Papers

Quantum uncertainty limits how strongly Wigner functions can concentrate in phase space. It is commonly conjectured that the vacuum Wigner function continuously majorizes that of any Wigner-positive state. However, by constructing Wigner-positive states whose localized quantum coherence lowers their Wigner entropy below the vacuum value, we show that this conjecture is incorrect. We restore vacuum majorization at finite resolution by integrating single-mode Wigner functions over concentric radial energy shells, obtaining probability vectors majorized by that of the vacuum for all Wigner-positive states and for Wigner-negative states with non-negative shell weights. Anchoring these shells to a fixed oscillator frame breaks affine symplectic invariance, rendering this relation strict for every non-vacuum Gaussian pure state. For Wigner-negative states, the persistence of negative shell weights defines a radial negativity scale with Airy-edge semiclassical asymptotics for highly excited Fock states. Operationally, we combine the majorization relation with partial transposition to obtain a two-mode entanglement criterion directly evaluable from radially binned joint homodyne outcomes without state reconstruction.

Detector outcome probabilities can be independent of a later measurement setting even when earlier timestamps, detector seeds, or environmental records depend on that setting. We characterize complete-record preservation for a positive wrapped-Cauchy retrocausal spin source. An antipodal identity yields necessary and sufficient conditions for passive and environmental readouts, and source compensation permits a common normalized analyzer for source spins and prepared continuations. Gaussian controller and reset calculations distinguish inverse raw history weights from normalized thermal operations. A quantum instrument provides an operational benchmark, whereas a setting-dependent separable source produces setting-dependent statistics at an earlier joint probe. For two equal-width contexts, a calibrated weak probe requires a minimum source change of $\operatorname{sech}(2g)/8$ in trace distance for exact protection at every nonzero strength. The signal–source-change tradeoff is sharp for this pair of contexts. A contextual positive-history construction recovers the isolated hidden law and preserves records for a specified class of finite adaptive quantum apparatuses, subject to quantum calibration and restricted field access. Direct readout of an added likelihood field distinguishes two future axes with unit probability. The analytical results are supported by continuous-angle and quantum-trajectory simulations, deterministic quadrature, and exhaustive enumeration of a finite policy class. The analysis concerns the specified statistical models; their microscopic physical realization remains an open question.

Recently, a hybrid qudit-qubit algorithm [1] was presented for solving the integer programming problem with a polynomial quantum advantage. In this work, we investigate the algorithm [1] to understand the role of qudits ($d$-dimensional quantum system) by conducting a comparative resource analysis with its qubit-only implementation and the classical simulability of the algorithm by exploring the entanglement structure. The resource analysis part is performed in terms of logical gate counts, and fault-tolerant physical resources, including non-Clifford gates. The hybrid qudit-qubit implementation has a more compact structure of the unitary operators as opposed to its qubit-only simulation which reduces the logical and fault-tolerant resource requirements. Two example problems, one with qutrits ($d=3$) and the other with ququint ($d=5$), when contrasted with their qubit-only implementation, within a simplified fault-tolerant resource model, showed $\sim 180 \times $ and $\sim 2220\times$ fewer total resource count, respectively. For the entanglement study, volume-law-like entropy growth and signatures of multi-partite entanglement is observed leading to increasing difficulty in the classical simulation of the algorithm. The algorithm generates synergistic tri-partite entanglement even for a quadratic problem, revealing that the algorithmic structure itself can generate higher-order entanglement in the system independent of the problem.

A spacetime seal, a cryptographic guarantee that a digital event has occurred at an approved location and time, can augment a digital signature with location attestation for legal, financial, and regulatory use cases. In adversarial settings any purely classical realization of such a seal can be spoofed. Quantum position verification (QPV) offers a physics-based solution, exploiting the no-cloning theorem and the no-signaling principle to certify a party's spacetime coordinates. While the feasibility of QPV has been recently shown via entanglement- and coherent light-based protocols, achieving loss tolerance for these schemes substantially increases implementation complexity at metropolitan scales. Here, we introduce and experimentally demonstrate a loss-tolerant QPV (LT-QPV) protocol whose security is independent of channel loss. We prove finite-size security against quantum polynomial-time entangled adversaries in the quantum random oracle model instantiated with cryptographically secure hash functions. Implemented entirely with commercial off-the-shelf components, our system certifies position within 22 minutes of net data collection time against a restricted adversary, with a clear path to real-time certification (<1s) with upgraded hardware. Our architecture, requiring only a single quantum verifier node alongside classical infrastructure, is naturally compatible with metropolitan-area quantum networks, establishing the foundations for scalable, physics-backed spacetime certification as a deployable service.

In the spirit of the Brown-Susskind conjecture, proven in \cite{haf} and \cite{li}, we study the growth of the dimension of the set of $n$-qubit unitaries which can be obtained as a product of a fixed number of $2$-qubit gates from a fixed set of pairs of qubits. We show that this dimension increases strictly when one more pair is added, for at least some choice of the $2$-qubit pairs at each step.

We construct boundary observables that retain memory for a quantified time window in quantum chains whose basis configurations carry a conserved ordered product of matrix labels. Under strong-irreducibility and proximality hypotheses on the label matrices, projective contraction of random matrix products localizes a conserved charge in the root-mean-square over uniform basis configurations. A finite-time inequality then converts readout overlap and reset leakage into a correlation bound: for a conserved reference observable $H$, a readout $F$, accumulated squared leakage $\mathcal B$, and the normalized Hilbert-Schmidt inner product, $\langle F,\Phi(F)\rangle\ge 2\langle H,F\rangle^2/(\|H\|_2^2+\mathcal B)-\|F\|_2^2$. Here $\Phi$ is a sequence of conserving channels and partial resets. The bound holds for each such circuit, without averaging its gates. It yields an exponential memory window in the distance from the noisy region, with quantitative corrections for spatially distributed noise and imperfect conservation. For a thirteen-state elementary-matrix model, exact polynomial certificates give root-mean-square localization error $e^{-r/1400}$ between the charge and its restriction to the last $r$ sites, and limiting variance at least $1/19$ for a rational charge. A related normalized-Gram charge gives an eight-site certificate retaining more than half the specified readout correlation through two boundary-reset rounds. Uniform depolarization imposes an inverse-noise-rate lifetime ceiling. A two-qubit IBM experiment illustrates the general reset inequality; it does not realize the matrix-product chain. We provide proofs, exact certificate programs, and an independent recount of the archived experimental outcomes.

Quantum-enabled semantic communication networks (QESCs) leverage quantum technologies to transmit data meaning efficiently, yet face challenges from costly resources and noise. This letter introduces Quantum Markov Blankets (QMBs) to QESCs, a novel framework to isolate essential quantum information for semantic transmission. We prove QMBs' validity using quantum conditional mutual information, showing that they shield semantic content from irrelevant subsystems. An implementation strategy optimises QMB detection, reducing resource use. Simulations suggest that QMB-based QESCs cut qubit consumption by 50%-75% while enhancing fidelity compared with non-optimised quantum semantic schemes. Unlike classical approaches, QMBs offer inherent security by limiting an eavesdropper's access to classical data outside the blanket. We outline future directions, including real-time QMB adaptation. This work bridges quantum information theory and semantic communication, advancing resource-efficient and secure quantum networks.

We prove that learning an unknown mixed fermionic Gaussian state on $m$ modes to trace distance $\epsilon$ requires $\Omega(m^3/\epsilon^2)$ copies when measurements act on one copy at a time, even with arbitrary POVMs, fresh ancillas and classical adaptivity, but without quantum memory between copies. The bound holds for $0<\epsilon\le1/3600$ and separates this model from the known collective rate $\Theta(m^2/\epsilon^2)$. It follows from a uniform single-copy Fisher-information budget and a dimension-independent comparison between trace distance and Gaussian parameters. On covariance matrices of operator norm at most $1-c$, we prove a Frobenius-to-trace-norm continuity bound with constant $[2c(2-c)]^{-1/2}$; matchgate shadows then attain $O(m^3/(c\epsilon^2))$ copies. This also gives explicit error certificates for thermal free-fermion states. For a class of mixed passive bosonic Gaussian states with total mean photon number at most one, a reduction to bounded-block qudit tomography gives a single-copy lower bound $\Omega(m^3/(\epsilon^2\sqrt{\log(m/\epsilon)}))$, versus collective complexity $\Theta(m^2/\epsilon^2)$. These separations answer the mixed-state measurement-resource question posed by Chen et al. A two-mode example has optimal two-copy Fisher trace $5$, versus the separable ceiling $4$. An IBM replication gave a pre-registered witness lower bound $4.12$ at one-sided $95\%$ shot-noise confidence; its interpretation assumes the prescribed preparations and a common measurement channel and does not bound preparation systematics.

We benchmark classical optimization of a fixed low-depth Quantum Approximate Optimization Algorithm (QAOA) ansatz across four cost-Hamiltonian families at $N=12$, $p=3$, and $D=6$. Ten optimizers are compared over 25 independent runs under common ceilings of 10\,000 and 30\,000 function evaluations (FEs), first with exact statevector objectives and then with two additive observation-noise levels. Exact objectives favor multistart BFGS and multistart CMA-ES. Under noisy feedback, adaptive population methods become more competitive, but the ranking depends on whether performance is measured by the best exact point visited or by the point selected from noisy observations. A targeted extension over all three pre-screened instances per family confirms this regime change while showing that named adaptive-DE winners are instance dependent: jSO-lite leads low-noise oracle search, iL-SHADE high-noise oracle search, and L-SRTDE high-noise selected solutions in the equal-instance summaries. Bootstrap analysis quantifies a non-negligible high-noise search–selection gap, and a retrospective fixed-budget verification proxy shows that reserving a small measurement budget for final re-evaluation improves selected quality across all ten methods at 30\,000 FEs. A supplementary structure-aware study further shows that QAOA cross-depth restriction and continuous basin refinement are more useful in these conditions than standalone Monte Carlo tree-search selection. Overall, optimizer choice depends jointly on landscape structure, observation noise, and final-point identification.

Quantum information processing requires efficient storage and manipulation of photonic states. In this work, we harness pre-created macroscopic spin coherence as an additional degree of freedom to control a cavity-assisted quantum memory. We derive equations of motion for such a memory that predict efficient emission and absorption of two-color fields under a generalized nonlocal spectral impedance-matching condition, which reduces to the well-known condition in the single-mode case. These equations reveal a new operating mechanism of cavity-assisted quantum memory wherein the controlled spin coherence couples the emitted spectral modes. As a result, our memory deterministically synthesizes arbitrary frequency-bin photonic qubits using simple radio-frequency rotations, while the temporal reversibility of the protocol provides perfect transformation of the qubit states. Our findings establish a unified platform bridging quantum storage with elementary signal processing for quantum networks based on spectral encoding of photonic qubits.

Quantum hashing is a well-known technique. In this paper, we present a new construction of a quantum hash function based on binary error-correcting codes. The construction of the quantum hash strongly resembles the quantum state preparation in QKD protocols (e.g., BB84 protocol) and can be implemented on current QKD-devices.

Traveling-wave parametric amplifiers (TWPAs) based on Josephson metamaterials provide broadband gain with near-quantum-limited added noise. Whereas long nonlinear metamaterial devices can deliver high gain, short arrays suffer less from dissipation, pump depletion, and internal standing waves which can degrade noise performance. Here, we demonstrate a cascaded TWPA architecture that combines the advantages of both approaches by employing a short (736-element), low-dissipation Superconducting Nonlinear Asymmetric Inductive eLement (SNAIL)-based TWPA as the first amplification stage, followed by a conventional long (1632-element) TWPA that provides additional gain. The resulting amplifier cascade achieves nearly 30 dB of total gain over a tunable bandwidth of approximately 1 GHz while maintaining added noise close to the quantum limit. Our results establish a cascade of TWPAs as a practical approach for high-gain, broadband, quantum amplification with applications in quantum information processing, multi-mode entanglement, and quantum sensing applications at microwave frequencies.

clifford_qc is a Python research toolkit for constructing quantum models, comparing variational and subspace eigensolvers, and estimating measurement resources. A common sparse Pauli algebra connects Hamiltonians, density operators, gates, and candidate-selection observables, while dedicated interfaces handle circuit programs, execution, and statistical estimates. We introduce the representation with a worked gradient example and trace a molecular calculation through reusable model preparation, an independent solve, and optional reference validation. Shared measurement caches reuse outcomes across observables on the same reference state; packed coefficient storage and streaming expose a memory-recomputation tradeoff. Committed small-system benchmarks show how these interfaces support comparisons with explicit accuracy and cost assumptions. Fully commuting measurement reduces the shots needed to certify a fixed first-order energy functional, but entangling-gate time and connectivity can offset the saving or make the protocol inadmissible under illustrative device models. Other studies identify a subspace bias floor that more shots cannot remove, an indeterminate comparison of fermionic encodings across instances, and an approximate-restriction screen whose required comparison fails before sampling. Generated tables, provenance records, and manuscript checks connect the reported claims to their inputs, although evidence labels are not yet validated uniformly. The package supports reproducible method development; these results establish neither hardware performance nor a general simulation speedup.

A quantum inspired framework was developed for polarized radiative transfer in the atmosphere to jointly model multiple scattering, absorption, and emission processes. The radiative field is represented by the Stokes vector and discretized using an n-directional two-dimensional spatial lattice on 3-dimensional uniformly distributed zenith and azimuth angular vectors. The formulation of this quantum computation system is based on the Lattice Boltzmann Method, which incorporates a physics-based polarized phase matrix. A classical lattice solver employing identical spatial and angular discretization and physical modeling as in quantum algorithm is implemented. The corresponding quantum algorithm is evaluated using the IBM Qiskit quantum simulator, enabling direct comparison of numerical accuracy to a classical simulation reference. The results demonstrate that fully physics-based polarized radiative transfer can be embedded within a quantum lattice framework, which provides an initial benchmark toward scalable quantum atmospheric radiative transfer and future quantum climate modeling

Simulating the showers that particles deposit in a calorimeter, the detector that records their energy across many cells, is one of the largest computing costs in high-energy physics, and fast generative surrogates are needed. Quantum circuits have been proposed as such surrogates, but demonstrations on calorimeter data have either required a register that grows with the image, roughly one qubit per cell, or have passed the information between parts of the image through a classical channel. We remove both constraints for this problem, using a construction drawn from the sequential-generation and hidden-quantum-Markov-model literature. A shower image is generated block by block on a fixed register of six qubits. Three of them, the memory, are never measured. They hold what the circuit knows about the blocks already generated as a quantum state, so the correlations between distant parts of the image cross each block boundary as unmeasured amplitudes. The other three are measured and reset once per block, and each outcome selects the energy pattern of one block. The register size is set by the block, so adding cells to the image adds steps to the sequence, not qubits. We call the model a coherent-memory Born machine (CoMB), a Born machine being a circuit whose measurement statistics are the generated distribution. Its training loss grows only linearly with the number of blocks and never requires enumerating the image distribution, and a depth-two instance runs on an IBM superconducting processor. On a twelve-cell benchmark the model reproduces the energy distribution of every cell, the correlation matrix between cells, and the total-energy spectrum. Removing the three memory qubits, with everything else unchanged, produces independent blocks. Every correlation between blocks is carried by the unmeasured qubits and by nothing else.

Quantum networks are usually framed by two hardware limits: how fast entanglement can be heralded, and how long a memory can hold it. We establish a third, geometric limit: entanglement decoheres while control information travels, so the distance to whoever allocates resources enters the fidelity budget directly. We develop a functional-graph abstraction weighting each link by its predicted multiplicative contribution to end-to-end fidelity, separating global but delayed state from local and immediate state, and compare centralized against local allocation in a replicated discrete-event model. Centralized delivery latency grows with network diameter while local latency is nearly scale invariant, differing up to twenty-fold for short-range traffic; the coherence threshold at which a global view outweighs a fresh one does not shift across the tested sizes; and as heralding accelerates, the dominant cost moves into the control plane. Slot synchronization instead obeys the product of slot rate and one-way link delay, so it is bounded by repeater spacing rather than diameter. Controller placement, decision locality, repeater spacing and slot rate are physical design parameters, not implementation details.

Quantum computing promises to outperform classical computing for certain computational tasks. One of the key concepts underlying this potential is universality. Universality has been extensively studied not only for qubits but also for higher-dimensional quantum systems, such as qutrits and qudits, which span Hilbert spaces of dimension greater than two. However, the concept of universality in Bose-Einstein condensates (BECs) qubit systems, which have been proposed relatively recently, remains insufficiently understood. In this work, we analyzed universality in BECs qubit systems. Our results clarify the theoretical aspects of universality in quantum computation within the class of ((N+1))-dimensional representations of SU(2), taking into account two distinct representations of the quantum states.

It is argued that many real-valued constructions of quantum mechanics are only nominally real in that the operators and states are restricted to impose a complex structure on the Hilbert space. That is, complex algebra between pairs of elements representing complex numbers is preserved in these formulations. It is therefore mistaken to think of these constructions as being `real' as they are actually a representation of complex linear algebra. It is then shown that under the assumptions of state normalisation and strict energy conservation, this complex structure (at the very least) is required to allow for time evolution in quantum mechanics. This is only a minimum requirement, as our arguments do not preclude the formulation of quantum mechanics in terms of hyper-complex entities, such as quaternions.

We determine the exact local precision limits for single-copy estimation of smooth multiparameter quantum statistical models contained in spin factors, a class of matrix Jordan algebras whose state spaces generalize the qubit Bloch ball. At any parameter point where the symmetric logarithmic derivative (SLD) Fisher information is positive definite, we characterize the entire attainable classical Fisher-information region over all finite-outcome positive-operator-valued measurements. After SLD normalization, this region consists exactly of the real symmetric positive semidefinite matrices with trace at most one, independently of the ambient Hilbert-space dimension. This yields a sharp weighted covariance bound for every positive definite weight, attained by an explicit locally unbiased estimator based on randomized spectral measurements of SLD directions. The proof combines a statistics-preserving positive projection onto the spin factor with the two-eigenvalue structure of its effects, revealing the Jordan-algebraic origin of the tradeoff. The result extends the qubit information tradeoff to models with more than three parameters. Since the optimal measurement depends on the unknown parameter, we simulate an adaptive scheme for a five-parameter model on a four-dimensional Hilbert space and observe performance close to the optimal local benchmark.

Deep learning models are powerful but opaque. As quantum machine learning matures, the field faces a defining choice: build quantum models that are equally opaque, or exploit the mathematical structure of quantum mechanics to make them inherently interpretable. We show that the latter is possible. By tracking quantum mutual information~(MI), entanglement entropy, and state fidelity through the layers of a Quantum Transformer Block (\qtb{}), a fully-coherent variational circuit with quantum analogues of both attention and feedforward, we gain direct insight into how the model processes information: which tokens it attends to, when correlations form, and why predictions fail. On four tasks with known dependency structure we show that (i)~learned MI matrices align with ground-truth task structure (AUC$\,{=}\,0.69$ on lookup), (ii)~disabling entangling gates collapses accuracy from 100% to 15% while MI$\to 0$, proving entanglement is the mechanism, (iii)~accuracy and MI co-evolve during training ($\rho\,{=}\,0.92$ on lookup), and (iv)~per-sample MI predicts prediction correctness on the conditional task with ROC AUC$\,{=}\,0.84$. All results are validated on IBM Quantum hardware (ibm\_kingston, Heron~r2): the circuit's reasoning process, from product state through structured entanglement, is directly observable on a superconducting processor. These proof-of-concept results, obtained on small synthetic tasks, suggest that the physics of quantum computation can provide intrinsic interpretability signals with no direct classical counterpart, motivating study of whether this advantage persists at scale.

The no-signalling principle lies at the heart of Bell-type experiments involving spacelike-separated parties. Although not all no-signalling correlations can be realized within quantum theory, the no-sinalling principle itself remains fundamental even for post-quantum theories, since its violation would imply superluminal signalling. In the spirit of device independent nature of the Bell inequalities, there has recently been growing interest in causal inequalities, which identify correlations admitting no causal explanation. Such correlations have been rigorously studied within the process-matrix formalism, which is built upon a constraint analogous to spacelike separation in Bell scenarios. We refer to this constraint as the single-interaction constraint, whereby each party interacts with the environment only once. Despite considerable effort, no fundamental guiding principle is currently known that characterizes the restrictions this constraint imposes on the correlations generated by Process Matrices. In this work, we address this gap by proposing a generalized causality principle for the bipartite case. We show that for certain cases, the generalised causality principle defines a strict subset of the set of all signalling correlations. This principle thus provides a fundamental limit on quantum and even post-quantum theories subject to the single-interaction constraint. By analogy with no-signalling, whose violation excludes certain causal structures among the parties, a violation of the generalised causality principle rules out a corresponding class of causal structures(causal structures with the single interaction constraint). More broadly, our techniques provide a general framework for deriving generalised causal constraints, applicable to a wide class of indefinite-causal-order scenarios.

Weak values are conventionally extracted in the limit of vanishing measurement strength. At finite strength, the corresponding post-selected conditional averages generally acquire nonlinear corrections and need not retain their weak value interpretation. Here we identify a class of measurement protocols for which this expectation fails: the conditional value reconstructed from the measuring probe is exactly independent of the probe strength and therefore coincides with the real part of the weak value. We first analyze this phenomenon in the measurement–disturbance protocol introduced by Lund and Wiseman. We then establish conditions under which this invariance persists, showing that it is determined by the interplay between the probe interaction, a subsequent measurement interaction with an ancillary apparatus, and the final post-selection. These results demonstrate that weak coupling, although generally sufficient for accessing weak values, is not always necessary.

Understanding the physical origin of the piecewise-linear computation in deep rectified linear unit (ReLU) networks remains a fundamental challenge. Here we establish an exact statistical-mechanical realization of arbitrary ReLU networks. Starting from a microscopic configuration space and its state multiplicities, we construct a partition function without prescribing a neural-network activation function. The resulting system admits equivalent descriptions in terms of cascaded quantum operations with post selection, or fermionic transport model. We rigorously prove that in $\beta\to+\infty$ limit, the thermodynamic observables of this system exactly reproduce the hidden states, outputs, and loss function of an arbitrary deep ReLU network. Crucially, we demonstrate that the piecewise-linear behavior of the ReLU network emerges from a first-order phase transition in the microscopic system, where the discontinuities precisely coincide with the boundaries of linear regions of ReLU network. This work establishes an exact physical foundation for deep neural computation and provides a novel statistical-mechanical perspective on neural architecture design.

Quantum key distribution (QKD) can deliver information-theoretic security, but its receivers are still typically assembled from cascaded bulk optics. Metasurfaces offer a radical reduction in this complexity. Here, we make the metasurface function as the QKD measurement device itself. We design wavelength-specific dielectric apertures at 780, 1550, 2000, and 10 600 nm that interweave the linear H/V and circular R/L phase libraries at a 0.44–0.49{\lambda} cell pitch, i.e., below half the operating wavelength, and map the complete passive-BB84 measurement directly onto four detector channels. This subwavelength basis co-location prevents an ordinary propagating-wave aperture mask from isolating one basis without simultaneously attenuating or perturbing the other. Simulated full-wave focal-plane intensities are converted directly into conditional Born probabilities using fitted, calibration-fixed detector regions. The selected designs achieve probability fidelities of 97.96–99.08%, four-port collected efficiencies of 17.43–40.94%, and mean intrinsic quantum bit error rates of 1.42–3.96%. At 1550 nm, the selected design gives an asymptotic device-level yield of 0.151 secret bits per incident photon under an ideal single-photon model. Six-state detector tomography gives positive both-basis security bounds for all six reconstructed receiver models, including their polarization-dependent loss, basis imbalance and crosstalk. These results establish protocol-matched meta-optics as a route to compact, passive QKD receivers.

Negatively charged nitrogen-vacancy (NV$^-$) centers located a few nanometers below the diamond surface are key quantum defects for nanoscale sensing of external spins. However, the creation of shallow NV$^-$ centers with high yield remains a materials challenge. Here, we demonstrate that high-angle ion implantation enhances the creation efficiency of shallow NV$^-$ centers. By implanting $^{15}$N ions at angles exceeding 60$^\circ$, we achieve high NV$^-$ yields approaching 10% with effective NV$^-$ depths below 10 nm. These yields are significantly higher than those typically reported for shallow NV$^-$ creation. The enhanced NV$^-$ yield is consistent with an increased vacancy-to-nitrogen ratio in the near-surface region, which is expected to promote NV formation during annealing. The created NV$^-$ ensembles show coherence properties comparable to those of single shallow NV$^-$ centers at similar depths, and allow detection of nuclear spins in van der Waals materials attached to the diamond surface. Our results establish geometric control of ion implantation as a simple and broadly applicable approach to engineer shallow vacancy-related quantum defects.

Local unitary (LU) equivalent states are crucial for understanding the structure of quantum entanglement. We investigate the LU equivalence based on the LU Bargmann invariants (LUBIs). We consider for which states the LUBIs are sufficient to ensure the LU equivalence. We focus on a class of multipartite states with complete local commutativity, called CLC states. We first show that for multipartite CLC states, all the LUBIs are sufficient to ensure the local permutation equivalence, if their single-party marginals are diagonal and non-degenerate. By virtue of the fact that the CLC property remains unchanged under local operations, we verify that the LUBIs are also sufficient to ensure the LU equivalence of multipartite CLC states whose single-party marginals are non-degenerate. Furthermore, when the single-party marginals are degenerate, we propose concrete examples of two-qudit and three-qubit systems, showing that there are states which share all the LUBIs but are not LU equivalent.

The problem of time in quantum gravity is often presented as a consequence of applying quantum theory to general relativity. These notes adopt a broader perspective. We first examine how time enters classical mechanics, relativity, quantum theory, and quantum field theory, distinguishing three principal aspects: causal order, temporal duration, and the present. This analysis shows that the conceptual difficulties associated with time do not arise only when gravity is quantised. Tensions between causal structure, clocks, observables, and measurement are already present in the theories from which quantum gravity is constructed. We then survey responses to the problem of time across the principal approaches to quantum gravity. These include canonical and Wheeler-DeWitt quantisation, path-integral and histories formulations, perturbative and background-dependent approaches, causal sets, and twistor theory. The programmes are compared according to whether they retain an external time, render time problematic through quantisation, or incorporate causal or temporal structure into their foundations. Particular emphasis is placed on questions arising from quantum foundations and relativistic quantum information. We conclude by examining linearised gravity and weak-gravity quantum systems. This regime shows that the problem of time is not confined to Planck-scale physics, but arises already in attempts to provide a predictive and operationally meaningful quantum description of spacetime near flat geometry.

Generally, the work output of stochastic heat engines is governed by the stochastic trajectory distribution and the energy spectrum. Because the trajectory distribution depends on the thermal reservoir temperatures, the work output is not only constrained by temperature but is also susceptible to thermal fluctuations. To address these limitations, we introduce two continuous Maxwell's demons into a quantum Otto cycle, forming an Otto information engine (OIE). We demonstrate that the work output of the OIE depends solely on the energy level gap, enabling arbitrary work extraction while eliminating work fluctuations, thereby ensuring cycle-to-cycle identical work output. Furthermore, we show that the engine's efficiency can surpass the standard Carnot efficiency even after accounting for the energy cost of demon's memory erasure. Finally, we show that the OIE can deliver superior output power even when the demon's measurement time is taken into account, and the corresponding Monte Carlo simulation has been executed.

Standard stochastic heat engines operate blindly, enforcing work extraction protocols indiscriminately on microstates, and consequently suppressing work output, stability, efficiency. To overcome this, we propose an Otto information engine (OIE) that employs a Maxwell's demon to filter out detrimental stochastic trajectories, and demonstrate that the OIE can provide enhanced work output and stability compared to the corresponding standard Otto engine. Remarkably, even after accounting for the energetic costs of the demon, the OIE efficiency surpasses both the standard Otto limit and Carnot bound. Furthermore, by applying the fluctuation theorem of information dissipation, we derive upper and lower bounds on efficiency, confirming that our results adhere to the second law of thermodynamics. Finally, and counterintuitively, measurement errors and quantum inner friction, traditionally considered deleterious, can be harnessed as resources, which improves robustness and enables us to ignore the adiabatic strokes time.

We present Hybrid Quantum Root Cause Analysis (HQ-RCA), an industrially grounded workflow for root cause analysis in banking IT operations, built on a hybrid Quantum Graph Neural Network (QGNN): the classical backbone of DynEdge (the IceCube neutrino-reconstruction GNN, which we call standalone DynEdge), with its classification head replaced by a Variational Quantum Circuit (VQC). On 13 months of anonymised IT data (13k alarm clusters) from a major European bank, the hybrid QGNN matches standalone DynEdge – the strongest classical baseline – on $F_1$, while standalone DynEdge leads the ranking metrics. A readout-sensitivity and layout-robustness study, analysed via Dimensional Expressivity Analysis (DEA), shows that the effective parameter dimensionality (rank) of the quantum observable has no measurable correlation with $F_1$; we therefore keep the simplest readout $\langle Z_0\rangle$ (the Pauli-$Z$ expectation on the first qubit), which in the deployed layout is rank-1, collapsing optimisation to a 1-D problem solvable by a gradient-free grid scan. Execution on IBM Heron r2 (no error mitigation) shows this gradient-free readout is executable on NISQ hardware after threshold recalibration.