Papers

A gap between achievable rates and converse bounds persists for energy-constrained bosonic communication in the presence of excess noise. We derive a unified adaptive weak-converse bound for thermal attenuation, noisy amplification, and additive Gaussian noise under an unconditional mean transmitted-photon-number constraint. The bound applies to arbitrary adaptive protocols with quantum memories and constrains the two-way quantum, entanglement-distribution, private, and secret-key capacities. It vanishes throughout the entanglement-breaking region and approaches the corresponding PLOB bound at infinite energy. At finite energy, it improves the evaluated Gaussian squashed-entanglement and PLOB bounds in relevant parameter regimes, while comparison with hashing rates quantifies the remaining gap to achievability. The result provides a common energy-dependent benchmark for noisy bosonic Gaussian channels and extends finite-energy converse methods beyond the quantum-limited setting.

The Mpemba effect challenges the intuition that states closer to equilibrium must relax faster. We ask whether an analogous magic-ordering reversal can occur in the generation of quantum magic (nonstabilizerness), a key resource for universal quantum computation: can a state with less initial magic overtake one with more and reach its asymptotic value sooner? Here, we uncover interaction-induced dephasing as a distinct mechanism for this magic Mpemba effect, requiring neither transport nor conventional thermalization. For tilted product states in an interacting $\ell$-bit model, a random-phase analysis predicts a reversal of the magic ordering: states with less initial magic attain higher saturated magic, independent of their spatial pattern. Exact simulations of the $\ell$-bit model and localized spin chains further show that these states also saturate earlier. We observe both features on IBM superconducting quantum processors. An effective $\ell$-bit implementation accesses long dephasing times at fixed circuit depth by encoding time in gate angles, while a microscopic spin model exhibits the reversal universally across initial patterns in the localized regime but only selectively in the ergodic regime. These results establish interaction-induced dephasing as a route to anomalous quantum-resource relaxation beyond transport-driven thermalizing dynamics.

In recent work Phys. Rev. X 16, 031057 (2026), we proposed a self-consistent approach to entanglement certification based on generalized noncontextuality. It requires no prior characterization of the measurement devices and, given access to all local measurements, can certify every entangled state in a Bell circuit. Here, we study the complexity of this protocol in a finite experiment. At fixed local dimension $d$, we show that the optimal number of distinct local effects needed to reach a trace-distance entanglement resolution $\gamma$ is $\Theta_d(\gamma^{-(d-1)})$. This scaling is necessary even when the measurements are tailored to the target state. Independent Haar-random projective measurements instead require $\Theta_d(\gamma^{-(d-1)}\log(1/\gamma))$ effects. Finally, we show that, once the exact operational identities are known, $\Theta_d(\gamma^{-2}\log(1/\delta))$ copies of the target state are necessary and sufficient for certification with error probability at most $\delta$. Determining the optimal sample complexity when those identities must instead be inferred from the same finite target-state data remains open.

Characterizing the set of quantum nonlocal correlations through information-theoretic constraints is a central problem in quantum foundations. We show that the convex hull of no-signalling behaviors in a bipartite Bell experiment satisfying a common-overlap no-disturbance-without-uncertainty condition is exactly the finite-dimensional quantum set whenever one party has two binary measurements and the other has an arbitrary finite number of settings, each with an arbitrary finite number of outcomes. In the simplest binary input-output Bell scenario, this characterizes the full eight-dimensional set of quantum behaviors, including the local marginals. The proof constructs a quantum realization directly from the conditional probabilities and no-signalling. The characterization also reduces optimization of any linear Bell expression in these scenarios to maximization over a one-parameter family of second-order cone programs. The results establish a connection between local uncertainty-disturbance constraints and quantum nonlocality, mediated by no-signalling and shared classical randomness.

Physical many-body quantum systems typically interact locally, giving rise to ground states where entanglement grows with the area of the region being probed. Beyond entanglement, non-stabilizerness (or "magic") has been established as another crucial resource linked to quantum complexity and the properties of error-correcting states. Unlike entanglement, non-stabilizerness typically behaves with a volume-law scaling in ground states, indicating inherent computational complexity. In this work, we show that under a recent classification of quantum states, area-law states split into two distinct classes. Entanglement-dominated states obey an area-law for non-stabilizerness and admit efficient quantum algorithms for entanglement manipulation. Conversely, magic-dominated states exhibit a a faster-than-area growth of subsystem non-stabilizerness and require non-efficient algorithms for entanglement manipulation tasks. Within this context, we introduce the concept of the stabilizer regime, a restricted quantum phase that admits efficient entanglement manipulation and hosts area laws for both magic and entanglement.

We prove copy-optimal learning of the full Gaussian orbit of paired magic states on $n$ fermionic modes. The unknown evolution may be any parity-preserving quadratic circuit, including pair creation and annihilation, and each copy is measured once, in a fixed basis, on a single quartic Majorana observable. A nonadaptive learner returns a Gaussian preparation within trace distance $\epsilon$ from $\Theta(n^6/\epsilon^2)$ copies at fixed confidence, and no learner in this measurement model, adaptive or not, can do better. Measured quartic correlations certify the trace distance of the result. Our second result extends learning to a broader family: pure states whose unknown input blocks are superpositions of disjoint occupation patterns with bounded particle number, under the same evolution. Using single-copy Gaussian rotations and occupation readout, a batch-adaptive learner returns an input and a Gaussian circuit with infidelity $f$ from $\widetilde O(n^7/f)$ copies and polynomial classical processing. Connected quartic correlations reveal the hidden mode groups, and fresh local measurements restore the branches and their coherences. No particle-number conservation, minimum branch weight or spectral gap is assumed.

Polynomial transformations are basic primitives in quantum algorithms: quantum signal processing and singular value transformation compile univariate polynomials into circuits with query complexity essentially set by degree. Multivariable transformations of noncommuting matrices, however, lack a comparable synthesis theory. We develop a complete constructive theory under joint block access for all polynomials contractive on the prescribed matrix domain. Given a compact finite-state description of a degree-$D$ polynomial $P$ and $0<\tau<1$, we synthesize $P$ with $(1+\tau)$-optimal normalization using $O(D/\sqrt{\tau})$ queries, and exactly $D$ under row-block access, matching a degree lower bound. The complete circuit realization is classically computable in polynomial time with polylogarithmic dependence on accuracy. The key to our construction is a finite algorithmic Schur–Agler theorem: the coefficient recurrence defines a polynomial-dimensional continuation space supporting a complete semidefinite certificate for contractivity on the prescribed domain. Factoring this certificate yields the contractive realization underlying the query algorithm. Beyond matrix transformations, our framework lifts multivariable polynomial synthesis to quantum channel transformations. Given coherent Kraus access $K=\{K_a\}_a$, we synthesize any finite jointly contractive family of noncommutative polynomial maps $K\mapsto\{F_b(K)\}_b$ as completely positive operations, allowing coherent interference among Kraus histories. Furthermore, channel-level transformations specified by causal Choi data can be synthesized explicitly as fixed-order quantum combs. Collectively, these results point to a broader program: multivariable approximation as a language for multi-operator quantum algorithms and higher-order quantum information processing.

Entanglement sudden death (ESD), explored through a series of works by Yu and Eberly, supports the notion of entanglement vanishing abruptly and completely at a finite time, even when the underlying open-system dynamics remain smooth. In this article, we revisit the development of ESD from bipartite origins to genuine multipartite entanglement. We first illustrate the canonical mechanism of ESD with two independently damped qubits, for which the concurrence vanishes at a finite time while populations and coherences remain nonzero. We next present our results on multipartite entanglement for generalized GHZ states under depolarization. Global and independent local depolarizing dynamics can be chosen to produce identical reduced evolution for every individual qubit, yet they yield different genuine-multipartite-entanglement sudden death times, whose ordering can reverse with the initial state. For N-qubit GHZ states, this distinction becomes asymptotically stronger since the ESD time scales as 1/N under independent local depolarization, whereas under global depolarization it approaches a finite value in the thermodynamic limit. Echoing a central lesson of Prof. Eberly's work, we report the lifetime of multipartite entanglement is not fixed by the local dynamics, but rather depends on the evolution of the joint quantum state.

Recent advances in algorithms for simulating Lindblad dynamics have clarified their theoretical potential for state preparation, but their practicality in the early fault-tolerant regime and beyond remains uncertain. In this work, we address this by investigating the cost of preparing ground states of the fermionic Hubbard model, following the single-ancilla approach of [Phys. Rev. Research 6, 033147 (2024)]. We derive rigorous error bounds including constant prefactors, and compare to empirical error behavior and practical convergence parameters obtained from circuit-level simulations. We find that empirically chosen parameters can reduce the required resources by orders of magnitude, resulting in an estimated $7.7 \times 10^8$ T gates to perform one unit of time evolution targeting the low-energy subspace of a 36-site fermionic Hubbard model. We identify the accurate filtering of energy transitions as the main source of this cost.

Local-basis Shannon entropies of critical wave functions contain universal subleading information, but the Shannon point of the critical transverse-field Ising chain is singular in the conventional Rényi approach. We treat it directly at $n=1$ by representing the complete computational-basis Born distribution as the odd-degree boundary of independent long-range Bernoulli edges. The Shannon chain rule separates the entropy into explicit independent-edge and conditional cycle-space terms. For the periodic chain this isolates the analytic edge anomaly and organizes the remaining constant by linked vertex support. Conditional on the stated finite-part matching and forest assumptions, every nonvanishing linked coefficient is represented by an explicit finite-dimensional integral, giving an all-orders analytic hierarchy; the four-vertex term is evaluated in closed form, and the first few linked sectors already nearly saturate the established periodic constant, which is also reconstructed independently from the exact finite-size distribution. For an interval, the exterior reduces exactly to one ghost vertex and the explicit squared logarithms cancel, leaving the analytic edge contribution $\gamma_E=\log2/4-1/16$. The conditional cycle term has an exact all-support decomposition into physical-line and ghost-linked sectors; conditional on closure of the boundary forest subtraction, these sectors define an all-orders hierarchy of renormalized line and monomer–dimer boundary periods for the remaining logarithmic coefficient. The first complete augmented linked coefficient is evaluated in closed form, with an exact cancellation between its line and ghost boundary-layer anomalies; an independent reconstruction from exact finite-size probabilities recovers the established coefficient $\gamma_1=0.060020(3)$.

Superconducting circuits have emerged as one of the most promising and scalable platforms for quantum com- puting, with substantial industrial adoption driving qubit counts steadily upward. Yet the layout of the corresponding chips is still primarily performed manually, consuming multiple days or weeks of expert effort, even for moderately sized designs. Existing automation approaches sidestep this bottleneck by simplifying the underlying problem and relaxing physical constraints. Therefore, they fall short of fabrication-ready results. To overcome this scalability wall without such compromises, we first introduce a formal abstraction that translates physical device characteristics into a rigorous geometric problem formulation. This abstraction bridges physical realization and design automation. Building upon this abstraction, we then propose a three-stage design automation flow comprising geometry-aware global partitioning, ILP-based port assignment, and a hierarchical routing pipeline. Evaluations conducted by our interdisciplinary team of design au- tomation researchers and superconducting hardware experts con- firm that the resulting flow produces complete, manufacturing- ready layouts that comply with the physical design rules at the push of a button. That is, it operates fully automatically within seconds to a few minutes, and solves complex instances up to 25x faster than the state of the art. All methods are released as the fully open-source tool mqt-scpd as part of the Munich Quantum Toolkit, providing the first readily usable, end- to-end design flow for planar superconducting quantum chips that explicitly addresses the underlying physical characteristics and requirements.

Whether the spin-1/2 Aharonov-Bohm Hamiltonian supports bound states has remained controversial since Hagen concluded that no such states exist for a Dirac particle. Here, we show that Hagen's solution corresponds to a particular member of the one-parameter family of self-adjoint extensions that describe the singular Zeeman interaction, and we identify which member the microscopic physics selects. Matching the extension parameter to a finite-radius flux tube yields $\nu=0$ precisely at $g=2$, and it does so in every flux sector. The critical $g$ factor is therefore universal, $g_c=2$, and depends on neither the flux sector nor the regularization radius. The flux sector controls the depth of the bound state energy, and we obtain a closed-form expression showing that binding deepens markedly with the integer part of the flux. Hagen's conclusion is thus confirmed and sharpened: it is not a statement about one arbitrary member of a family of extensions, but about the member that the physics selects when the magnetic moment takes its Dirac value, and an anomalous moment is a necessary and sufficient condition for binding in the singular channel.

We determine the least Greenberger-Horne-Zeilinger (GHZ) extractability compatible with a Mermin-Ardehali-Belinskii-Klyshko (MABK) Bell score for every number of parties greater than two. Extractability is the largest squared overlap with a GHZ state obtainable by separate local quantum channels. Between the biseparable bound and the quantum maximum, the exact minimum is the affine interpolation from one half to one. The bound holds for normal states on tensor products of arbitrary local dimension and arbitrary binary measurements. We settle the previously unresolved range of six or more parties with an analytic proof that is uniform from four parties onward. We also determine the exact minimum when every local system is a qubit, and show that it lies strictly above the unrestricted bound at every interior score. One qutrit and qubits at all remaining parties attain every point of the bound with measurements fixed as the score varies. For at least four parties and strict interior scores, we classify all states attaining the bound with the minimum product of local support dimensions. For at least four parties on one qutrit and qubits elsewhere, we also prove that, when the extractability excess above the affine minimum is small, the trace-norm distance from the attaining mixture, up to local unitaries, is bounded by a constant times the square root of that excess. The exponent $1/2$ is optimal, and the constants are independent of the number of parties on every fixed interior interval of normalized scores.

Gaussian steering sets a sharp threshold for creating Wigner negativity at a distance. A measurement by Bob can make Alice's part of a shared Gaussian state Wigner negative only if Alice can steer him with Gaussian measurements. We ask whether multiple copies, ancillas, or catalysts can lift this requirement when Alice is restricted to Gaussian operations. We introduce the steered negativity, a multiplicative monotone whose logarithm equals the Gaussian steerability for Gaussian states. It bounds the negativity that Bob can herald and rules out activation by copies, by ancillas of Bob, and by catalysts without remote negativity of their own. For a strictly unsteerable Gaussian state and a single round of feed-forward to a Gaussian unitary of Alice, we further prove that even a Wigner-negative or steerable catalyst cannot help if it is returned exactly. Gaussian steering thus remains a barrier to remote Wigner negativity beyond the single-copy setting.

Clustering is a fundamental task in unsupervised learning. The goal is to partition unlabeled data into clusters such that similar elements are assigned to the same cluster, while elements in different clusters are dissimilar. We propose a quantum Monte Carlo approach to density estimation, a key routine in density peak clustering. Building on this approach, we develop quantum algorithms for the full clustering problem and three related tasks: decision clustering, cluster counting, and heavy cluster counting. For each one, we establish a polynomial quantum query speedup under assumptions on the scaling of dataset-dependent parameters. Numerical experiments suggest that these conditions are satisfied for several practically relevant settings.

Quantum memories are key ingredients for future quantum networks. Developing methods for their certification is therefore an important, yet challenging, problem. In this work, we present a general framework for certifying quantum memories and quantifying their performance in an operational and efficient manner, taking advantage of developments in the theory of quantum channels. We start by giving a pedagogical introduction to these concepts and tools and illustrate their natural application to quantum memories. Specifically, we quantify the fidelity of a quantum memory via the notion of average channel fidelity, which can be estimated precisely in an experiment via a finite set of probe states forming a so-called $2$-design. We then present a number of witnessing techniques for certifying this quantity, and show that it gives access to other important properties of the channel, such as its dimensionality and its capacity to transmit quantum information. We consider mostly a simple prepare-and-measure scenario, but discuss also the case of an entanglement-based setup, as well as a semi-device-independent approach. Finally, we apply these methods to a solid-state quantum memory experiment, certifying an average channel fidelity of 98.6%. Our certification methods can be readily applied to other quantum devices, such as fibers, transducers and gates.

We investigate how post-selected von Neumann measurements modify the nonclassical properties of two-mode entangled coherent states (ECSs). From the conditional pointer state, we characterize squeezing, photon statistics, intermode correlations, entanglement, fidelity, and post-selection probability. Anomalous weak values with moderate coupling enhance squeezing, antibunching, sub-Poissonian statistics, intermode correlations, and bipartite entanglement, while fidelity captures the crossover from weak perturbation to strong distinguishability. These results demonstrate post-selection as a tunable approach to engineering ECSs.

We propose an unified view to three well known quadratic Hamiltonians widely considered in quantum mechanics, i.e. those of the harmonic oscillator, of the inverted harmonic oscillator, and the Berry-Keating Hamiltonian. We describe an unified approach to determine the discrete spectrum of these operators, and to deduce their (generalized) eigenstates. We also look at these Hamiltonians as the generators of $\mathfrak{su}(1,1)$, and of a generalized version of it relevant in presence of non Hermitian generators.

We report a 3D-printed microwave-resonator Paul trap that operates at the GHz frequencies required for electron confinement while preserving an open geometry suitable for laser access and imaging ion Coulomb crystals. The resonator exhibits moderate quality factors of approximately 1000, enabling large confining electric-field amplitudes at low input power, and is in good agreement with finite-element-method (FEM) predictions despite manufacturing imperfections, which we experimentally characterize. The validated FEM model is then used to calculate the electromagnetic fields in the trapping region. These field distributions, together with surface-roughness measurements, are incorporated into a model of electron spin-qubit decoherence to estimate the coherence time. Our analysis predicts that electron spin-qubit coherence times on the order of 10 ms should be achievable under the assumption that motional heating is dominated by Johnson noise, making such systems relevant for quantum information processing. The method of obtaining the coherence time is applicable to any electron Paul trap.

We develop a computational framework for the quantum relative entropy based on the replica trick and apply it to analyze the evaporation process method of Jackiw-Teitelboim black holes. We show that the relative entropies between the exact radiation state and the Hawking saddle state and the replica wormholes saddle state quantify information-theoretic costs inherent to coarse-grained semiclassical descriptions. During evaporation, the relative entropy for the Hawking saddle increases monotonically, reflecting a progressively higher thermodynamic cost of sustaining the Hawking description. Conversely, the relative entropy associated with the replica wormholes saddle decreases, which indicates that the description of connected geometries becomes progressively more accurate. Moreover, the sign of the difference between the two quantities reverses precisely at the Page time, providing an information-theoretic diagnosis for the transition between competing gravitational saddles. Our results recast the Page transition as a flow of relative entropy costs between competing semi-classical descriptions, revealing an information-theoretic structure underlying the emergence of effective irreversibility in coarse-grained black hole evaporation.

Space-Time Wave Packets (STWPs) have enabled numerous nontrivial properties, such as tunable group velocities, nondiffraction and nonlocal spin textures in optical fields. However, this has not been properly studied in matter waves. Here, we investigate free-electron STWPs, which are propagation-invariant and group-velocity-tunable matter wave packets, constructed by constraining the spatiotemporal spectrum of the electron wavefunction in momentum space. Due to the unique dispersion of free-electrons, the electron STWP can carry two different topologies, and host both meron and skyrmion topological textures in momentum space. We demonstrate the topological phase transitions and tunable skyrmion numbers by spectral geometry tuning. We also show the topologically robust propagation of the electron pulses and corresponding real-space skyrmionic expectation value textures encoded within each single electron wavefunction. Our results open a platform for topological free-electron wavepackets uses in sensing and information transfer.

For perfect state transfer (PST) on unweighted mixed graphs, we classify the normalized transfer times of complete PST classes. A finite set $\Lambda\subset\mathbb R/\mathbb Z$ containing zero occurs at a nonstationary periodic vertex if and only if $\cos(2\pi(x-y))\in\mathbb Q$ for all $x,y\in\Lambda$. Every admissible set has a connected oriented realization. We also classify the possible return phases of oriented realizations at the minimum vertex period. Transfers at rational multiples of the common minimum vertex period partition a complete class into sets of size at most six, or at most three in an oriented graph with return phase $-1$; both bounds are sharp. We construct complete classes of every finite size, including classes in which all transfers between distinct vertices occur at irrational multiples of the period and no switching automorphism maps a class vertex to a distinct class vertex. We also characterize simultaneous realization in connected oriented graphs with prescribed relative minimum vertex periods and return phases. The proof combines an imaginary quadratic field restriction with an unweighted construction that selects the complete target set.

We study the interplay between symmetry defects insertion and the phenomena of quantum many body scarring. We exploit a class of models obtained from an embedding mechanism that defines a stochastic matrix form hamiltonian, hosting zero energy many body scarred states. Such models display an interesting playground to explore the consequences of dualities, half-gauging operations and so on. We first show that inside this class of models, what are the conditions to still have scared states after defect insertion. The main result of our work is a detailed analysis of half-gauging in such chains, which introduces a non-trivial interface in our system, leading to scarred states protected by the underlying symmetries. The conclusions for half-gauged scarred systems are general and may lead to fruitful directions for higher dimension scarred physics and their robustness.

Pauli decomposition underpins Trotterization, phase estimation, sparse-Hamiltonian simulation, and variational observables, at exponential naive cost. From the character theory of $(\mathbb{Z}_2)^n$, characters $\chi_z(v)=(-1)^{\langle v,z\rangle}$ are the diagonal Pauli strings, so any diagonal operator is already Pauli-decomposed. A general operator still needs the shifts: each $X^{\otimes x}$ couples to a character $\chi_z=Z^{\otimes z}$, and the products $X^{\otimes x}Z^{\otimes z}$ – up to phases in $\{\pm 1,\pm i\}$ – form the Pauli group, the central extension of $(\mathbb{Z}_2)^n\times(\mathbb{Z}_2)^n$ by that phase group fixed by the symplectic pairing. A section of that extension remains a choice: the bare products $X^{\otimes x}Z^{\otimes z}$, or the genuine operators that insert $Y=iXZ$ at every qubit where $x$ and $z$ overlap. As Fourier analysis on an abelian shift-character lattice (a natural DFT), this formulation is not qubit-bound: $(\mathbb{Z}_p)^n$ recovers Heisenberg-Weyl qudits. The fast algorithm is the FFT for the group at hand; on $(\mathbb{Z}_2)^n$ that FFT is Walsh-Hadamard, at cost $O(n\cdot 4^n)$. paulikit is a memory-bounded realization of that qubit transform: peak usage need not materialize the dense $2^n\times 2^n$ operator, unlike prior codes whose $O(1)$ extra sits on that buffer, checked beyond a billion oscillator terms against Work-Span and bandwidth ceilings.

We proposed to boost the photon bunching effect of classical light via a modified Fabry-Pérot cavity with one of the cavity mirrors being replaced by a spatial light modulator, through which multiple independent transverse modulations, each was to encode independently spatially correlated phase on the wave front of the light field, was cascaded in sequence in the longitudinal propagation direction in the cavity. The two-photon bunching peak and the three-photon bunching peak of the generated superbunching light field were measured to be $36.9\pm2.0$ and $\rm (2.46\pm0.12)\times10^{3}$, respectively, which, as compared to those of thermal light, were improved by one-order and three-order of magnitude, respectively. Correspondingly, the ghost image visibility reconstructed with the superbunching light was demonstrated experimentally to be improved by $\sim 40$ times as compared to that with the pseudo-thermal light. Such classical superbunching light field is of essential importance not only for fundamental physics but also for potential applications such as correlated imaging, ghost interference and nonlinear optics.

Non-classical dynamics in open quantum systems can be hidden in temporal correlations that are invisible to standard state- and channel-based tests. We define coherence for multi-time quantum processes and show that access to intermediate times can reveal coherence absent from all corresponding pairwise channels. Incoherent processes are fixed points of dephasing on all input and output spaces, and their coherence is quantified by relative entropy. As a proof of principle, we use an Ising model in which all three pairwise channels are incoherent while the full three-time process remains coherent. We observe this multi-time coherence on a superconducting quantum processor using a coherence witness and full process tomography.

We introduce an inertial counterdiabatic (CD) protocol that reformulates shortcut-to-adiabaticity design as a moving-frame diagonalization problem. The method employs the Magnus expansion to construct a variational propagator generated by an accessible CD ansatz. In the new rotating frame, the controls are optimized to suppress the off-diagonal Hamiltonian terms, and the CD terms are defined to counteract the corresponding inertial contribution. The propagator generated with the Magnus expansion naturally exploits additional control directions generated through its nested commutator, while the sequential design of the propagator introduces temporal nonlocality into the optimization. We benchmark the method on a two-qubit system and on the one-dimensional quantum Ising chain, where it consistently outperforms variational CD protocols based on action minimization. The largest improvements are observed near gap-closing regions, demonstrating the advantage of combining temporal and algebraic nonlocality for suppressing diabatic excitations.

Conventional compressed sensing (CS) has a measurement lower bound of M = {\Omega}(K log(N/K)) under non-adaptive measurements. Recent experiments on quantum compressed sensing (QCS) have reported numbers of measurements below this classical lower bound. In this work, we establish lower bounds on the measurement complexity of QCS from an information-theoretic and quantum-physical perspective. QCS exploits quantum parallelism, enabling a unitary domain-alignment evolution to act on a superposition of all N basis states and map the sparse basis onto the measurement basis in a one-to-one manner. Consequently, the locations of nonzero components are explicitly carried by measurement-index labels. If only basic statistical information about the K nonzero components is required, the total number of effective index samples satisfies the coarse necessary condition Ms = {\Omega}(K). Under independent single-index projective measurements, when the support is unknown, the nonzero probabilities satisfy pn = {\Theta}(1/K), and exact support recovery is required with a fixed success probability, the sampling-coverage requirement leads to Ms = {\Theta}(K ln K). If each nonzero amplitude coefficient is further required to achieve a coordinate-wise relative root-mean-square error {\epsilon}, the optimal effective index sample complexity is Ms = {\Theta}(K ln K + K/{\epsilon}2), which reduces to {\Theta}(K ln K) for fixed {\epsilon}. Multimode photon-number-resolving detection can reduce the number of experimental rounds but not the total effective index sample complexity. These results show that quantum parallelism is not only a core resource for quantum computing but can also play a transformative role in measurement science.

Quantum automated learning (QAL) trains quantum models by directly updating quantum states, offering an approach to quantum machine learning that avoids optimizing variational circuit parameters. However, post-selection constrains the probability of obtaining the final learned model. We develop a post-selection-free QAL algorithm that organizes a complete training path into a coherent quantum circuit and uses fixed-point amplitude amplification to increase the probability of obtaining the learned model. We provide theoretical guarantees on output error and learning loss, and identify conditions under which additional coherent resources reduce the cost of restarting failed trajectories. The construction gives QAL a coherent implementation with explicit learning guarantees and resource costs, enabling a model with certified learning quality and controlled output error to be obtained with high probability.

Multimodal vision-language systems typically fuse image and text embeddings through classical operators such as concatenation, attention, bilinear pooling, or tensor interactions. We propose Quantum Entangled Multimodal Fusion Networks (QEMFN), a hybrid quantum-classical framework that introduces parameterized entanglement as a structured inductive bias for multimodal fusion. Pretrained visual and textual features are projected into compact latent spaces, encoded as angle-parameterized quantum states, processed through intra-modal and paired cross-modal entangling circuits, and measured to produce fused representations for retrieval. Under matched parameter budgets and identical frozen CLIP backbones, QEMFN outperforms classical fusion baselines on COCO-5k and Flickr30k, including multilayer perceptron, tensor fusion, FiLM, cross-attention, compact transformer, and a dequantized paired-topology analogue. An ablation suite isolates the quantum module's contribution from the surrounding classical projections, and quantum-centric analyses report Meyer-Wallach entangling capability, expressibility, gradient variance against barren-plateau bounds, and entropy-performance correlation under controls for training progress alongside an intervention study on the entangling component. QEMFN is executed under shot-based estimation, a noise-modeled fake backend, and a real superconducting device with zero-noise extrapolation. This work does not claim quantum computational advantage; the contribution is the framework together with a controlled empirical and quantum-centric evaluation that positions trainable entanglement as an interpretable, hardware-executable fusion mechanism at scales accessible on contemporary devices.