Papers

One of the main challenges in numerical simulation of quantum dynamics is the prohibitive cost in the semi-classical regime, in which the de Broglie wave length is small compared with the characteristic length scale and the solution is highly oscillatory. For the von-Neumann equation for mixed-state quantum dynamics, this difficulty is overcome by using the Weyl variables, under which the solution is not oscillatory. Furthermore, we use the integral representation of the potential difference, which robustly captures the classical limit as the semi-classical parameter approaches zero. By using exact Hermite moments and quantum singular value transformation to treat the polynomial and sparse coordinate matrices of the dense projected smooth non-polynomial potentials respectively, we obtain a quantum algorithm efficient for all ranges of wave lengths, with complexity polynomial in the spatial dimension and discretization and query bounds containing no negative powers of the small wavelength. Thus it can capture the correct physical observables even if the spatial grid does not resolve the frequency, hence defying the Nyquist-Shannon sampling theorem.

Genuine multipartite Bell nonlocality (GMNL) aims at capturing correlations between many distant observers that are globally Bell nonlocal. A commonly used definition for GMNL is based on biseparable models constructed from non-signalling correlations. Here we uncover an effect of superactivation of GMNL in this framework. Specifically, by locally wiring together two copies of a biseparable correlation, i.e. not GMNL, one can obtain another correlation that is GMNL. We show that this is possible for any number of parties, and for quantum-realizable correlations. Finally, we show that superactivation of GMNL is also possible at the single-copy level, via a catalytic protocol involving only local wirings. These results question the operational meaning of this definition of GMNL.

Controlled quantum communication enables secure state transfer between a sender and receiver with the assistance of one or more controllers. However, practical implementation over optical fibre networks is severely hindered by amplitude damping, which reduces fidelity exponentially with distance. We address this challenge by combining two powerful techniques: cat-state encoding for error correction and optimal non-local CNOT gates for distributed gate implementation. The protocol eliminates the need for the physical position qubit itself to travel through the optical fibre, reducing damping events. We show, through density-matrix simulations, that our cat-code-protected protocol with a non-local CNOT operation achieves higher fidelity at 50 km, significantly outperforming the standard protocol. We analyse the protocol's security against beam-splitter attacks and show that CHSH tests provide security against beam-splitter attacks on the distributed entanglement resource despite the cat code's error correction. Our results establish that cat-code-protected controlled quantum communication is feasible with current technology and structurally extensible to multiple controllers, providing a theoretical framework for studying error-corrected controlled quantum communication over long-distance star quantum networks.

Bicolor quantum imaging can reach, in principle, phase supersensitivity approaching the Heisenberg limit using squeezed light from high-gain parametric down-conversion, but established quantum-imaging setups typically operate in the low-gain, spontaneous regime, where such scaling is inaccessible. Here, we show experimentally and theoretically that a symmetric nonlinear interferometer, even in the spontaneous regime, retains a phase-sensitivity advantage over configurations where entanglement is not exploited as a quantum-metrological resource, although the achievable phase sensitivity remains shot-noise-limited. This advantage appears as a shift of the optimal working point toward the dark fringe, the low-gain signature of the mechanism underlying high-gain supersensitivity. We derive design choices for phase-optimized nonlinear interferometers accordingly, favoring configurations that exploit entanglement as a metrological resource and specifying their optimal operating point.

Ancillary photons allow passive linear-optical Bell-state discrimination to exceed the one-half probability of success limit achievable with vacuum auxiliary modes. For a fixed analyzer and ancillary resource, the discrimination probability is determined by the photon-counting patterns that occur uniquely for each Bell input. We develop a photon-number-resolved tree tensor network method for evaluating these detector supports in recursively structured analyzers. Photon-number conservation and mode symmetries separate most of the Bell-state outputs before the remaining detector support is examined. We establish a tree tensor network based construction to evaluate the remaining support without need of recalling all relevant photon detector patterns separately. We apply the method to recursive, product, and asymmetric ancillary states with up to $32$ optical modes and reproduce known analytical and literature benchmarks. For factorized ancillary resources with fixed photon numbers in halves of the analyzer and the symmetry property used in our analysis, we also derive an exact composition relation; for reflected asymmetric pairings the success probability is the arithmetic mean of the corresponding symmetric configurations. The complete enumeration for smaller systems, permanent-based amplitude calculations, and independent evaluations provide additional checks of the numerical results.

Tunable photonic architectures that improve the extraction efficiency of light from embedded epitaxial quantum dots across a wide spectral range are key enablers for developing bright sources of single and indistinguishable photons. In this study, we experimentally demonstrate planar multilayer antenna structures consisting of epitaxially grown AlGaAs and InGaAs membranes containing quantum dots sandwiched between metallic Au (or Ag) reflector and director layers together with Al$_2$O$_3$ spacer layers. We show that the linewidths and fine-structure splitting of the neutral exciton emission remain comparable to those measured in the corresponding unprocessed samples, demonstrating that the fabrication process preserves the optical quality of the emitters. In addition to broadband operation, we demonstrate that the planar architecture is compatible with electrical tuning via integrated diode structures, and strain tuning using piezoelectric actuators. In spite of limitations related to optical losses in the ultrathin metallic layers, the demonstrated fabrication simplicity, scalability, and compatibility with tunable quantum emitters establish planar antennas as a promising platform for solid-state quantum photonic devices.

Long-range Ising models (LRIMs) with dense nonlocal and competing interactions are central to statistical physics, quantum simulation, and complex networks. Although the spatial photonic Ising machine (SPIM) exploits intrinsic optical parallelism for Ising computation, its ability to faithfully encode dense long-range couplings and capture the resulting thermodynamic signatures remains underexplored. Here, we present a momentum-space-engineered SPIM framework that maps prescribed long-range coupling kernels onto momentum-space masks for parallel Hamiltonian evaluation. Based on a high-fidelity optical field propagation model, the annealing dynamics of LRIMs with power-law and Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions are systematically investigated. For the power-law model, we investigate the modulation of the estimated critical temperature by the decay exponent {\sigma} and coupling cutoff radius R. For the RKKY model, we reproduce diverse ordered states induced by complex competing long-range interactions. A proof-of-principle experiment demonstrates the physical feasibility of our approach. This framework broadens the class of many-body systems accessible to the SPIM platform.

Quantum error mitigation (QEM) is essential for extracting chemically accurate results from near-term quantum hardware. Many widely used QEM methods rely on uncontrolled heuristics whose bias depends on the specific circuit and noise realization. In this work, we employ QESEM—a characterization-based, unbiased quasi-probabilistic mitigation method—on IBM's Aachen quantum processor to compute the ground-state potential energy surface (PES) of the symmetrically-stretched water molecule. We consider a classically-optimized, single-layer perfect-pairing tiled unitary product state ansatz. We map this ansatz to an 8-qubit register corresponding to a (4,4) active space and the STO-3G basis set. Compared to the statevector reference, we find that raw QPU results typically overestimate the ground-state energy by around 500~mHa across the scanned geometries. On the other hand, QESEM-mitigated results fall approximately within 100~mHa, 30~mHa, or “chemical accuracy” ($\sim$1.5~mHa), depending on the target precision. We benchmark QESEM at both loose (0.1~Ha) and tight (0.01~Ha) precision targets, evaluating both individual and merged batches of runs. As the precision target is tightened, the accuracy improves systematically, matching or exceeding results reported in the literature. We further quantify the sampling cost of these results, reporting the number of shots required at each precision level. Our results show how, with the current levels of hardware error, reaching the highest accuracies demands substantial QPU time. The results demonstrate that the characterization-based, unbiased error mitigation provided by QESEM allows to measure quantitatively meaningful potential energy surfaces on current quantum hardware. Concurrently, they highlight the sampling overhead associated with QEM, which remains a central bottleneck en route to larger chemical problems and higher precision.

We study disorder-free localization in a spin-coupled quantum walk on the hypercube within the quantum Bernoulli noises framework. We derive a general criterion for disorder-free localization: it occurs if and only if some spectral subspace of a reduced unitary evolution contains a vector whose position marginal probability is non-uniform. For the Grover walk with distance-dependent coupling \(\phi_\sigma=|\sigma|\pi/(n+1)\) in dimension \(d=4\), we explicitly construct a non-uniform fixed point in the all \(+1\) spin configuration. This implies that disorder-free localization occurs in our model.

High-fidelity single-shot readout of superconducting qubits is essential for fault-tolerant quantum computation. Without a quantum-limited amplifier such as a Josephson parametric amplifier, the cryogenic high-electron-mobility-transistor (HEMT) low-noise amplifier (LNA) at the 4 K stage is the dominant noise source in the readout chain. HEMT LNAs are conventionally characterized by Y-factor measurements of the noise temperature $T_N$, independently of the quantum measurement they ultimately serve. Here we present a qubit-in-the-loop benchmarking method. The method uses the two-dimensional IQ histogram of single-shot readout as a direct figure of merit. We apply it to three state-of-the-art cryogenic InP HEMT LNAs with 53%, 60%, and 70% channel indium content, together with a commercial reference amplifier. The 60% and 70% devices have similar $T_N$ in Y-factor measurements, both lower than the 53% device. The 70% device has the highest gain, but qubit readout SNR and assignment fidelity $\mathcal{F}_a$ instead peak at 60%. Using this method, we map $\mathcal{F}_a$ against HEMT LNA dc power consumption for each device. $\mathcal{F}_a$ does not simply saturate with increasing power. For several devices it declines above a device-dependent power well below typical operating points. For the 60% device, which has the highest overall $\mathcal{F}_a$, about 1~mW is needed to maintain $\mathcal{F}_a > 85\%$. Across all four devices, $\mathcal{F}_a > 80\%$ is reached with as little as about 0.3~mW, roughly an order of magnitude below typical operating points. These results establish a qubit-referenced benchmarking methodology and provide practical guidance for amplifier selection and bias in power-constrained multi-qubit readout systems.

Hudson's theorem states that a pure state of a bosonic mode has a non-negative Wigner function if and only if it is Gaussian. It underwrites the reading of Wigner negativity as a faithful signature of pure-state non-classicality. We show the statement has no analogue on curved phase space. For the positive discrete series of $SU(1,1)$, realised on the upper sheet of a two-sheeted hyperboloid, the Wigner-positive pure states form a strictly larger set than the Perelomov coherent orbit. Superpositions of the lowest weight state with the first excited state stay positive up to a mixing angle of $24.93^\circ$ at Bargmann index $k=1$, and the admissible set has positive volume, with a maximal width that is not attained in the two-state direction. We show analytically that the quadratic form controlling positivity degenerates in the far field onto a single mixing angle. That degeneracy bounds the window by $\arctan(1/\sqrt{2k})$ and leaves the threshold itself fixed at intermediate hyperbolic distance.

Noise is a major challenge for current quantum computers. It can be broadly categorized into bit-flip and phase-flip errors. These two types do not necessarily affect the executed algorithm, thus also the application, in the same way. We illustrate this general effect for the example of the quantum approximate optimization algorithm (QAOA) applied to a small instance of the flight-gate assignment (FGA) problem. We compare bit-flip and phase-flip Pauli noise under both layer-level and gate-level noise models, using two circuit decompositions of the same ideal QAOA unitary: a CNOT-based decomposition and a native-$R_{ZZ}$ decomposition. In the simulations, bit-flip noise produces the larger degradation in the performance of the quantum optimization. The asymmetry is most visible in the layer-level and native-$R_{ZZ}$ simulations. We explain this by how the errors affect mixing, final measurements, and how they propagate inside the circuit. We then exploit these insights to tackle noise particularly efficiently using asymmetric error-correcting codes. As an illustration, we use the quantum parity code (QPC), a generalization of the 9-qubit Shor code, and show that a smaller asymmetric code can achieve nearly the same improvement as a larger symmetric choice. This demonstrates that error-correction resources should be assigned not only according to physical error rates, but also according to how strongly each error channel affects the application. As a result, asymmetric quantum error correction proves useful even in cases where the noise model is symmetric. Finally, we discuss how information about the noise obtained through calibration can be exploited in our approach.

More than two decades ago, Bennett et al. [Phys. Rev. A 59, 1070 (1999)] asked whether perfect local discrimination of orthogonal quantum states can require more than two copies. This question was subsequently answered for adaptive protocols that process the copies separately [Phys. Rev. Lett. 126, 210505 (2021)], but remained open when each laboratory is allowed to process its local copies collectively. Here we resolve this stronger setting and identify collective access across repeated local inputs as a distinct resource. For every fixed odd-prime local dimension, there exist complete maximal-stabilizer eigenbases whose copy complexity under individual-copy separable measurements diverges with system size. Under collective processing this behavior changes sharply: every maximal-stabilizer eigenbasis in odd-prime local dimension is perfectly decoded by one-round collective LOCC using at most three copies. Collective processing, however, does not remove multicopy hardness in general. For every fixed local dimension $d\ge2$, we prove the existence, within an explicit phase family, of complete bases whose copy complexity remains unbounded even under collective separable measurements, with a square root of the number of subsystems as lower-bound scale. Thus sample number, spatial measurement power, and coherent access across repeated local inputs are distinct resources in distributed quantum measurement.

Motivated by recent breakthroughs in the development of spin-based quantum processing units based on exchange-only (EO) spin qubits, we provide a roadmap for the implementation of quantum algorithms on the EO platform, ranging from the NISQ to the fault-tolerant era. To provide an algorithm-driven perspective on the scaling of quantum chips, we consider a range of applications targeting different stages of hardware maturity and formulate requirements for a successful realization. We show that the compilation method Parity Twine perfectly complements the hardware's capabilities to perform tasks such as the quantum Fourier transform or QAOA. Furthermore, we describe an error detection technique native to Parity Twine, which EO qubits can leverage in a unique and advantageous way to improve algorithm performance. Finally, since both near-term algorithmic benchmarks and a long-term perspective can be found in digital quantum simulation, we specifically discuss the fermionic fast Fourier transform and the simulation of Fermi-Hubbard models. The latter is explicitly discussed in the context of quantum error correction and a partially fault-tolerant realization. By providing detailed resource estimates and identifying scaling bottlenecks on each level, our work offers a quantitative perspective on EO-based quantum computing and will inform future hardware design choices.

Compact states embedded in a propagating band can carry quantum information, but finite-time transfer can populate modes outside their subspace. We show that a remote flux can refocus this amplitude without changing the transfer states or the motion-induced coupling out of their subspace. In a resonator ring, this separation is exact because both endpoints of the flux-bearing bond are nodes of every compact transfer state. For the same pulse, zero and refocusing flux both produce substantial excursions, but only the latter yields near-complete logical transfer. Interference between matrix amplitudes associated with different windings suppresses the endpoint error. Under matched control bounds, numerical optimization yields higher worst-input fidelity at the refocusing flux, providing a route to accurate transfer through coherent return.

We propose a cold-atom platform for precision tests of nonlinear and stochastic modifications to the Schrödinger equation, utilizing strongly correlated ultracold $^{133}$Cs in a uniform array of one-dimensional tubes formed by a two-dimensional optical lattice. Objective collapse models can be tested using the metastable super-Tonks-Girardeau gas. Based on a calibration test performed on our existing experimental setup, we project a sensitivity to the Continuous Spontaneous Localization collapse rate of $\lambda_c \simeq 1.8\times10^{-11}\,\mathrm{s^{-1}}$ at a correlation length of $r_c = 10^{-7}\,$m. This would establish a new bound an order of magnitude below the strongest existing constraint that remains robust against a cutoff in the collapse noise spectrum. Additionally, we can test deterministic nonlinear modifications by probing the symmetry-protected breathing mode frequency of the Tonks-Girardeau gas in harmonic traps. Crucial to both measurement schemes is the capability to independently tune the atom number and the linear density. By exploiting the different scaling laws associated with these parameters, we can cleanly distinguish genuine new physics signals from technical systematics.

Self-hybridized exciton polaritons in layered semiconductors emerge from the hybridization of excitonic resonances with confined photonic modes in films and provide a versatile platform for controlling light–matter interactions at the nanoscale. Yet, the nature of exciton–photon interactions and the collective and synchronous strong coupling of multiple excitons to the same photonic mode remain largely unexplored. Here, we use complementary momentum-resolved photoluminescence and cathodoluminescence spectroscopy to compare self-hybridized exciton polaritons in Ruddlesden–Popper perovskite flakes under optical and electron-beam excitation. We find that cathodoluminescence exhibits remarkably larger polaritonic level repulsion than photoluminescence, revealing an enhanced effective coupling strength under electron-beam excitation. We attribute this enhancement to the collective coherent excitation of multiple excitons by fast electrons, which couple to the same photonic mode and increase the interaction strength according to a $g_N=g_1\sqrt{N}$ scaling, with an effective number of up to $N\approx23$ coherently coupled excitonic oscillators. By reducing the electron kinetic energy, we further uncover a crossover to a partially incoherent excitation regime in which higher-order Fabry–Pérot exciton-polariton resonances disappear, leaving only the lowest polariton branches while coherent transition radiation persists. This transition arises because low-energy electrons excite excitons over extended spatial volumes, washing out the phase coherence required to sustain collective coupling and form polaritonic resonances. Our work shows that electron beams can actively modify collective light–matter coupling in layered semiconductors and establishes cathodoluminescence as a route to access excitation regimes beyond all-optical excitation schemes.

After a recollection of some of my encounters with Gilles Brassard, on the occasion of his 70th birthday I present, first, a new idea on creation of new information at a limited rate. Next, I develop the idea that "indeterminacy is relative" [Entropy {23} 1326 (2021)] and how this illuminates the compatibility between relativity and non-locality.

Compressed quantum encodings aim to overcome hardware limitations towards tackling challenging problems at scale, with many classical variables mapped onto noncommuting observables of fewer qubits. Classically, relaxations such as the semidefinite program formulation of MaxCut trade solution quality for computational efficiency. By contrast, quantum relaxations based on compression can amplify the worst-case complexity of the problem being solved. We study quantum random access optimization (QRAO), a special case of the Pauli correlation encoding (PCE) framework that assigns up to three binary variables to the Pauli $X$, $Y$, and $Z$ observables of each qubit, with the packing choices determining the compressed Hamiltonian to be optimized. We identify explicit QRAO optimal energy promise problems complete for NP, StoqMA, and QMA, with inverse-polynomial promise gaps for the latter two. Our problem reductions preserve inverse-polynomial promise gaps without requiring gadgets or ancillas. For any prescribed packing, we show that weighted MaxCut instances compress, up to a known shift and rescaling, to arbitrary nonnegative-weight pairwise Pauli couplings allowed by the packing. For QRAO, using one aligned axis gives an NP-complete energy problem. Using two or three positive aligned Pauli axes generally gives QMA-complete problems, with bipartite restrictions in BQP $\cap$ StoqMA. We show that this computational hardness survives compilation and is practically relevant. Notably, this result applies directly to the current QRAO compiler implementation in Qiskit Optimization 0.7.0, confirming our hardness results are not artifacts of artificial or contrived packing rules. Altogether our results identify worst-case complexity barriers arising from quantum compression, while making no broad claims about typical cases or the performance and trainability of algorithm pipelines that use it.

X-ray projection radiography is a non-invasive imaging technique used in medical diagnostics and industrial inspection. The simulation of X-ray projections is commonly used to optimise acquisition protocols and improve image quality before performing costly scans. Classical photon transport simulations that include realistic X-ray scattering physics are computationally expensive because they require the sampling of a large number of distinct scattering paths. This limits the practical exploration of parameter spaces such as beam energy. Quantum computing offers the potential to solve high-dimensional problems faster by making use of quantum properties such as superposition. This work introduces a discrete-time quantum walk algorithm that simulates the transport of X-ray photons through heterogeneous volumes. It approximates the physics of X-ray projection radiography, including processes such as photoelectric absorption and higher-order scattering, including Compton and Rayleigh scattering. The quantum walk encodes all admissible photon paths into a single quantum state, enabling all scattering histories to be propagated simultaneously via the superposition principle. This quantum state representation enables flexible readout of various imaging modalities, including the primary, i.e., unscattered, image, or images exclusively containing Rayleigh and Compton scattering of specified orders. A quantitative comparison with classically computed reference simulations shows that the proposed quantum walk accurately reproduces radiographic projections, given the limitations of the underlying physical model. These results indicate that quantum circuits for X-ray transport can produce accurate radiographic images and imply that, as quantum hardware scales up, these algorithms could outperform classical Monte Carlo-based approaches in large-scale, scatter-aware virtual imaging studies.

Nondestructive quantum state discrimination is a fundamental primitive in distributed quantum information processing, where shared multipartite entangled resources need to be identified without being consumed. In this work, we present a scalable ancilla-assisted protocol for the strict nondestructive discrimination of $n$-qubit GHZ-class states distributed among distant parties. By employing multipartite GHZ ancillary states and local unitary interactions, we show that the computational-pattern and relative-phase information of the system GHZ state can be coherently mapped onto two ancillary registers while leaving the system state unchanged. We explicitly derive the discrimination rules for three- and four-qubit GHZ-class states and develop a systematic extension to arbitrary $n$. We further investigate the discrimination protocol in the presence of depolarizing and amplitude-damping noise in the ancillary system and obtain analytical expressions for the success probability and the corresponding critical noise thresholds. The protocol is also implemented using the IBM Qiskit platform to demonstrate its experimental feasibility and reproduce the expected ancillary measurement signatures. The proposed framework provides a scalable approach to the strict nondestructive discrimination of multipartite GHZ-class states and suggests a broader interpretation of the ancillary GHZ resources as probes of decoherence, opening a possible connection to quantum decoherence sensing in distributed quantum systems.

Bosonic error correction provides a hardware-efficient route to protected qubits for accurate quantum information processing. A critical component for error correction of rotation-symmetric bosonic (RSB) codes, like the well-known cat codes, is the two-mode controlled-rotation (CROT) operation. The CROT gate is useful because of its code-agnostic generality and its error-propagation properties. While the CROT gate can in principle be composed from existing bosonic physical primitives, the desirable properties are typically lost when composed as a sequence of imperfect primitive operations. Past work has focused on direct implementations that rely on features of specific codes. Here, we present a direct route to CROT within the circuit-QED architecture that retains its code-agnostic and error-propagation characteristics. By driving a transmon simultaneously coupled to two microwave cavities, we controllably enhance the effective nonlinearities between the microwave cavities and thus engineer the necessary two-mode interaction underlying the CROT gate. Using only a single drive frequency, we can achieve an on-off ratio sufficient for gate implementation, while minimizing mode distortions. We provide simple analytical formulas that permit the identification of potential working regimes, further refined by exact numerics, and illustrate the efficacy of our CROT approach in an error-correction example involving different RSB codes within the same circuit. Our CROT gate adds to the arsenal of direct two-mode gates available for general bosonic information processing.

We show that 2-fold Forrelation with inverse-polylogarithmic promise gap can be solved, with bounded error, by polynomial-size QAC$^0$ circuits. Unlike the standard oracle-based Forrelation algorithm, our circuits receive the input explicitly, in the same form as the AC$^0$ circuits against which Forrelation is known to be hard. At constant gap, this yields a natural promise-problem separation between QAC$^0$ and AC$^0$.

A quantum error correction decoder is a library other people's results depend on, judged in one dominant way. Sample errors, decode, and count wrong logical observables. We ask what else can be checked there. Our conformance contract needs no oracle. One check asks that a returned correction explain the syndrome in the caller's index space. The other hands a decoder one instance under two presentations differing only in bookkeeping, where two feasible corrections of different weight prove the heavier is not minimum-weight. Verdicts are gated on what each library declares, so a firing contradicts a published guarantee. Nine configurations from five public libraries give three results. Documentation answers 4 of 54 capability questions. Bounded-distance correctness, the property callers most depend on, has a direct declaration yield of 0.0%, though its hypotheses hold in 62.1% of cases. Presentation sensitivity is real but shallow. One solver moved to a 26% heavier correction under a different numbering, which reaches the logical class at most once in twenty thousand shots. Established evaluation misses corruptions that preserve logical parity, while one summation over the caller's weights catches every one we injected. All 639 certificates ship as bundles a standalone verifier re-derives from first principles.

Classical shadows extract quantum properties from reusable classical records, typically obtained through randomized measurement settings. Although individual settings may be shallow, switching among them introduces control, calibration, and reconfiguration costs beyond conventional metrics. Here we construct, for every $n$, a single fixed shallow quantum analyzer whose Born outcomes replace externally sampled settings as labels for reusable shadow snapshots. The analyzer combines a freshly prepared $n$-qubit fiducial register $A$ with parallel Bell readout of $A$ and the unknown system $S$, producing one $2n$-bit record per copy. The same circuit realizes a rank-one minimal informationally complete measurement: one fixed setting replaces the $3^n$ local-Pauli settings conventionally used for complete reconstruction while retaining the minimum $d^2$ outcomes with $d=2^n$. Its Pauli-diagonal frame admits an analytic inverse. For fixed Hermitian observables, the Haar-averaged conditional variance has a dimension-independent coefficient, whereas the state-uniform coefficient is dimension dependent. For $n\ge3$, worst-state Pauli variances remain bounded in the axial sector and scale as $\Theta(d)$ in the mixed sector. Fiducial preparation before system contact uses $n-1$ arbitrary two-qubit gates, no work qubits beyond $A$, and logarithmic depth under all-to-all connectivity. The unknown system undergoes one parallel system-ancilla entangling layer followed by local Hadamards and readout. Measurement-assisted preparation achieves $O(1)$ adaptive quantum depth using $n+1$ extra qubits in the heralded route, or $O(n\log n)$ auxiliaries for deterministic completion. These tradeoffs show that part of the measurement-setting randomness and control complexity normally supplied shot by shot can instead be compiled into a fixed reusable analyzer.

We study the operator Michelson contrast Delta(A) = (kappa(A)-1)/(kappa(A)+1), with kappa(A)=||A|| ||A^{-1}||, for positive invertible operators, and introduce its logarithmic parametrization via arctanh(Delta(A)) = (1/2) ln kappa(A). This defines the Operator Logarithmic Contrast (OLC), extended to all invertible operators via polar decomposition. We prove OLC is subadditive under multiplication: OLC(AB) <= OLC(A)+OLC(B). For positive invertible A, we identify OLC(A) exactly as the projective Thompson distance from the identity ray to the ray of A. We establish a sharp dimensional threshold for equality in subadditivity: for dimensions 2 and 3, equality forces commutativity, while n=4 is the smallest dimension admitting noncommuting equality examples. Moreover, equality still forces commutativity in any total dimension if the operators factor as pure Kronecker products X = tensor X_i and Y = tensor Y_i with each factor dimension <= 3. We derive contraction inequalities, sum bounds, trace estimates for density operators, Lipschitz continuity (including singular limits), and limiting behavior for Cesaro means and infinite products. For density operators, we obtain an exact closed-form bijection between OLC and von Neumann entropy for qubits; prove this bijection does not exist for d >= 3; and establish upper/lower entropy envelopes at fixed condition number, showing the admissible range [S_min(kappa), S_max(kappa)] satisfies ln 2 <= S_max(kappa) < ln 3 for every kappa > 1. The qubit case recovers, as an operator lift, the classical Michelson-Jensen-Shannon equivalence of Bruni, Rossi, and Vitulano, while a counterexample shows this equivalence fails for d > 2 as a direct consequence of the non-bijectivity.

We study a single-particle Lindblad lattice in which nonreciprocal incoherent hopping is combined with a tunable coherent boundary link. The link changes the Hamiltonian boundary condition while the incoherent jump rates are kept fixed, so it does not directly alter the diagonal population generator. Its effect on the Liouvillian gap comes from population-coherence-population feedback: the Hamiltonian couples populations to damped coherences, and eliminating those coherences produces a frequency-dependent self-energy for the slow population branch. For the periodic reference system, where translation symmetry is imposed on both the Hamiltonian and the dissipator, we derive an exact fixed-momentum reduction, a scalar secular equation for the population-connected branch, and the associated hydrodynamic drift and coherence-corrected diffusion. For open finite lattices, exact diagonalization and sparse near-zero eigensolvers show that the coherent boundary link can enhance or suppress the gap in one dimension and produce geometry-dependent responses in two dimensions. We also show that an observed relaxation scale can differ from $1/\Delta_{\mathcal L}$ when the gap family has weak visibility in the chosen perturbation and observable. The periodic construction gives exact analytical benchmarks, while finite-size simulations in one and two dimensions demonstrate how the same coherence-mediated mechanism controls open-boundary gaps and observable relaxation.

We determine the spectrum of the predual generator of an irreducible Gaussian quantum Markov semigroup on trace-class operators, the natural space for density operators. The drift matrix governs the linear part of the Gaussian evolution and organizes the spectral classification. When the linear flow generated by this matrix is not periodic, the spectrum is the closed left half-plane. If all drift eigenvalues have negative real part, every interior point is an eigenvalue. There are no trace-class eigenvectors if some drift eigenvalue has positive real part or all have zero real part. For periodic flow, the spectrum consists of unions of horizontal half-lines or filled parabolic regions. Examples show that irreducibility cannot in general be omitted. We apply the results to oscillators, free particles, and boson chains.

Programmable control of individual pulses in a high-repetition-rate (typically MHz) ultrafast pulse train is a long-standing goal for optical arbitrary waveform synthesis. Here, we report a programmable pulse-by-pulse shaper that enables deterministic spectral-temporal control of ultrafast pulses at a repetition rate of $\sim$ 20~MHz. By synchronizing an FPGA-driven electro-optic modulation on the stretched waveform in a temporal 4$f$ shaping system, the regime writes pulse-index-dependent spectral phase profiles onto individual pulses. We demonstrate three levels of programmable ability: zero-order phase coding that maps pulse-by-pulse phase sequences into double-slit-like spectral-temporal interference; first-order phase programming that produces arbitrary temporal trajectories with deterministic delay; and fractional-order phase engineering that generates programmable temporal breathing. By launching the shaped pulse train into a nonlinear fiber stage, the programmed temporal breathing is converted into one spectral breathing. We further construct a phase-level-dependent regime map of nonlinear spectral breathing, revealing transitions from weak single-envelope breathing to multi-peak spectral splitting and strongly breathing merged-spectrum dynamics, in agreement with numerical simulations. This pulse-by-pulse spectral-temporal synthesis platform establishes pulse index as a programmable degree of freedom for ultrafast pulse shaping and provides a route toward real-time and pulse resolved optical arbitary waveform synthesis.

Quantum predictive advantage under shift usually requires known target labels. We derive the assumption-free sharp identified interval for the finite-batch advantage of a fixed candidate over the best member of a prespecified fixed classical-kernel family under any bounded loss and unrestricted completions of the unaudited labels; zero-one accuracy has exact closed-form partial-label updates. Across eight security shifts, zero-label upper endpoints against 115 classical kernels span 0.002-0.088. Retrospective auditing reduces every endpoint to 0.010 with 0-33 of 500 labels, including entangling-ZZ models. Prospective corroboration on two eligible tasks met predefined criteria: four task-classifier medians require 0-3 labels (overall median 0; maximum 76), and all 20 realized effects are negative; a third task fails its feature gate. Protocol controls reverse an apparent advantage, while finite-shot noise can increase predictive distinctness without useful advantage. The framework separates protocol validity, target predictive indispensability, and quantum relevance.