Papers

We adapt to the context of quantum theory the treatment, familiar in relativity theory, of a reference frame as a tetrad. Since a tetrad is a set of four orthonormal vectors at a spacetime point, it encodes a timelike direction, three orthogonal spatial directions, and units; and so it gives a configuration in spacetime (a spatial orientation and state of motion) of an idealized infinitesimal apparatus (“rulers and a clock"). So a natural “first guess" is that the state of a quantum reference frame should be an assignment of complex amplitudes to a set of tetrads. We develop this idea, in terms of bundles over spacetime of bases of the tangent spaces. This paper is a companion to two other papers. It emphasises the main conceptual aspects of our proposal, while the other two papers give physical details. It also explains the main contrast between those two papers. Namely: (i) the first considers a single spacetime geometry, so that a quantum reference frame, on our proposal, gives a superposition of perspectives on that geometry; while (ii) the second considers the spacetime manifold with no geometry given a priori, which will imply that a quantum reference frame, on our proposal, can describe a superposition of perspectives on a superposition of geometries—not “just" a superposition of perspectives on a single geometry. The main mathematical idea for representing this contrast will be choosing between (i) the orthonormal frame bundle, for a given spacetime geometry; (ii) the frame bundle in the usual sense of containing all bases of all spacetime points' tangent spaces.

Interacting fermions owe both their non-trivial correlations and their computational power to their departure from Gaussianity. Yet, quantifying that departure geometrically faces two challenges: the Gaussian manifold is non-convex, and perturbative treatments are confined to weak interactions. Here, we introduce a geometric measure of fermionic non-Gaussianity, the fidelity distance of a target state to the manifold of fermionic Gaussian states. We construct an iteration formalism to numerically access it, applicable also at strong coupling. Further, we prove a sharpened operator Jensen inequality, of interest in its own right. We use it to derive a witness that involves only two- and four-point fermionic correlators. Numerical benchmarks on the one-dimensional Fermi–Hubbard model show that the quality of the witness improves with system size and, for strong coupling, is tighter than antiflatness. Our results open a scalable route to charting non-Gaussianity of strongly-interacting fermionic quantum simulators.

A recent experiment reported coherent parity oscillations between minimal Kitaev chains, demonstrating a Majorana parity qubit (arXiv:2607.09511). Operations on this qubit are controlled by coupling two Kitaev chains and are intrinsically unprotected against noise in the coupling strength. Here we show how the exponential protection in the underlying chains can nevertheless be revealed through unprotected qubit operations. To this end, we develop an analytical theory of quasistatic dephasing for two coupled $N$-site Kitaev chains at the sweet spot. In Rabi experiments, protection can be resolved by adapting the operating point with chain length: depending on the coupling architecture, it appears as an exponentially increasing optimized number of coherent oscillations or as a longer coherence time. Ramsey experiments show an exponentially increasing coherence time, provided the chains can be sufficiently decoupled. Our analytical theory takes into account the non-Gaussian splitting statistics of the Kitaev chains, allowing us to quantitatively predict the scaling with chain length. Moreover, we determine how residual noise and imperfections limit the range of chain lengths over which this scaling can be observed. Our results show how qubit dynamics can be used to probe Majorana protection in experimentally realistic devices.

The use of artificial intelligence (AI) in physics research is increasingly common, yet few guidelines exist for its effective use. Starting with a principles-based approach, we outline a set of ten requirements for collaborative AI agents in experimental physics, spanning scientific norms, effective agent use, and domain expertise. We take a human-centered approach in which agents act as collaborators that amplify rather than replace the expertise of a human researcher (user) who directs the work and is responsible for its results. We then present a framework designed to enforce these requirements, detailing methods for improving off-the-shelf behavior of large language models (LLMs) with custom scaffolding and describing general-purpose scientific workflows and skills. In particular, we highlight the power of closed-loop campaigns where agents work iteratively toward a well-defined goal. We demonstrate the potential of this mode of research through six case studies in experimental physics, covering device design, hardware control, neural network optimization, physical model identification, and data analysis. All six case studies result in useful work products that add utility to our research, including a neural network architecture and solid-state quantum defect photodynamic model that substantially outperform our published work; a microwave waveguide design that extends a published design concept to a fabrication-ready device meeting our experimental constraints; a quantum control pulse sequence candidate that improves simulated performance by more than an order of magnitude; commissioning of an NMR spectrometer to $\sim$1~Hz frequency precision on live hardware; and finally a data-fitting pipeline that achieves, to our knowledge, the first reconstruction of the Ising microstate of an artificial spin-ice array from diffraction-limited magnetic imaging.

Quantum random-access memory (QRAM) enables coherent queries to classical data. However, the \(O(N)\) qubits required for a memory with \(N=2^n\) addresses make QRAM appear vulnerable to noise. Though bucket-brigade routing provides intrinsic noise resilience to reduce the error in QRAM, improving the fidelity of QRAM queries is still an important and challenging problem. We introduce a low-overhead protection framework for bucket-brigade QRAM with two complementary components. First, we propose a one-fault-tolerant repeat-until-success logical controlled-SWAP gate using the \([[4,2,2]]\) code under erasure noise channel. Interleaved erasure checks and local recovery correct every single erasure, so the leading logical failure probability is second order in the physical erasure error rates. Second, we exploit validity constraints of bucket-brigade routing to define local parity checks directly on the router states, without adding extra data qubits to create code redundancy. Under bit-flip noise, minimum-weight perfect matching with noiseless syndrome measurements corrects single interior faults, while open spatial boundaries retain a first-order contribution in the residual bit-flip rate. Monte Carlo simulations confirm quadratic suppression for the protected controlled-SWAP and improved depth scaling for decoded QRAM router-state snapshots. The two codes admit a concatenated realization in which the inner code supplies erasure protection and the outer code optionally corrects interior logical bit flips. Together, these results show how routing constraints and a protected non-Clifford routing gate can improve QRAM reliability under biased and erasure-dominant noise.

We investigate whether controlled motion of a quantum sensor offers a metrological advantage in a field-detection task. We consider a localized field of known strength $B$ occupying an unknown contiguous region making up a fraction $1/N$ of the total search space, with a qubit sensor controlled for a total time $T$ to maximize the probability of detecting the field. We study the regime in which the characteristic timescale of the field is slow compared to the time to move the sensor between any two regions, and we distinguish classical motion, where the sensor follows a definite trajectory, from quantum motion, where the sensor can be in a coherent superposition of locations. For a single classically moving sensor, we derive an optimal multi-stop protocol and obtain the exact maximum detection probability. Allowing coherent spatial superposition maps the single-sensor problem onto Hamiltonian search and reduces the interrogation time for successfully detecting the field from $\Theta(N/B)$ to $\Theta(\sqrt{N}/B)$. We then extend the problem to $M$ sensors and identify a hierarchy of optimal time scalings for constant success probability determined by the available spatial and inter-sensor quantum resources. Unentangled coherently moving sensors achieve $T=\Theta(\sqrt{N/M}/B)$ by searching disjoint regions in parallel, while entanglement among the sensors can further enhance the effective field coupling and achieve $T=\Theta(\sqrt{N}/(MB))$. Matching lower bounds establish the optimality of these scalings in the presence of arbitrary controls and ancilla systems. Our results separate the roles of classical motion, spatial coherence, and entanglement in spatial field detection.

A Latin square can be extended by replacing its symbols with probabilities or quantum states. We relate these two extensions through explicit examples, from classical and fractional Latin squares to quantum Latin squares and a real solution of Euler's quantum 36 officers problem. A simultaneous cyclic-shift ansatz on a four-torus of tensor coefficients gives a real absolutely maximally entangled (AME) state of four six-level systems. A local orthogonal change of basis yields a representative with 96 nonzero amplitudes. Two single-party arrays obtained from the corresponding quantum orthogonal Latin square yield fractional Latin squares. Signs matter: comparison with the independent real construction of Bruzda and its sign variant distinguishes three local-unitary classes, two of which have identical probabilities. We extend this probability representation to existing seven- and nine-party AME states with six levels each. Their amplitude matrices reveal 48 complex Hadamard blocks of order $3^3$ and six of order $6^4$, respectively. These constructions separate what can be read from a probability picture from the coherent conditions responsible for maximal entanglement.

We consider unstructured search using multimode bosonic quantum systems under energy constraints. The task is to locate an unknown marked mode among $N$ possibilities using arbitrary control, subject to a time-averaged mean-boson-number budget $n_{{\text{b}}}\gg 1$. We analyze a continuous-time phase-shift oracle of strength $B_{0}$, with cost given by the total oracle time, and a discrete oracle with fixed phase $\phi_{0}$, with cost given by the number of queries. We give algorithms that identify the target with query complexity $O(\sqrt{N}/{n_{{\text{b}}}}B_{0})$ for continuous-time oracles or $O(\sqrt{N}/n_{{\text{b}}} |{\sin(\phi_{0}/{2})}|)$ for discrete oracles with $n_{{\text{b}}} |{\sin(\phi_{0}/{2})}|=O(1)$. In contrast, for discrete oracles with $n_{{\text{b}}} |{\sin(\phi_{0}/{2})}|=\Omega(1)$, we provide an algorithm using $O(\max\{1,\sqrt{N/n_{{\text{b}}}|{\sin(\phi_{0}/{2})}|}\})$ queries. We also prove matching lower bounds on the query complexity, showing that these algorithms are asymptotically optimal. Furthermore, we show that, in the absence of loss, non-Gaussianity is necessary to achieve the optimal joint query scaling in $N$ and $n_{{\text{b}}}$, but entanglement is not. Under uniform boson loss at rate $\gamma$, we prove a query lower bound of $\Omega ( \gamma N / n _{{\text{b}}} B_{0}^{2} )$, attained for $\gamma = \Omega(B_{0} \sqrt{n _{{\text{b}}}/N})$ using coherent-state probes. Finally, we propose experimental implementations using multipass optical microscopy or superconducting circuits as potential routes to speeding up imaging or device calibration with a low boson-number budget.

Quantum sensing is typically based on phase accumulation and is therefore fundamentally tied to the coherence time of the sensing system. Here we introduce an alternative sensing paradigm based on programmable Floquet locking in periodically driven two-level systems. We show that periodic control generates an effective Floquet locking field whose orientation and amplitude depend on global offset, allowing information to be encoded in the driven population relaxation dynamics, not in the integrated phase. By controlling transfer between distinct Floquet locking manifolds, external perturbations can be mapped onto engineered relaxation responses whose characteristics are programmable through the driving sequence. We numerically demonstrate this approach for both DC and frequency-selective AC sensing, and show that temporal encoding of the response can provide enhanced precision in the presence of slow instrumental fluctuations. These results illustrate the potential of programmable Floquet responses and open the way to exploring new sensing strategies in driven quantum systems.

Can quantum advantages in computational efficiency coexist with quantum advantages in privacy? In this paper, we construct and use MasonQ, a universal brickwork transpiler, to answer this question with a resounding yes. We approach this question by bridging two seemingly disparate paradigms: universal blind quantum computation (UBQC), based on measurement-based quantum computation, and quantum machine learning (QML) algorithms such as the Harrow-Hassidim-Lloyd (HHL) algorithm and quantum recommendation systems. We provide new upper bounds on the depth of UBQC brickwork graphs, establishing that $D = \mathcal{O}(\omega n)$, where $\omega$ is the circuit width and $n$ its computational gate complexity. This is enabled by our newly developed transpiler MasonQ, which maps arbitrary quantum circuits to computational brickwork graph states. Given an optimal Qiskit circuit as input, we prove optimality (up to logarithmic corrections) of the MasonQ transpiler in terms of asymptotic scaling of the total brickwork graph width and depth after decomposition into bricks, enabling systematic cost analyses of blind implementations in near-term experiments and asymptotic regimes. Leveraging MasonQ, we derive depth bounds for several representative blind quantum machine learning (B-QML) algorithms, including the quantum Fourier transform, the HHL algorithm, recommendation systems, and quantum transformers. Lastly, we analyze concrete resource estimates for near-term demonstrations of blind quantum machine learning. We propose a minimal B-QML implementation requiring only a $12$ qubit quantum server. To the best of our knowledge, MasonQ is the first functional and optimal universal circuit-to-brickwork-graph transpiler to implement the full brickwork transpilation process from first principles.

Periodically driven quantum systems exhibit a wide range of complex dynamics, including chaos. Yet, at special parameter values, their evolution can recur exactly. Several quantum protocols have recently been proposed that exploit exact Floquet recurrences to demonstrate genuine quantum advantage. Such recurrences can be studied through the arithmetic structure of the Floquet unitary. In this work, we establish a necessary and sufficient arithmetic criterion for exact recurrence and determine the minimal recurrence period when one exists. Because recurrence is a global property of the unitary, it holds for every initial state. Applying our framework requires only knowledge of the number field associated with the Hamiltonian parameters. We demonstrate the method using the kicked Ising chain, establishing exact recurrences in both Clifford and non-Clifford regimes. We further show that, in the recurrent non-Clifford regime, magic–a resource for quantum computation–is generated at intermediate times and undergoes exact periodic revivals enforced by the recurrence of the full Floquet unitary. By connecting number theory, quantum many-body dynamics, and quantum information, our work shows that exact recurrence extends beyond Clifford circuits and opens new avenues for magic generation and quantum hardware benchmarking.

Scaling fault-tolerant quantum computing (FTQC) requires orchestrating millions of operations continuously across a tightly coupled classical-quantum control stack. A critical challenge in this orchestration is determining the optimal hardware-software boundary, i.e., the Quantum Instruction Set Architecture (QISA). We focus on cryogenic, fixed-connectivity qubit platforms, such as superconducting and topological Majorana qubits. For these, existing QISA choices either operate at too low a level, violating cryogenic thermal budgets at scale, or at too high a level, imposing unrealizable complexity on the control engine. To reason about these tradeoffs, we introduce the ARIES instruction set hierarchy, which categorizes QISAs into distinct abstraction levels. To systematically evaluate these levels, we develop an end-to-end evaluation toolflow featuring a cycle-accurate classical driver and hardware engine simulator. Using eight quantum applications across superconducting and topological qubit platforms, we measure instruction bandwidth, transceiver power dissipation, and measurement processing overheads. We demonstrate that while physical-level abstractions exceed the thermal limits of dilution refrigerators by orders of magnitude, canonical-level abstractions significantly underestimate hardware routing congestion and execution runtimes. Our Level 4 QISA (local logical operations) offers an optimal architectural balance. As quantum hardware platforms scale toward FTQC in the coming years, our findings provide concrete architectural guidance for the design of their classical control stacks and instruction interfaces.

Molecular systems with optically addressable electron spins are emerging as versatile quantum sensing platforms, offering tunable qubit properties and molecular-scale spatial control. Owing to their longer lifetimes, coupled nuclear spins provide an attractive resource for enhancing sensing performance. For molecular spin systems, the ability to initialise, coherently control and readout nuclear spins at room temperature is crucial for realising such benefits. Here, we present the first optical detection of nuclear magnetic resonance and coherent nuclear spin control with a molecular system at room temperature. Specifically, we demonstrate optically detected Rabi oscillations of $^{14}$N nuclear spins in the photoexcited triplet state of the organic chromophore 6,13-diazapentacene. The strong hyperfine coupling between the electronic spin and $^{14}$N nuclei enhances the nuclear Rabi frequency, enabling fast coherent nuclear-spin rotations. This work lays the foundation for leveraging nuclear spins as memories for enhanced molecular-based quantum sensing.

Nonlinear effects are widely utilized in quantum metrology to enhance measurement precision by leveraging complex dynamical behaviors. Here, we propose a quantum scrambling-integrated scheme that optimizes the selection of initial states and parameter encoding by exploiting the nonlinear dynamical trajectories and their geometric properties in phase space. We consider a two-mode Bose-Einstein condensate as a typical example. Within a certain parameter range, using uncorrelated spin coherent states located at saddle points and separatrices enables the measurement precision to reach the Heisenberg scaling. An analytical expression for the quantum Fisher information under long-time evolution is provided, and our analysis further reveals that the enhancement mechanism is governed by the sensitivity of the energy spectrum to parameter variations. Compared to the criticality-enhanced protocol that requires parameters to approach the critical point, our scheme offers a distinct advantage in its applicability over a broader range of parameters. Moreover, this scheme can also be applied to models that include one- and two-axis countertwisting interactions and chaotic dynamics. This Letter offers a new perspective for advancing the application of nonlinear dynamics to enhance the parameter estimation precision in quantum systems.

Spatial sudden death of entanglement refers to the disappearance of quantum correlations between subsystems after a certain distance called the entanglement length. Specifically, given a density matrix $\rho_{ABC}$ on a tripartite system $ABC$ with $B$ spatially separating $A$ and $C$, the entanglement length is the distance $\ell(A,C)$ after which the reduced density matrix $\rho_{AC}$, given by tracing out the $B$ subsystem, is separable. We show in the case of gapped ground states in any dimension that the entanglement length is finite on finite subsystems. Restricting to one-dimensional systems, we prove that normal matrix product states have a finite entanglement length independent of $A$ and $C$, and that a finite pure state with such uniform entanglement length has a matrix product state representation with bond dimension independent of $A$ and $C$. Consequently, in one dimension, entanglement length distinguishes matrix product states from all other pure states.

Bosonic codes often read out their syndrome with a transmon ancilla whose computational levels $g$ and $f$ have equal parity and matched dispersive shifts: a decay $f\to e$ is then heralded and leaves the code intact, while the direct $f\to g$ is forbidden by parity. We show that the photons of the code open this decay at first order in the ancilla's decay rate. Dressing by the code mode lets the charge noise that limits the ancilla's $T_1$ drive a photon-stimulated Raman decay $|f,n\rangle\to|g,n+1\rangle$, at $(n+1)(\chi_{ge}/2g_{01})^2$ times the $f\to e$ rate for a smooth noise spectrum. When the matching is set by the detuning, the decay costs $\approx\Gamma_{fe}/\alpha$ per gate and photon, whatever the coupling strength; a deliberate mismatch or matching by a drive lowers this cost, and a qubit ancilla has no such channel. The opened decay is unheralded and flips a cat with probability $\approx 1/2$; being first order, it overtakes the second-order double decay $f\to e\to g$ as the ancilla improves. In a microscopic model of the Ocelot repetition cat code, it makes the bit-flip floor of the gates grow linearly with the cat size, by a factor 1.2-1.7 from four to ten photons, which would limit the noise bias to $\sim 10^3$. The published gate data end at four photons and do not yet test this growth.

The vortex structures in the momentum distributions of multiple particle-antiparticle pairs produced from the vacuum by a spatially uniform, time-varying electric field with arbitrary polarization are investigated using the Bogoliubov transformation. For linearly polarized fields, as the field strength increases, the nodal lines in the multi-pair momentum distribution break up into vortex-antivortex pairs in both the bosonic and fermionic cases. Each vortex carries a topological charge that is an integer multiple of the single-pair vortex topological charge. For circular polarization, a central vortex appears at all field strengths. For bosons, its topological charge is an integer multiple of the single-pair vortex topological charge; for fermions, it is an integer multiple of the vortex topological charge for single-pair production with zero total spin projection along the field propagation direction. For elliptical polarization with suitable ellipticity, discrete vortices coexist with a central vortex. In this case, however, the integer-multiple relation for fermions generally fails because the two-pair production amplitude is a determinant and spin-channel contributions are separated in momentum space. These results provide a theoretical basis for understanding the vortex topology of multi-pair production in strong-field QED and for its potential control.

The second quantum revolution is a revolution of information. Advances in quantum computation, communication, and sensing offer new capabilities while raising questions about how quantum infrastructures will be organised, accessed, and governed. We argue that their significance for governance lies not in transforming political principles, but in how their technical and infrastructural requirements may affect existing relationships of authority, responsibility, legitimacy, and power. This paper develops a quantum governance lens that connects governance scholarship with quantum information science, examining interactions between technical design, institutional arrangements, and infrastructural dependencies. We apply this lens to five areas: quantum computation, quantum key distribution, Quantum Byzantine Agreement, blind quantum computation, and dual-use quantum sensing. These applications illustrate how technical capabilities may influence access, trust, privacy, oversight, and accountability, while demonstrating that technical guarantees cannot resolve institutional questions independently. We conclude that quantum technologies do not necessarily introduce unique governance challenges or require entirely new governance frameworks. Rather, they provide a context in which established questions of legitimacy, accountability, and equity must be reconsidered in relation to emerging technological capabilities and institutional choices.

What quantum mutual information adds to conventional correlation functions is often unclear. We study the spin-1/2 $J_1$-$J_2$ Heisenberg chain, using DMRG on infinite chains and periodic rings and an SU(2) decomposition of the mutual information into correlation channels. For singlet ground states the two-site mutual information is an exact function of the spin correlator, so any additional content must come from blocks. In the dimerized phase, blocks resolve bond-energy correlations in the SU(2)-scalar channel without an independent asymptotic length: singlet and triplet correlation lengths agree to about 1%. The scalar channel dominates block mutual information at large distances in the commensurate regime up to $J_2/J_1=0.40$, but falls to a few percent beyond the disorder point, which coincides numerically with the Majumdar-Ghosh point $J_2/J_1=1/2$; the structure-factor peak splits only at the Lifshitz point $J_2/J_1=0.520622(2)$. On the gapless side we compare block mutual information on rings extrapolated to infinite size with the two-interval prediction of SU(2)$_1$ conformal field theory across the Kosterlitz-Thouless point $J_2/J_1=0.241167$. There, for block lengths $l\le6$, the correction decays as $l^{-p}$ with $p=1.96$-$2.07$, and any logarithmic term is at least 60 times smaller than in the Heisenberg chain. Expanding in the marginal coupling (from level spectroscopy) the first-order coefficient is consistent with $l^{-2}$ scaling and the second-order coefficient is positive for $x\le1/4$, suggesting that the mutual information relative to the field-theory value becomes stationary at the KT point for large blocks. The scalar-channel share approaches 1/4 at small cross ratio $x$, as expected from SO(4) symmetry; under two stated assumptions its first-order response to the coupling is $(3/8)\ln x-5/8$ at small $x$, matched by the $l=4$ data within 1-3% at $x\le1/9$.

Can collective quantum-noise measurements distinguish different mode temperatures from one common temperature when the coupling spectrum is unknown? For stationary Gaussian oscillator environments, we derive a sharp bandwidth threshold for an exact thermal alias on the integer-time sampling lattice. The threshold depends on temperature order through the quantum response. For frequencies within the first alias period, fixing sufficient integer-time correlations makes one additional fractional-time fluctuation observation enough to exclude every common-temperature fit. A calibrated second pulse width provides another route through the same collective port: both widths must probe one spectrum and retain their measured variance scales. For a specified two-mode example, continuous-frequency certificates cover all common temperatures and uncertainty in a shared pulse ramp. A binary-readout protocol combines randomly interleaved matched references with collective-variance and coherence checks to handle Gaussian oscillator loss and predictable readout drift. The selected fractional-clock and two-width designs require approximately $3.8\times10^7$ and $1.6\times10^8$ outcomes for at most 5% type-I error and at least 95% power on the stated alternative class. These theoretical and numerical acquisition guarantees assume independently validated preparation, spectral support and control specifications; validation costs are additional. The result identifies which new observation makes thermal-model testing informative when mode-resolved access is unavailable.

Seeking a pictorial representation of four-party absolutely maximally entangled (AME) states of local size six, we independently construct a real AME$(4,6)$ state from a table of signed Pauli matrices. Its two-unitary matrix has $60$ nonzero entries, equal to $1$ or $\pm 1/\sqrt{2}$. A locally equivalent representative yields a genuine geomagic square, where every row, column and main diagonal tiles a hexagon and all $36$ pieces are pairwise non-congruent. Colors, shapes and hatching retain the full tensor, allowing its reconstruction from the picture.

Weak measurements are used to amplify small signals, to address foundational questions, and to characterise quantum states without tomography. In direct state reconstruction each amplitude of the state vector is proportional to a single complex weak value, which for a temporal pointer is read from the mean arrival time and the mean frequency of the postselected pulse. Such an experiment requires three quantities to be fixed, the coupling, the angular resolution demanded of the reconstruction, and the set of states over which the method remains usable, and these are commonly set by the available apparatus rather than derived. We derive all three for a Gaussian temporal pointer and an arbitrary postselection state. The states that cannot be reconstructed form a spherical cap centred on the state orthogonal to the postselection, whose geodesic half-angle follows from the largest of three independent thresholds and involves no adjustable parameter. Two states are distinguishable only if they differ by more than a minimal step fixed by the coupling, by the number of incident photons and by the sensitivity of the weak value along the path followed. For an inversion at first order in the coupling the systematic and statistical errors are opposed and fix an optimal coupling that varies as the inverse sixth root of the number of incident photons, whereas an exact inversion at finite coupling removes the systematic error, the remaining bound being one on the two-centroid readout rather than on the inversion, since below an amplitude equal to a quarter of the coupling two states give the same pair of centroids while their profiles differ. These results allow a direct reconstruction experiment to be dimensioned before the apparatus is assembled.

Liouville equation contains an excess coupling term in addition to the Poisson bracket. Neglecting this term yields the Poisson bracket mapping equation (PBME). We expand the mapping dependence of the density in Hermite functions about the Gaussian factor common to all physical mapping densities. In this basis, the excess coupling term acts purely as a raising operator and exactly cancels the raising contribution generated by the back–reaction force. Consequently, the exact dynamics does not generate higher Hermite orders and closes on a finite, sparse system of equations for the coefficient fields. Within the physical sector, these equations reduce to the subsystem quantum–classical Liouville equation. In contrast, the PBME retains the raising contribution of the force, modifying the back reaction within the physical sector while continuously generating higher Hermite orders. For Tully's dual avoided crossing model, direct propagation of the coefficient equations confirms this finite closure and agrees with independent solutions of the subsystem equation. Comparison with converged full quantum dynamics further shows that, across all regimes examined, the PBME is less accurate than the quantum–classical description for populations, coherences, and momentum distributions.

We describe an optimal-control strategy designed to accelerate the dissipative preparation of complex, highly entangled quantum many-body states. Analogous to optimal steering of isolated quantum systems, our scheme identifies control pulses that guide the evolution of open quantum systems along trajectories of instantaneous steady states while minimizing leakage resulting from non-adiabatic transitions. In many cases of interest, these control parameters can be derived analytically and without the need for computationally expensive numerical simulations of the full many-body master equation. We apply this technique for the preparation of bi- and multipartite entangled states in qubit systems coupled to a common photonic waveguide or a distributed squeezed reservoir. In both scenarios, our optimal-control strategy significantly outperforms the bare relaxation dynamics after a quench, reducing preparation times of near-maximally entangled states by orders of magnitude. This drastic speedup makes dissipative entanglement distribution protocols compatible with high-fidelity quantum information processing applications and illustrates more broadly the potential of leakage minimization for accelerating reservoir-engineering schemes.

Bastidas et al. (2025) highlighted the importance of exploiting group symmetries to reduce computational overhead and unify simulation methods across both condensed matter physics and ab initio quantum chemistry. I discuss the discrete character transform, which is the group Fourier transform restricted to $Z(\mathbb{C}[G])$, the center of the group algebra, where class functions form a commutative convolution algebra and irreducible characters are its spectral basis. The normalized character table of a non-abelian group can be obtained through a restriction operator, which means an efficient quantum character transform for any finite group with an efficient quantum Fourier transform. I give complementary quantum algorithms for class convolution based on direct class-sum block encoding and spectral implementation in the character basis, explaining their applications to symmetry-adapted many-body dynamics, molecular and spectroscopic symmetry analysis, and quantum walks, as well as characterizing the central information used in hidden-subgroup problems, including its limitations for graph isomorphism.

Photonic technologies are among the leading platform contenders for demonstrating quantum advantage. Nevertheless, photon losses represent the major hurdle for the realization of a fault-tolerant optical quantum computer, and the need for an accurate characterization of this phenomenon is crucial for classical simulations of quantum algorithms on noisy backends. The noisy regime would require the simulation of the algorithm on a Fock backend or rather assuming the a priori hypothesis on the uniformity of the optical losses, which may lead to wrong predictions about the outcome from the algorithm on a cerain hardware. We propose a Gaussian model that can reproduce a lossy dynamics through the experimental characterization of imperfect interferometers, yielding the corresponding mean vector and the covariance matrix. Such model can be adapted to any continuous-variable architecture (spatial or time-bin encoded) and for both the Gaussian boson sampling or general-dyne based algorithms. Eventually, we quantify the drift of optical losses from being uniform throughout the multiport interferometer by a numerical simulation. This work proposes a blueprint for future characterizations, tailor-suited for specific devices and architectures, as well as for potential error correction and mitigation techniques, and it paves the way for realistic simulations of quantum algorithms on NISQ optical platforms.

Bell-test data are typically used to certify nonlocal correlations, while quantum metrology is concerned with the sensitivity of measurement statistics to unknown parameters. Here we connect these tasks at the level of experimentally accessible Bell statistics. Using standard moment-based Fisher-information inequalities, we derive lower bounds on the classical Fisher information directly from Bell scores and their parameter dependence, without requiring full state tomography. For CHSH measurements we establish a hierarchy between the information contained in the full outcome record, the set of individual correlators, and the compressed Bell parameter, thereby quantifying the metrological cost of data compression. In polarization-phase sensing, this hierarchy reveals a Bell-metrology tradeoff: the point of maximal CHSH violation need not maximize, and can even suppress, the Fisher information carried by the Bell score itself. We further derive finite-sample lower-confidence bounds from coincidence counts and analyze the effects of biased marginals, accidental coincidences, visibility loss, and multipair emission. The framework provides a practical route for extracting metrological guarantees from Bell-type experiments using only standard correlation measurements.

Absolutely maximally entangled states of four six-level systems, AME$(4,6)$, are the quantum solutions of Euler's problem of the thirty-six officers. Until recently all reported solutions were complex, and it was conjectured that no real orthogonal 2-unitary matrix of order $36$ exists. We give real AME$(4,6)$ states with $60$ non-zero coefficients in $\{\pm1,\sqrt2\}/\sqrt{72}$. Of their thirty-six officers, $12$ are classical, as some must be whenever fewer than $72$ coefficients are non-zero. They lie in the $-1$ eigenspace of an order-$4$ local symmetry, and on their support the AME conditions become linear. We derive two closed-form families of AME$(4,6)$ states that meet at one of these states: a $10$-parameter family that is supported on $72$ basis states, and an $11$-parameter family on $60$ basis states. At each of its two ends the first family loses $12$ coefficients, and the AME states on the remaining $60$ basis states form an $11$-parameter family: the second family at one end, and an analogous family at the other. These two $60$-term families contain $4096$ real AME states up to diagonal local unitaries, $1024$ of which are limits of the first family. They fall into exactly $20$ classes under local unitaries and permutations of the parties, and we certify their separation with interval arithmetic.

Quantum aging transition has recently been reported, whereby the oscillatory dynamics of a network of globally coupled quantum self-sustained oscillators is degraded sharply when the fraction of inactive nodes exceeds a critical value. Here we explore the reverse process: the revival of rhythmic dynamics from an aged state in a quantum oscillator network by introducing a controlled incoherent single-boson pumping channel. Using a self-consistent quantum master equation in the Lindblad form for globally coupled active–inactive quantum Stuart–Landau oscillators, we show that increasing the pumping strength progressively suppresses the aging transition and eventually eliminates it, restoring rhythmicity even when all oscillators are inactive. Remarkably, complete compensation of the coupling-induced dissipative loss is not required; a substantially weaker pumping strength is sufficient to eliminate the aging transition. We show that the revival is governed by a redistribution of the Fock-state population of the inactive oscillators toward higher-occupation states. Our results establish controlled incoherent pumping as an effective mechanism for restoring dynamical robustness in quantum oscillator networks.

This article aims to introduce the bosonic asymmetric quantum conditional mutual information (QCMI), $I_{B}(A; B|C)$, as a rigorously defined information-theoretic quantity for continuous-variable (bosonic) systems. After defining $I_{B}(A; B|C)$ through quantum instruments on infinite-dimensional Fock spaces, we prove that Bose-Einstein condensation (BEC) induces a logarithmic divergence $ I_{B}(A; B|C) \geq \alpha \log_2 (N_{0}^C+1)$, which further establishes $I_{B}(A; B|C)$ as a quantum-information order parameter for BEC with power-law scaling near the critical point. We provide the complete five-step proof of this result, connecting measurement back-action, off-diagonal long-range order, and Jensen's inequality. In the condensed phase, the effective causal propagation velocity is set by the Bogoliubov sound speed $c_s$ in the long-wavelength limit, and vanishes continuously at the superfluid–Mott-insulator transition. Applications to composite bosons, the BEC–BCS crossover, and a quantum-gas-microscope measurement protocol are presented. Finally, we demonstrate how the reduced bosonic QCMI serves as a finite-size scaling probe analogous to the Binder cumulant.