Papers

The term “partition logic” denotes two constructions at different levels. In automaton and generalized-urn models, selected partitions generate Boolean event algebras whose contextwise union forms a concrete pasted event structure; in Ellerman's framework, whole partitions are classifications governed by refinement and partition operations. For a finite set $U$, Ore's correspondence maps each generator $\pi$ to its Boolean algebra $\BA(\pi)$, but it neither identifies the pasted carrier with $\Part(U)$ nor makes pasting a partition operation. It yields $\BA(\pi\wedge\sigma)=\BA(\pi)\cap\BA(\sigma)$ and $\BA(\pi\vee\sigma)=\langle\BA(\pi)\cup\BA(\sigma)\rangle_{\rm BA}$, where $\langle\cdot\rangle_{\rm BA}$ denotes Boolean-algebra generation. Thus meet captures the common event algebra, whereas join gives the ambient Boolean closure. Chinese-lantern, Firefly, and triangular examples distinguish shared events, atomic intertwining, and inherited concrete order. Ellerman's direct-sum decompositions (DSDs) provide a vector-space analogue: component projections of an orthogonal DSD resolve the identity and encode exclusive outcomes, but its components are not equivalence classes of vectors. Gleason and Kochen–Specker applications require globally context-consistent valuations on those projections.

Whether entanglement with a negative partial transpose (NPT) can be undistillable is a longstanding open problem. In the canonical family of DiVincenzo et al., the one-copy-undistillable region was conjectured to remain undistillable at all copy numbers. We refute this: in every dimension $d\geq3$, one vertex of this region is two-copy distillable, via an explicit Schmidt-rank-two tight-frame witness. The separation persists on an open set, while other states in the same region are provably two-copy undistillable. Twirling our counterexample into Werner form makes it two-copy undistillable, so this standard reduction can erase finite-copy distillability.

Quantum circuits with measurements and unitary feedback (MF) can prepare long-range entangled states in constant depth, but a systematic construction of the MF preparation circuit for a given target state remains underexplored. We develop such a scheme for one-dimensional states, based on the notion of pushable defects: virtual-bond operators of a matrix product state that can be pushed through the tensor at the price of a physical feedback unitary. We show that the set of pushable defects, together with their pushing relations classifies finite-depth MF-preparable states and dictates their preparation circuits. To each class of the target state $|A\rangle$, we associate a state $|B\rangle$ from which $|A\rangle$ can be prepared using a 1-round MF circuit; in particular, $|A\rangle$ is preparable from a product state using a circuit with 1 round of MF whenever $|B\rangle$ is preparable by a finite-depth local unitary (FDLU) circuit. For a general target state, the scheme is obtained by iterating this procedure until the associated state is FDLU-preparable. For open-boundary matrix product states, the scheme is complete: it constructs a preparation circuit whenever finite-depth MF preparation with left-conditioned feedback corrections is possible. Pushable defects and pushing relations thus emerge as a unifying principle for quantum state preparation via measurements and feedback. This characterization further reveals an intrinsic connection between MF circuits and non-invertible symmetries: states with certain classes of pushing relations are related to a product state by Tambara-Yamagami duality operators, or by continuous cosine symmetry operators with fusion rules $L_{\alpha} L_{\alpha'} = L_{\alpha+\alpha'} + L_{\alpha-\alpha'}$, together with their generalizations up to (not necessarily transversal) gates.

Neural quantum states (NQS) offer highly expressive variational wavefunctions, but their optimization is frequently bottlenecked by redundant parameters and poorly conditioned landscapes. We demonstrate that embedding Hamiltonian symmetries directly into the variational parameterization geometrically regularizes this learning problem. For Boltzmann-family NQS, we enforce symmetries by tying local Pauli-$Z$ generators along physical geometric orbits, analytically collapsing the trainable coefficient space prior to optimization. To quantify the resulting optimization geometry, we introduce a geometric metric built on the Jacobian and Hessian of the optimization landscape. This framework evaluates the fraction of the physically accessible state space that corresponds to high-quality, low-energy solutions. Evaluating our approach on transverse-field Ising (TFIM) and XXZ spin chains shows that symmetry compilation excises the vast majority of parameters while maintaining ground-state accuracy within the resolution of the reported benchmarks. In large TFIM systems, strong spatial constraints compress thousands of parameters down to tens, delivering substantial runtime accelerations. Our geometric diagnostics indicate that symmetry produces a more favorable target-aware geometry by concentrating the reachable state space around low-energy solutions while retaining broad target basins. Together, our results indicate that symmetry compilation concentrates the expressive power of NQS on states relevant to the target problem, thereby reducing model size and training cost without sacrificing accuracy.

We propose an experiment to test Bell nonlocality, a genuine nonclassicality, for the gravitational field. Two masses with embedded entangled spins (e.g., two diamonds with their NV-centre spins entangled) are placed well outside each other's light cones, ensuring a locality-loophole-free scenario. The spins are then coupled to the motion of their respective masses to generate spatial superpositions. Finally, local measurements are performed only on the gravitational fields of the two masses. If gravity is quantum, then the two entangled masses would entangle their gravitational fields, leading to correlations certifying Bell nonlocality of gravity. Trapped and ground-state cooled nano-objects with micron-sized spatial superposition are sufficient for this test. This goes beyond the recent proposals to test nonclassicality of gravity by providing, for the first time in the literature, a minimal tool to (i) create Einstein-Podolsky-Rosen (EPR) state of gravitational curvatures, (ii) witness entangled gravitational curvatures, (iii) rule out any local-realist description of gravity, and (iv) achieve a loophole-free test of gravity's nonclassicality in a fully device-independent way.

The management of ancilla qubits has become a critical technique for reducing quantum circuit width. Dirty ancillas, which may be borrowed from any temporarily idle qubit regardless of their initial states, offer substantial flexibility for width optimization, but their use has so far required manual and error-prone handling. We formalize the dirty-qubit borrowing problem and establish a fundamental computational limit by proving its NP-hardness. To support practical optimization, we present \bona, the first scheduler for dirty-qubit borrowing, built on a novel depth-aware heuristic algorithm. We evaluate \bona~ across a variety of benchmarks, including practical quantum circuits and randomly arranged compositions of real circuit modules, and find that it reduces nearly 99% of dirty ancillas on average with controlled depth overhead. In particular, for parallel quantum walk—an essential component of parallel Hamiltonian simulation—\bona~ matches the circuit width achieved by the clean-qubit schemes of \citeauthor{jiang2024recycling}~(\citeyear{jiang2024recycling}) and \citeauthor{quantinuum}~(\citeyear{quantinuum}), but attains significantly smaller circuit depth, providing concrete evidence that dirty ancillas offer unique optimization advantages in circuits with certain parallelism.

Nuclear gradients and Hessians are fundamental quantities in computational chemistry, essential for a wide range of applications including geometry optimization, vibrational spectroscopy, and molecular property calculations. In this work, we present their analytical implementation on quantum hardware. The methodology is formulated within an active-space framework combining orbital optimization and linear-response theory. On the quantum-computing side, the approach employs the tiled unitary product state (tUPS) ansatz to directly evaluate the tensor elements required for solving the response equations. Moreover, the expectation values are corrected using an adapted confusion-matrix error-mitigation scheme in combination with post-selection criteria. The resulting workflow is assessed on molecular hydrogen and on water through the calculation of potential energy surfaces, nuclear gradients, Hessians, and vibrational frequencies, enabling the evaluation of both its capabilities and current limitations. The results demonstrate good performance for the hydrogen molecule, whereas the water molecule provides a more demanding test of quantum-hardware resources and highlights the trade-offs associated with error-mitigation strategies. The quantified analysis of the results identify the main sources of errors, suggesting improvement directions for more accurate quantum computer applications.

Estimating the quality of raw entangled states and distilling high-fidelity entanglement traditionally require two separate link-layer protocols in a quantum network stack, each consuming its own share of fragile entangled pairs. The recently introduced distimation concept merges these two protocols by directly extracting state estimation data from the classical syndromes generated during entanglement distillation. By removing the dedicated "test-then-distill” stage, distimation lowers the number of raw entangled pairs required to operate the network, reduces latency, and streamlines the network control plane. The paradigm is especially attractive for near-term hardware platforms, where entanglement generation remains a severe bottleneck. Alongside these promises, distimation introduces new engineering challenges, ranging from accurate local-device modeling to protocols for tracking time-varying sources. This article surveys the core principles of distimation, quantifies expected gains for realistic architectures, and outlines a research roadmap toward making distimation a standard building block in future quantum networks.

Quantum subspace methods are often compared by basis dimension or energyerror, although their dominant experimental costs arise from different statepreparations, measurement settings, and shot allocations. We present theDyadic Adaptive Clifford-Algebra Subspace Eigensolver (DA-CASE), whose basisstates are virtual directions $A_i|\psi\rangle$ generated from one reference.Overlap, Hamiltonian, and observable matrices are reconstructed from onecached set of Pauli expectations on that reference. The method thereforetrades multiple prepared basis states for a potentially wide measurement bank.We make that trade explicit on a frozen eight-qubit H$_4$ Hamiltonian. Twogenerator resolutions reach the same nine-dimensional subspace and the sameenergy to machine precision, while the retained bank changes from 7371 to 2240Pauli words. A reference-conditioned symmetry test certifies the narrower spanwithout asserting that its individual Pauli words conserve the sector asabstract operators. Independently, a dyadic commuting hierarchy reduces thedeterminant bank from 913 qubit-wise-commuting settings to 64 fully commutingsettings, while exposing the added logical-CX cost. In a separate four-qubitfinite-shot diagnostic, covariance-aware allocation reduces theprojected-matrix variance target by 68.9%. Mode-wise overlap regularizationremoves the observed catastrophic energy estimates and lowers RMSE, butdoubles the median error relative to a fixed cutoff. These are small-instanceexact and Monte Carlo results, not a hardware demonstration, scaling result,or quantum advantage claim. The contribution is a single-referencemeasurement architecture and a resource ledger that keeps contexts, settings,shots, circuit depth, and post-selection retries in their proper units.

We report experimental and theoretical investigations of interacting excitons of the yellow series in cuprous oxide (Cu$_2$O) with principal quantum numbers up to by means of second harmonic generation (SHG). Using picosecond pulsed laser excitation up to 10 GW/cm$^2$ peak intensity we observe a pronounced change of the spectra with increasing pump laser intensity: an energetic shift to lower absolute energies and a spectral broadening. The absolute intensities of the spectral lines scale for low powers with the square of the pump power, but saturates at higher powers. At still higher powers the SHG intensity is actually reduced. To explain these results quantitively, we developed a semi-classical theory of resonant SHG where the process of SHG is fully coherent. The excitons are assumed to be bosons interacting by a distance dependent potential giving rise to both the changes in spectral line shape and the saturation by a $\it{Rydberg}$ blockade. The concomitant measurement of two-photon absorption allows to derive quantitative values for the exciton-exciton interaction. While the results agree in order of magnitude with those calculated by state-of-the art atomic-like van der Waals interaction theory, the scaling with principle quantum number is quite different. As a possible screening by an electron-hole plasma created by three-photon absorption into blue and violet band states could be ruled out, our results point toward fundamental differences between excitons and atoms.

Many industrial optimization tasks can be modeled as graph coloring, where adjacent vertices must have different colors. This NP-hard problem is challenging for large graphs. We present a quantum encoding requiring qubits that scale logarithmically with the number of colors and linearly with vertices. Using adiabatic evolution with a novel mixer Hamiltonian and vertex terms, we compute the chromatic number and demonstrate robustness by solving constrained truck loading problems.

Recent studies have revealed that not only does the correspondence between spectral winding numbers and skin modes break down in non-Hermitian systems, but the energy spectrum itself is highly sensitive to generic perturbations, system size, and boundary conditions. In amorphous non-Hermitian systems, where the positions of lattice sites are uncertain, the spectral instability becomes even more severe, making it difficult to identify stable topological edge states from the eigenvalue spectrum alone. To overcome this challenge, we introduce a correspondence between stable zero-mode singular states and mid-gap states of the energy spectrum in the thermodynamic limit. Because the singular value spectrum is highly robust against small perturbations and variation in size, topological edge states can be reliably probed via singular values even in finite-sized systems. Based on the singular-value decomposition of the Hamiltonian, we construct a topological invariant in real space to characterize the associated topologically protected edge states. Our approach provides a general strategy for exploring point-gap topology in real space and redefine the non-Hermitian skin effect from a new perspective.

The Born-Oppenheimer (BO) and single-surface Born-Huang (BH) approximations replace the full molecular problem by nuclear motion associated with one clamped electronic state, whereas the full BH expansion and exact factorization (EF) are exact representations. We use two analytically transparent models to identify what controls one-surface error. For Fernández's bilinearly coupled oscillators, the Brattsev ground-state bracket was already known; we derive closed-form differences proving strictness for every positive nuclear mass and nonzero stable coupling. Using Hunter's conditional-amplitude construction, we place the closed-form ground-state EF potential alongside BO and single-surface BH. Exact excited-state calculations show that the bracket does not extend through the spectrum. The diagonal BH correction is the quantum-metric coefficient of the retained electronic state divided by twice the nuclear mass. Fernández's sixth-order expansion shows that the next omitted correction contains the same derivative couplings, an additional inverse electronic-energy separation, and a factor depending on the nuclear state. We therefore add a two-state model with a position-dependent gap. Decreasing its minimum separation makes the metric higher and narrower while leaving the total Fubini-Study length equal to pi/2. The exact EF, BO, and BH potentials can differ visibly even when their nuclear ground-state amplitudes are nearly identical. The two models show that one-surface accuracy depends on nuclear mass, electronic-state variation, energy separation from omitted states, and the nuclear wavefunction.

Suppressing coherent energy backflow while maintaining extractable energy in a stable nonequilibrium state remains a central challenge for quantum energy storage. Here, we introduce a reservoir-engineered dual-charger quantum battery architecture, in which nonequilibrium dissipation is exploited as a control resource to stabilize useful stored energy. A hot-reservoir-coupled driver supplies excitations, while a cold-reservoir-coupled cache biases the resonant three-body transition toward charging and suppresses the dressed-state coherences responsible for energy backflow. This mechanism establishes a population-inverted steady state with finite ergotropy and converts reversible charger–battery exchange into persistent energy storage. For uniformly spaced multilevel batteries, we show that the stored energy and ergotropy scale approximately linearly with the number of accessible levels, while the stored-energy utilization approaches unity. The accompanying stationary heat current provides a thermodynamic signature of the charging regime. Our results demonstrate dissipation engineering as a strategy for achieving stable and scalable quantum energy storage beyond transient coherent charging protocols.

We investigate the redistribution of continuous-variable quantum discord within the framework of an expanding universe. We find that quantum discord exhibits stronger sensitivity to the spacetime expansion rate than to the expansion volume. As both the expansion rate and expansion volume increase, the initial quantum discord shared by the two bosonic modes decays, while quantum discord is induced in additional mode pairs by the underlying spacetime expansion, signaling a global redistribution of quantum correlations across the system. Specifically, the induced discord is largest for cross-observer bosonic-antibosonic pairs, followed by same-observer bosonic-antibosonic pairs, and smallest for the pair of antibosonic modes. Furthermore, our quantum discord analysis demonstrates that particles with lower momentum and optimal mass serve as more favorable candidates for extracting information about the expanding universe. This work substantially enriches the theoretical framework of quantum discord in expanding spacetimes, and provides new perspectives as well as a solid theoretical foundation for further investigations.

Levitated mechanical oscillators are emerging ultrasensitive sensors with tremendous potential in both applied and fundamental physics. Levitated ferromagnets, with internal spin noises rapidly averaged, promise ultrahigh magnetic sensitivity. Here, we demonstrate a milligram-scale diamagnetically levitated ferromagnet system operating at room temperature. Through optimized geometry and multi-channel dissipation control, we achieve a magnetic sensitivity of 23~fT$/\sqrt{\text{Hz}}$ at frequency of 100-Hz level. We anticipate that a ferromagnetic magnetometer with subfemtotesla sensitivity is within reach, after modest technical improvements. This platform establishes a high-performance magnetometer for biomagnetic field detection and beyond-standard-model force searches.

Spin-photon interfaces are essential for communications between distant spin qubits in quantum technologies, but the interband optical excitation can also damp electrically driven hole-spin Rabi oscillations in semiconductor self-assembled quantum dots (SAQDs). We report a device-level modeling workflow that integrates realistic SAQD geometry and multiband electronic-structure analysis with models of electrically driven spin control, interband optical transitions, and open-system dynamics. This workflow enables device-level estimation of Rabi-oscillation damping arising from repeated interband absorption-emission cycles. As an example, for a gated GaAs SAQD subjected to a uniform magnetic field $B_0$ along the growth direction of the SAQD, we predict the Rabi frequency of the hole spin qubit and its damping under external illumination. At $B_0=2$ T, the calculations yield a hole-spin Rabi frequency of 37.3 MHz. When the electrically driven SAQD is illuminated by a broadband LED centered at a wavelength of 790 nm, increasing the optical power from 0.3 to 1.5 mW shortens the Rabi-oscillation decay time from 90.3 to 17.5 ns. Increasing the SAQD height reduces the electron-hole overlap and thus the emission rate, but the resulting redshift moves the interband transitions into stronger spectral overlap with the LED spectrum, thereby increasing the rate of repeated absorption-emission cycles and enhancing photon-induced Rabi-oscillation damping. The results show that geometry, spin-control conditions, and illumination spectrum should be co-optimized in semiconductor spin-photon devices.

The relativistic dynamics of bound states across inertial reference frames are investigated using the computational quantum field theory (CQFT). The results reveal that the spatiotemporal properties of bound states within a given potential well are strictly frame-dependent. Crucially, this spatiotemporal modulation of the external field enables a reduction in the laser intensity threshold required for vacuum electron-positron pair creation. Analytical and numerical calculations demonstrate that this threshold reduction originates from the Lorentz transformation of the four-momentum, which reshapes the vacuum excitation pathways in phase space. By developing CQFT, we establish a comprehensive framework in which relativistic effects intrinsically govern the quantum vacuum decay process

Quantum algorithms are conventionally presented with their input state supplied for free. When the input is classical data, this convention conceals a cost that is frequently larger than the algorithm it precedes. We review what the three standard encodings, such as basis encoding, amplitude encoding, and Grover–Rudolph distribution loading, actually cost once transpiled to a hardware gate set, and argue that the resulting $\Theta(N)$ bound is a counting theorem rather than an engineering limitation that improved hardware will remove. Measured gate counts for a representative loading task are reported: an optimal library implementation requires $247$ CNOT gates at $n=8$ qubits and doubles with each additional qubit, while the classical preprocessing that produces the rotation angles requires reading the entire input vector. We show how this cost eliminates the quadratic advantage of quantum amplitude estimation for Monte Carlo integration, and argue that the same accounting constrains quantum machine learning more broadly: the strong input models that make quantum algorithms fast on classical data also enable classical dequantization, and quantum kernel methods carry a $\Theta(M^2)$ state-preparation cost for the Gram matrix that does not amortize. We explain that the efficiently preparable states, device-generated distributions, variationally learned loading, and amortized preparation are required to get advantage from quantum machine learning and close with a checklist for evaluating input-dependent advantage claims. Executable notebooks reproducing every construction and measurement discussed here are available.

Shadow tomography addresses the task of efficiently predicting many expectation values of an unknown quantum state from randomized measurements on comparatively few copies. Existing analyses promise large scaling advantages, but the optimal strategies realizing these guarantees are not always known, and the required measurements are potentially challenging to implement on current hardware. We address this gap for Pauli observables by computing optimal sample-complexity parameters and constructing optimal measurement strategies under realistic resource constraints. We focus on memoryless protocols, where each copy is measured only once, and on measurements with bounded interaction range. Our approach reduces the problem to the analysis of graph parameters of the frustration graph encoding the Pauli anticommutation relations. We provide efficient numerical methods for the general case and analytically prove that Clifford measurements are optimal in many situations. This includes all perfect graphs, all single-qubit, all two-qubit measurement scenarios, and more. Applied to Hamiltonian energy estimation, our framework yields constructive strategies and improved variance bounds for molecular benchmarks.

We determine the covering radius of the topological closure of the single-qubit Clifford hierarchy in $\SU(2)\cong S^3$. This closure is a union of $18$ great circles — the Clifford–Pauli circles — and we prove that its covering radius is $\arccos\sqrt{5/6}$. The extremal points, which we call deep holes, form a single orbit of size $192$ under left and right multiplication by Clifford gates, and are described in closed form. Equivalently, the minimum over one-qubit unitaries of the all-level Clifford fidelity is $5/6$. The proof rests on two structures attached to the configuration of $18$ planes in $\R^4$: their centered rank-two projectors form an orthonormal basis of the irreducible $\SO(4)$-module $\Sym_0(4)$, and the projection profile of a unit quaternion is exactly its image under the double cover $\SU(2)\to\SO(3)$. These reduce the covering problem to a minimax statement for the $\ell^\infty$-norm on $\SO(3)$ which we solve exactly, classifying its equality cases.

Fisher information appears in quantum theory in two mathematically distinct settings: as a classical probability functional in variational reconstructions of Schrodinger dynamics and as the quantum Fisher metric of parameterized density operators. Here we examine how far these roles can be connected without identifying the two objects. Starting from a Hamilton-Jacobi ensemble action, we recover the Fisher term that generates the quantum potential and isolate its contribution to the kinetic-energy expectation. We then analyze the quantum Fisher information matrix (QFIM) of bipartite states. For any pure two-qubit state, the optimized magnitude of the off-diagonal QFIM element for normalized local generators equals the concurrence, while a collective phase generator yields FQ = 4 C^2. Extending the optimized pure-state quantity by a convex roof gives an exact identity with Wootters concurrence for arbitrary mixed two-qubit states. This differs from evaluating the QFIM directly on a mixed density operator: for Werner states the raw optimized cross-QFIM is 2 p^2/(1 + p) and remains nonzero inside the separable region. The gap between the raw and convex-roof quantities therefore isolates, for this family, correlation geometry not captured by entanglement. Finally, in a two-path interferometer with a which-way marker, the optimal phase Fisher information available from local output statistics is I_phi^opt = V^2. These results place probability-gradient energy, bipartite correlation geometry, entanglement, and decoherence-induced loss of local phase sensitivity in a common mathematical setting while preserving the distinctions between classical Fisher information, QFIM geometry, Bell nonlocality, and global phase quantization.

For a many-particle pure state in a fixed position representation, we consider the mixed cross-particle derivatives of the logarithm of the wave function. Their real part is one half of the Holland-Wang local dependence function of the configuration density, while their imaginary part is the cross-Jacobian of the Madelung velocity field. On a node-free product region, vanishing of all cross blocks throughout the region is equivalent to local multiplicative separability. Under Schrodinger evolution with a real scalar potential, the initial growth of a cross block from a separable state is sourced by the corresponding mixed Hessian of the potential and is purely imaginary to first order in time. The construction is a local separability and dependence diagnostic, rather than a basis-independent entanglement measure.

Frequency-multiplexed superconducting-qubit control requires more than carrier assignment: the RF budget of a shared source can perturb multi-qubit rotations through finite bandwidth, crest factor, clipping, quantization, jitter, spurs, compression, crosstalk, and leakage. We present an RF-budgeted frame-compilation and validation workflow that combines qubit-control identity (QID) records, a MATLAB/Simulink-based circuit-informed RFSoC source-chain model, QuTiP qutrit dynamics, and Qiskit-derived algorithm workloads. QID records encode qubit-specific computational and leakage transition frequencies, pulse parameters, and drive-scale calibration, while the RF-chain profile and effective crosstalk-coupling matrix are provided as separate compiler inputs. Candidate multitone RF frames are scheduled under RF-budget constraints, propagated through the RFSoC model, decoded into computational and leakage transition frames, and evaluated in QuTiP for rotation error, leakage-aware fidelity, computational-subspace survival, and transient leakage. The studies progress from single-qutrit pulse closure to pairwise coexistence, multitone RF-frame capacity, and Bernstein-Vazirani (BV) and QAOA microwave layers extracted from Qiskit circuits. The simulations show that longer pulses improve per-frame aggregation but do not necessarily minimize time-normalized layer cost; clustered frequency maps, larger rotations, and multitone leakage stacking tighten closure. Under the nominal RF budget, a Qiskit-derived 12-qubit BV -Y90 layer closes in three validated four-tone frames at 240 ns, while QAOA mixer partitions vary with rotation angle and pulse duration. All reported results are model-based, decoherence-free simulation diagnostics rather than measured hardware fidelities or wiring-reduction claims.

Non-Hermitian degeneracies are usually discussed through spectral coalescence, whereas entanglement is a property of eigenvectors and need not be fixed by the eigenvalues alone. We formulate a compact bipartite model that separates these two notions. A Hermitian operator with a degenerate eigenspace is transformed by an invertible non-unitary similarity map. The resulting Hamiltonian is non-Hermitian and retains a non-defective degeneracy at every finite value of the non-Hermiticity parameter. For an exactly solvable two-qubit realization, the right eigenstates evolve continuously from product states to maximally entangled states although the spectrum is unchanged. We distinguish the positive right-state reduced density matrix from the generally non-positive biorthogonal reduction, for which entropy may become complex. The same two-qubit solution gives a closed partial-transpose negativity and a Schmidt-gauged non-local magic. Entanglement grows monotonically with the non-Hermiticity parameter, whereas the non-local magic vanishes for both the product and maximally entangled limits and is largest at an intermediate coupling. In larger bipartite spaces, the Page entropy and Haar-averaged purity provide reference values for eigenstate typicality. These diagnostics separate non-defective degeneracy, exceptional-point sensitivity, Haar-typical entanglement, and non-stabilizer correlations without relying on a proliferation of basis-dependent spectral quantities.

We investigate the prepare-and-broadcast scenario, a multipartite extension of dimension-constrained prepare-and-measure experiments in which a quantum system is distributed to multiple receivers. We derive fundamental trade-offs between prepare-and-measure witnesses, Bell nonlocality, and quantum random access code performance. We further develop a semi-device-independent randomness certification framework based on prepare-and-broadcast witnesses, showing that the maximal quantum violation certifies two bits of joint randomness, exceeding the limit achievable from the CHSH inequality while remaining robust to noise. Finally, we show that the prepare-and-broadcast scenario naturally accommodates stronger adversarial models in which the eavesdropper retains a quantum system correlated with the measurement device, providing a natural framework for semi-device-independent randomness certification against quantum side information.

Quantum Key Distribution (QKD) provides information-theoretic security grounded in the laws of quantum mechanics, yet practical deployment increasingly extends beyond conventional point-to-point fiber links. Several rapidly emerging QKD directions are often studied separately, including adaptive protocol and parameter support; free-space, satellite, UAV, and high-altitude platform (HAP) channels; integration with IoT and 6G networks; quantum-secured federated learning; Quantum Machine Learning (QML) assisted decision support; and steerability-aware estimation for one-sided device-independent QKD. This survey examines how Machine Learning (ML), Reinforcement Learning (RL), and QML address these specialized scenarios and organizes the literature into five thematic pillars: (I) adaptive protocol and parameter support; (II) free-space, satellite, UAV, and HAP-assisted QKD; (III) QKD for IoT, 6G, and quantum-secured federated learning; (IV) QML-assisted QKD functions; and (V) steerability-aware and one-sided device-independent QKD security estimation. For each theme, we follow a consistent problem, conventional solution, and ML/RL/QML solution structure and summarize reported gains using metrics such as accuracy, mean absolute percentage error, QBER reduction, and secret key rate improvement. We further provide thematic and cross-theme comparison tables and identify open challenges, including dataset scarcity, transferability across weather and mobility conditions, interpretability, trustworthy QML, and the boundary between ML-based decision support and security certification. This survey serves as a focused reference for adaptive, non-terrestrial, and application-integrated QKD systems.

Quantum reservoir computing offers a promising route toward energy-efficient machine learning by processing temporal information with minimal training overhead. Yet, the physical principles linking its energetic cost to computational performance remain largely unexplored. Here we show that, in an interacting spin reservoir, information encoding and information processing are governed by distinct physical mechanisms. In the weak interacting regime, we derive an analytical expression for the average (switching) work, showing that the energetic cost of encoding new inputs is determined by the local response of the reservoir units. In contrast, interactions primarily redistribute the encoded information, generating memory and nonlinear features while only weakly affecting the work. This separation produces opposite correlations between energetic cost and performance for representative linear and nonlinear benchmark tasks. Our results identify the switching work as the energetic signature of information encoding and clarify when energetic efficiency and computational performance are compatible.

Quantum software development requires provenance describing programs, compilation, execution, hardware characterization, results, and software environments, but providers expose this information through heterogeneous software development kits, application programming interfaces, and resource models. We analyze publicly documented provenance access across 15 quantum platforms spanning five hardware technologies and find fragmented, incomplete coverage, with compilation provenance weakest. We propose an evidence-aware OpenAPI 3.1 provenance contract and provider-adapter architecture, evaluated through a fixture-backed reference prototype at QMill covering Amazon Braket, IBM Quantum, and IonQ. All records validate against one common contract while preserving provider-specific semantics, explicit evidence origins, and graceful handling of incomplete data.

Nuclear quantum memories in the hard X-ray regime offer some key advantages over their optical counterparts, such as broader bandwidth and lower background noise. A Doppler frequency comb protocol has been theoretically proposed [X. Zhang et al., Phys. Rev. Lett. 123, 250504 (2019)] and recently demonstrated experimentally [S. Velten et al., Sci. Adv. 10, eadn9825 (2024)] for the storage and retrieval of X-ray photons. However, achieving on-demand retrieval remains challenging because of the requirement for precise and synchronous mechanical motion of multiple absorbers. We propose a hybrid, magnetic-Doppler nuclear frequency comb composed of Doppler-shifted resonant absorbers with lifted nuclear spin degeneracy, which expands the Doppler comb structure. By synchronously reversing the directions of both the magnetic fields and absorber velocities, the system achieves time-reversed phase evolution dynamics that allows for efficient on-demand photon retrieval with significantly reduced mechanical complexity.