqrt{\mu}\,c_nc_{n+1}$, $\gamma_n=\mu(1-c_n^2)$, which reduces the problem to a positive sequence $(c_n)$ satisfying a discrete Painlevé II equation. Linearization around $c_n=0$ yields a discrete Bessel equation whose recessive solution is $J_n(2\sqrt{\mu})$. We prove that the ratio $c_n/J_n(2\sqrt{\mu})$ converges to a finite limit $L(\mu)$, which we identify exactly as $L(\mu)=1$ by combining Bessel comparison with a global analysis based on the sector decomposition of the associated Hankel determinant. This yields the exact connection formula \[ c_n \sim J_n(2\sqrt{\mu}), \qquad n\to\infty, \] and consequently the precise asymptotics \[ \beta_n-n\sim \frac{\mu^{n+1}}{n!(n+1)!}, \qquad \mu-\gamma_n\sim \frac{\mu^{n+1}}{(n!)^2}. \] We further develop a complementary approach based on Hankel determinants interpreted as a discrete logarithmic gas. We show that the Hankel determinant factorizes as $\Delta_n(\mu)=\mu^{n(n-1)/2}T_n(\mu)$ and admits a sector decomposition $T_n(\mu)=1+\sum_{q=1}^{n}S_q(\mu)$ with sector contributions independent of $n$. We establish $S_q(\mu)\sim e^\mu\mu^q/(q!)^2$, providing an independent derivation of the factorial corrections. Together, the Bessel comparison and sector decomposition reveal a rich integrable structure linking discrete Painlevé dynamics, Toda deformations, and Hankel–partition representations.

In the framework of Scalar-Tensor-Vector Gravity (STVG), this paper investigates the quasinormal modes and time-domain evolution of Reissner-Nordström Modified Gravity (MOG) black holes under massless scalar, electromagnetic, and gravitational perturbations. Quasinormal frequencies are calculated by extending the 3rd- to 6th-order WKB method and combining it with Padé approximation to the 13th order, while complete time-domain waveforms are obtained using a finite-difference method based on light-cone coordinates. The results indicate that increasing the MOG parameter $\alpha$ raises the effective mass of the black holes, leading to a decrease in the damping rate $|\omega_I|$ and a slower ringdown decay. An increase in charge $Q$ produces a similar effect, with the damping approaching zero in the near-extremal limit. Regarding the ringdown decay times for the three types of perturbations, the gravitational field has the longest duration, the electromagnetic field is intermediate, and the scalar field is the shortest. The oscillations and decay observed in the time-domain waveforms are qualitatively consistent with the frequency-domain results, and the power-law exponent governing the late-time tail aligns with that of asymptotically flat spacetimes. This study provides a systematic theoretical reference for testing modified gravity theories using black hole spectroscopy.

A hidden-variable model can reproduce context-independent individual readouts while failing to preserve observable records when devices are connected or reused. We distinguish two composition requirements. For a finite family of nonnegative instrument matrices, an invariant space generated by normalization defects characterizes unit continuation mass under every finite adaptive policy. Its annihilator defines the maximal admissible positive cone closed under outcome-conditioned updates. A separate observation space characterizes indistinguishability of context-dependent hidden preparations under joint readout. A finite-state example passes every fixed sequence but fails under outcome-dependent stopping. For a wrapped-Cauchy spin source with an explicitly stipulated unchanged-source passive extension, two individually fair probes acquire a setting-dependent agreement probability with contrast $\epsilon^2\operatorname{sech}(2g)/4$. More generally, protection under one and two identical uses forces a continuous binary passive response to be constant; measurable two-valued exceptions remain possible. Exact rational calculations, exhaustive finite-policy experiments, continuous source sampling, and quadrature test the stated examples. The criteria apply to specified instrument families and accessible records; they do not construct a microscopic detector or establish consistency under unrestricted network composition.

How much precision must be allocated, and to which uncertainty channels, to meet a prediction requirement? We formulate a minimum one-shot specification cost over initial state variables and persistent forcing parameters. The central result is that prediction accuracy can select the horizon-scaling law of this resource by activating different physical uncertainty channels. Within any common uniformly scale-separable regime with the same active channels, changing a fixed tolerance changes the required precision by only $\cO(1)$ bits. An exactly solvable multiscale toral system shows that one fixed dynamics and target can nevertheless switch from $B_N(\eps_c)=\Th(\log N)$ to $B_N(\eps_f)=\Th(N)$ when finer accuracy activates an expanding channel. A forced Lorenz–84 calculation then realizes the same channel-switching mechanism numerically over finite horizons in a single two-scale diagnostic field: a sampled post-transient eddy envelope supports a coarse branch controlled by the phase rate of a large-scale forcing, whereas finer accuracy activates exponentially sensitive atmospheric degrees of freedom and produces an approximately linear increase of the linearized one-shot cost over the resolved window. Thus accuracy can determine not only how much predictive precision is required, but which physical channel controls its growth with horizon.

Recent James Webb Space Telescope (JWST) measurements quantify the fraction of ultraviolet-selected galaxies showing detectable Lyman-alpha (Ly-$\alpha$) lines at $z \sim 6-14$. These Ly-$\alpha$ fractions are partly shaped by Ly-$\alpha$ scattering from neutral hydrogen in the surrounding intergalactic medium (IGM), and so the observed Ly-$\alpha$ fraction evolution can inform our understanding of the reionization history and the size distribution of ionized bubbles during reionization. We compare the JWST measurements with Ly-$\alpha$ transmission calculations based on both the THESAN reionization simulations and a flexible semi-analytic model. In each case, we calibrate a sub-grid model for the intrinsic Ly-$\alpha$ emission lines emerging from the interstellar medium (ISM) and circumgalactic medium (CGM) of the host galaxies using empirical estimates of the Ly-$\alpha$ equivalent width (EW) distributions at $z \sim 6$. We find that the reionization history and bubble sizes in THESAN yield good agreement with current JWST Ly-$\alpha$ fraction observations, with a reduced $\chi^2_\nu = 0.4-1.2$. Our semi-analytic models and THESAN Ly-$\alpha$ transmission calculations agree well, allowing us to explore a wide range of reionization models. We derive $1\sigma$ bounds on the average mass-weighted neutral fractions of: $\langle x_{\mathrm{HI}} \rangle$ = $0.38^{+0.14}_{-0.38}$ ($0.52^{+0.09}_{-0.21}$), $0.57^{+0.23}_{-0.57}$ ($0.68^{+0.12}_{-0.39}$), and $0.93^{+0.05}_{-0.17}$ ($0.89^{+0.11}_{-0.15}$) at $z \sim$ 7, 8, and 11, based on the Ly-$\alpha$ fraction measurements with EW $>25\,\mathring{\rm A}$ ($>10\,\mathring{\rm A}$).

Given multiple uses of an unknown quantum channel, we determine whether it is a specified non-mixed-unitary channel or belongs to the set of mixed-unitary channels. Formulating this as a composite channel hypothesis testing problem, we characterize the Stein exponents achievable by parallel strategies under progressively weaker restrictions on probe states and auxiliary memory. In particular, we consider block-i.i.d. probes, which allow arbitrary correlations within blocks of fixed size while remaining i.i.d. across different blocks, and derive finite-letter expressions of the corresponding Stein exponents. Varying the block size, which interpolates between fully i.i.d. and arbitrary probes, together with further restrictions on intra-block correlations and access to auxiliary memory, results in a multifaceted hierarchy. We establish several strict separations within this hierarchy. Without auxiliary memory, we prove that fully i.i.d. probes yield a vanishing Stein exponent for every unital non-mixed-unitary channel, while blocks of three product probes suffice to obtain a strictly positive exponent for the qutrit Werner-Holevo channel. For block size two, although product probes seem to be insufficient for $O(3)$-covariant channels, an entangled probe achieves a strictly positive exponent for the qutrit Werner-Holevo channel, even though every maximally entangled probe fails. In contrast, access to auxiliary memory makes fully i.i.d. probes sufficient by yielding a strictly positive exponent for every non-mixed-unitary channel, even without requiring input-reference entanglement, and this exponent admits a lower bound determined by the diamond-norm distance from the mixed-unitary set. Moreover, for odd-dimensional Werner-Holevo channels, we find that this exponent is infinite, with every full-Schmidt-rank pure state being optimal.

Optical nonlinearities arise when the response of a photonic system depends on light intensity. Radiation pressure can create such a nonlinearity by moving a mechanically compliant reflector, thereby shifting the phase of the reflected light. Based on measured properties, we predict a giant phase responsivity of 263 rad W$^{-1}$ and a device-equivalent $n_{2,\mathrm{eff}} = 5.4 \times 10^{-7}$ m$^2$ W$^{-1}$ for a silicon nitride membrane trampoline with serpentine springs. We introduce strength-range-aperture metrics for reflective phase elements. Among reported mechanical resonators compared under a common direct-reflection protocol, this trampoline is an outlier, combining high compliance, practical optical accessibility, and 99.85% retention of its small-signal phase responsivity through a full $2\pi$ reflected-phase shift. Practical implementation requires optical and thermal co-design. Our framework indicates design priorities for future mechano-optical phase elements.

We derive the half-space KPZ equation as a continuum limit from a general class of Ginzburg-Landau SPDEs under weak nonlinearity scaling. To our knowledge, this is the first half-space universality result for the KPZ equation beyond integrable models (and their perturbations).

It is well-known that every $n$-qubit unitary can be implemented by a $2^{O(n)}$-depth quantum circuit using single- and two-qubit gates. It has been open whether exponential depth is *necessary* for general unitaries, even when allowing an unlimited number of ancilla qubits. Here we show, perhaps surprisingly, that all unitaries can be implemented exactly by a circuit of one- and two-qubit gates of depth $\mathsf{poly}(n)$ with $2^{O(n)}$ ancilla qubits. In other words, every $n$-qubit unitary can be parallelized to polynomial depth. In fact, our depth bound is *linear* in $n$, which is the best possible, and an exponential improvement on the previous best bound of $2^{n/2}$ due to Rosenthal [TQC 2022, Quantum 2026]. Moreover, if we allow unbounded fan-out gates, these circuits can be further reduced to *constant* depth. Our construction takes advantage of a novel relationship connecting the unitary synthesis problem of Aaronson and Kuperberg to locally-decodable codes and private information retrieval from complexity theory and cryptography, and has a natural interpretation in bosonic quantum computation.

Pseudorandom permutations are ubiquitous in theoretical and applied cryptography. PRPs that offer security even against adversaries making quantum queries are of increasing interest, and used in applications ranging from constructing pseudorandom unitaries to separating SZK from BQP. A successful framework for constructing classically-secure PRPs is the key-alternating Even-Mansour approach, which interleaves applications of public permutations with additions of round keys. The single-round construction is already classically secure in the ideal permutation model (IPM), with added rounds offering improved concrete security. However, in the quantum-query setting, the status of this framework is presently unclear. A simple quantum-query attack based on Simon's algorithm breaks the one-round cipher. For two or more rounds, security is only known against non-adaptive adversaries who must prepare all queries in advance. In this work, we show that the two-round Even-Mansour cipher is information theoretically secure in the IPM against adversaries making polynomially-many adaptive forward and inverse quantum queries to all available oracles. Our proof uses compressed permutation oracles and a specially crafted isometry relating the ideal and real experiments. We also show that this construction is minimal, in the sense that essentially any cipher constructed via a single call to a public permutation is quantumly insecure.

A majority of measurable dynamic quantities of a physical system is described as an equilibrium correlation function of the form $G_{AB}(t-t') = \left<A(t)B(t')\right>$, where $t'$ represents the impact time and $t$ represents the response time. Conventional quantum algorithms to compute such quantities via Hamiltonian simulation such as the Hadamard test, variational methods, or linear-response-based algorithms share one feature in common: each time point $t-t'$ is calculated by a different quantum circuit, leading to at least $O(N_t)$ total shots, and at least $O(N_t^2)$ total quantum gates. Here, we provide a different approach: utilizing $O(\log N_t)$ ancilla qubits to store time as a quantum variable, and effectively parallelize the computation of an equilibrium correlation function by requiring only a single quantum circuit for all time points. We show that this circuit needs to be run only $O(\log N_t)$ times, which in total requires $O(N_t \log N_t)$ quantum resources in the large system size limits. We prove that this scaling is optimal, and demonstrate our algorithm calculating the Green's function of a one-dimensional spinless Hubbard model.

Multiterminal Josephson junctions, in which one weak link couples three or more superconductors, are studied as hosts of topological Andreev bands, multi-pair supercurrents and tunable circuit elements. Their currents are modeled both as pairwise networks of two-terminal couplings and through genuinely multiterminal processes such as quartets. We ask how accurate the pairwise description is and what controls its error. In a microscopic scattering model of planar junctions, we compare exact currents with the best pairwise approximation, which allows arbitrary nonsinusoidal couplings. In ensembles of disordered three- and four-terminal junctions, the pairwise terms capture nearly all of the energy variation, yet the median current error ranges from 8.0 to 21.2 percent, about twice the energy error, because currents weigh the multiterminal harmonics more strongly. Designed devices extend the comparison to sixteen terminals. We identify a mechanism that controls this error. A normal-region mode near the Fermi level that couples to three or more terminals produces large nonpairwise currents, and detuning it with a gate suppresses them. Shifting only this mode, selected from normal-state properties, predicts the gate dependence of the error in eight three- and four-terminal devices without fitting currents. Finite-gap calculations in two clean devices confirm a drop from tens of percent near resonance to below one percent. An analytic single-level model gives a sufficient detuning for pairwise accuracy at any terminal count. Planar junctions thus inherit the resonant and cotunneling regimes known from quantum dots, and normal-state properties identify the mode that selects between them.

We apply Decoded Quantum Interferometry (DQI) to sample from the Gibbs measures of classical Ising spin Hamiltonians. We show that this Gibbs sampling problem reduces to a quantum decoding problem, and the temperature achievable by DQI is determined by the performance of decoding algorithms. We then focus on the task of Gibbs sampling for classical Ising $k$-spin glasses (or Max-$k$-XORSAT) on random Erdős-Rényi hypergraphs with average degree $D\ge k$. In a temperature range beginning asymptotically at the predicted dynamical phase transition, $\beta_{\rm dyn}(k,D) = \sqrt{(2\ln k)/D}\times [1+o_{k\to\infty}(1)]$, we show that shattering and disorder chaos form a topological barrier that obstructs many algorithms, including Glauber dynamics and any algorithm whose output distribution is "stable" under perturbations of the input. In contrast, we prove that this barrier can be broken both by a classical algorithm based on Prange's method, and by DQI equipped with a quantum decoder. For example, when $D=\alpha k$ with fixed $\alpha>1$, both Prange's algorithm and DQI can sample at any inverse temperature $\beta < \tanh^{-1}(1/\alpha)$ for sufficiently large $k$, well beyond the dynamical threshold $\beta_{\rm dyn} \sim \sqrt{2\ln k / (\alpha k)}$. Therefore, our results show that DQI can overcome topological barriers that obstruct stable algorithms.

Standard finite quantum de Finetti theorems approximate the $k$-system marginals of permutation-invariant states of $n$-systems by mixtures of independent and identically distributed (iid) states, usually in trace distance. We prove both standard and Renner's exponential de Finetti theorems in the stronger form of operator inequalities, implying bounds in every Schatten norm and for every quantum Rényi divergence satisfying data processing. In the standard case, for fixed local dimension, our $k/n$ error bound in max-relative entropy improves on the previously best known $k^2/n$ scaling, even in the classical setting. The operator-inequality approach is particularly suited to study channel de Finetti representations because operator order between Choi states is equivalent to completely positive (CP) order between the underlying channels. For permutation-covariant channels $N^{(n)}:A^{\otimes n}\to B^{\otimes n}$, where $d_A=\dim A$, we prove that the $k$-system reduced channel is CP-dominated by a mixture of tensor-power channels with error $O(k/\sqrt{n})$ and polynomial dependence on the local dimensions, addressing a question raised by Berta et al. [Math. Program. 194, 781-829 (2022)]. Under the no-signalling condition, we also prove an exponential channel de Finetti theorem where the approximating mixture consists of Choi-almost-iid channels, whose normalized Choi states are almost-iid in the sense of Mazzola-Sutter-Renner. In the case of $r$ defects, the representation error is at most $\mathrm{poly}(n)\bigl(2d_A^4k^3/(nr^2)\bigr)^{(r+1)/2}$ and decays exponentially in $n$ for a suitable choice of parameters $r$ and $k$.

We study multi-armed bandits whose arms supply unknown quantum states and whose mean rewards are defined by a known effect $F$. Each fresh copy may be measured by an arbitrary, adaptively chosen POVM. We prove an exact collapse: the measured relative entropy from an arm state to its confusing reward half-space equals the classical Burnetas-Katehakis functional of $F$'s spectral statistics, and the spectral measurement of $F$ together with an explicit least-favorable state, built from the derivative of the matrix logarithm, forms a saddle point of the underlying measurement game. Consequently, spectral measurement followed by classical KL-UCB is asymptotically instance-optimal among all consistent single-copy policies, in every finite dimension and for every reward effect under the stated nondegeneracy assumptions: adaptive and randomized measurement design cannot improve the leading logarithmic regret coefficient, and neither can storing copies for later single-copy measurement. A self-contained finite-time bound covers general effects and boundary distributions. Any further improvement must come from measurements outside the single-copy class. For consistent policies with arbitrary quantum memory, an amortized relative-entropy argument gives a converse with the Umegaki half-space divergence, and the two per-arm regret floors, $1/K_{\mathrm{inf}}$ and $1/D_{\mathrm{inf}}$, coincide if and only if the arm commutes with $F$. Whether the Umegaki floor is attainable involves a composite quantum Stein problem and a separate reduction to adaptive regret; we pose it as an open problem, with two-copy numerical evidence.

The integer quantum Hall effect remains the most paradigmatic and remarkable example of exact quantization in condensed matter physics. Its Hall conductivity $\sigma_{xy}$ is fixed to $e^2/h$ times an integer to a precision limited only by measurement and independent of disorder or interactions. This robustness has several explanations, each capturing a strikingly different piece of the physics. In Laughlin's gauge argument, flux insertion pumps an integer charge between edges, so quantization follows from gauge invariance alone. The edge-channel picture instead attributes transport to chiral, ballistic 1D channels at the sample boundary, one per filled Landau level. Bulk arguments tie $\sigma_{xy}$ to a topological invariant of the disordered system, with extended states compensating exactly for the current not carried by localized ones. Here we demonstrate an additional route to understanding quantization, rooted in the finite-frequency dissipative electrodynamics of the bulk. Using high-precision terahertz Faraday rotation and numerics, we show that the cyclotron resonance alone does not give quantized plateaus under Kramers-Kronig transformation. Quantization is recovered only once a faint, low-frequency, topologically enforced dissipative contribution from impurity states is included. This dynamical mechanism, hiding in plain sight within the dissipative response, ties the DC value to the finite-frequency optical response and offers a new route to quantization through the optical Hall effect, complementary to previous pictures.

Convex relaxation hierarchies provide lower bounds to the ground state energy of quantum many-body systems that can be computed in polynomial time on a classical computer, at any fixed hierarchy level. However, scaling these methods to large systems and accurate approximations remains challenging due to the computational cost of traditional solvers and the scarcity of efficiency guarantees. In this work, we develop local relaxation hierarchies and efficient, highly parallelisable message passing algorithms for estimating the relaxed ground state energies. We show that the first level of the hierarchy—based on local consistency of pairwise reduced density matrices—is exact for commuting Hamiltonians on trees. We further establish that another hierarchy, based on consistent intervals, converges exponentially fast in the interval size to the ground state energy for weak perturbations of separable Hamiltonians on a chain, thereby providing an efficient classical algorithm for these systems. Then, we introduce two variants of message passing algorithms that run in $\mathcal{O}(n/\epsilon^2)$ and $\mathcal{O}(n/\epsilon)$ time for any fixed level of the local hierarchy on bounded-degree graphs, where $\epsilon$ is the precision for the relaxed ground state energy per site. This assumes that the optimal messages have $\mathcal{O}(1)$ norm—a condition we observe in practical settings in our experiments. These algorithms are based on the subgradient method and the Nesterov-type accelerated gradient descent method applied to an entropy-smoothed objective. Finally, we benchmark the message passing algorithms across different quantum Hamiltonians, lattice geometries, and relaxation levels, validating the theoretical predictions and their potential to surpass standard convex optimisation solvers for this problem. We release the resulting library at github.com/rick1924/gse-message-passing.