Papers

The mobility edges (MEs) that separate localized, multifractal and ergodic states in energy are a central concept in understanding Anderson localization. In this work we study the effect of several mutually commensurate quasiperiodic frequencies on the mobility edge formation. We focus on the example of the addition of a constant offset to the quasiperiodic potential of the one-dimensional all-bands-flat diamond chain. We show that this additional offset can transform the anomalous mobility edges (AMEs), i.e. the energies, separating localized and multifractal states, into conventional mobility edges, separating localized from delocalized states. Also this appears to be the first example which shows the inability of Avila's global theory to analytically predict the ME location. We observe this both quantitatively, through the ME location mismatch, and qualitatively, via the formation of multiple MEs, not predicted by the theory.

Efficient sampling from ensembles of Hamiltonian cycles is critical for predicting the thermodynamic properties of compact polymers, with applications including modeling protein and RNA folding and designing soft materials. Although classical Monte Carlo methods are widely regarded as the standard approach, their efficiency is strongly limited when applied to compact polymers. In this work, we enable a quadratic speedup in the estimation of thermodynamic properties of maximally compact polymers and heteropolymers by quantum computation. To this end, we encode the target thermodynamic ensemble into the amplitudes of a quantum state, i.e., a quantum sample, which can be processed via amplitude amplification. Using quantum equational reasoning, we construct a local parent Hamiltonian whose unique ground state realizes a quantum sample of all Hamiltonian cycles. This state can be prepared on quantum hardware using ground-state preparation methods, such as quantum annealing, and subsequently manipulated to generate quantum samples of polymers and heteropolymers at a target temperature. Finally, we approximate the quantum sample as a tensor network, revealing an entanglement area law. For fixed-width rectangular lattices, we obtain a time-efficient and compact encoding of the full ensemble of Hamiltonian cycles, enabling the efficient evaluation of expectation values, partition functions, and configuration probabilities via tensor contractions, without resorting to sampling.

Traveling-Wave Parametric Amplifiers (TWPAs) are ubiquitous in superconducting circuit readout, providing high gain with near-quantum-limited noise performance across a wide bandwidth. Their operation, however, relies on a strong microwave pump tone that is typically delivered using off-chip passive components, such as directional couplers or diplexers. These external elements add loss, increase system complexity, and limit scalability. Here, we present a traveling-wave parametric amplifier that incorporates on-chip input and output diplexers for pump routing. This co-fabricated architecture offers a compact and scalable solution for superconducting-circuit readout.

High fidelity qubit readout is a cornerstone for quantum information protocols. In traditional superconducting qubit readout, a chain of microwave amplifiers and nonreciprocal components aid in detecting the qubit's state with tolerable added noise and backaction. However, the loss, size, and magnetic field of standard nonreciprocal components have sparked a decades-long search for more efficient and scalable alternatives. One prominent approach employs networks of parametrically coupled modes to achieve nonreciprocity. While this class of devices can be directly integrated with the qubit's readout cavity, current understanding of the resulting single quantum system is substantially lacking. Here we provide a first-principles theoretical tool to understand and design networks of linear modes integrated with embedded qubits. We utilize this theory to inform and analyze the experimental implementation of a qubit readout with an integrated three-mode nonreciprocal system. In doing so, we achieve excellent agreement between the experimental and theoretical qubit measurement and dephasing rates. We then theoretically analyze the same system operated as an integrated nonreciprocal amplifier, predicting high efficiency for reasonable experimental parameters.

This replaces v1, which reported a ten-order shot-noise suppression from a quantum reservoir autoencoder and a two-phase protocol reconstructing unseen inputs at MSE ~ 10^-4. We withdraw both claims: under one consistent evaluation the suppression reverses sign (reset channels degrade reconstruction 144x), the two-phase target is invertible in closed form without training, and a polynomial using no quantum features matches the full model. We trace these to four evaluation artifacts; the fourth also invalidates the companion latent code, which never leaves its initialization. What survives the same controls is a joint scrambling channel: injected on one reservoir half, read out on the other, decoded by a readout calibrated once on training messages. Over 32 realizations the held-out error is below chance in 31-32 (permutation p<10^-4) with a shuffled control at chance. Scrambler T-doping is necessary for one-shot injection, while interleaved injection supplies its own non-Cliffordness; a matched classical scrambler decodes the task better, so the transport is not evidence of a quantum mechanism. The access threshold, recomputed on nested subsystems with right-censoring, gives interleaved medians f* = 0.25-0.33; one-shot injection reaches full detectability in only half the realizations at the largest settings. A trained variational ansatz loses to the fixed untrained circuit by 2.6-4.4x. Three extensions pass the same discipline: streaming requires dissipative reset of the accessible half; the decoder does not transfer across the eight keys tested; a receiver holding the key matches the supervised ceiling from self-simulated pairs. A first hardware run decodes at 0.23 with the shuffled control at chance, while coherent device errors partially open the t=0 control. We close with the controls that separate transport from interpolation.

Understanding how isolated quantum many-body systems thermalize remains a central question in modern physics. We study the onset of ergodicity in a two-dimensional disordered Heisenberg Floquet model using digital quantum simulation on IBM's Nighthawk superconducting processor, reaching system sizes of up to $10\times10$ qubits. We probe ergodicity across different length scales by coarse-graining the system into spatial patches of varying sizes and introducing a measure based on the collision entropy of each patch, enabling a detailed study of when ergodic behavior emerges across scales. The high sampling rate of superconducting quantum processing units, together with an optimal sample estimator, allow us to access patches of sizes up to $3\times3$. We observe that as the Heisenberg coupling $J$ increases, the noiseless system undergoes a smooth crossover from subergodic to ergodic behavior, with smaller patches approaching their random-matrix-theory values first, thereby revealing a hierarchy across scales. In the region of parameter space where classical tensor-network simulations are reliable, small patches or small values of $J$, we find excellent agreement with the error-mitigated quantum simulation. Beyond this regime, volume-law entanglement and contraction complexity growth causes the cost of classical methods to rise sharply. Our results open new directions for the use of quantum computers in the study of quantum thermalization.

The theoretical efficiency of classical shadow tomography is predicated on a perfect Haar-random unitary ensemble, yet this mathematical ideal remains physically unattainable in near-term hardware. Here, we report the experimental discovery of a fundamental accuracy bound on integrated photonic processors: a “Hardware Horizon” where the reconstruction error undergoes a sharp phase transition. While the error initially obeys the predicted statistical scaling $\mathcal{O}(M^{-1/2})$, it abruptly saturates at a floor determined by the spectral distortions of the realized unitary group. By deriving a phenomenological error model, we decouple the competing mechanisms of static coherent spectral distortion and dynamic decoherence, demonstrating that this intrinsic noise floor imposes a hard bound that statistical accumulation cannot overcome. These findings establish that the utility of shadow tomography on NISQ (noisy intermediate-scale quantum) hardware is defined by a specific scaling law involving hardware parameters, necessitating active compensation strategies to bridge the gap between theoretical purity and the noisy reality of integrated photonics.

We develop a microscopic theory of thermalisation for a thermometer coupled to a many-body bath beyond standard Markovian and Fermi-golden-rule assumptions. By modeling interaction matrix elements in the non-interacting basis as independent random variables, we derive a diffusion-propagator expression for the reduced dynamics and show that relaxation is controlled by the distribution of interaction-induced level broadenings. The theory predicts a thermalisation timescale set by the inverse typical broadening and yields a non-Markovian generalization of global balance. Exact-diagonalization tests for heavy-tailed Lévy couplings, an all-to-all transverse-field Ising model, and the one-dimensional Imbrie model show good agreement with these predictions.

Efficient preparation of nonclassical bosonic states is a central requirement for quantum computing, simulation, and precision metrology. We study resource-efficient quantum state preparation in bosonic qudit systems using the SNAP-displacement (SD) protocol. Existing SD-based approaches typically require a large number of gates and SNAP phases, resulting in complex control pulses with longer ansatz durations and amplified impact of photon-loss and control errors. In this work, we focus on the near- to medium-term regime, in which noisy quantum devices impose trade-offs on the fidelity that can be achieved, which must be taken into account. Specifically, we propose to optimize only a subset of the SNAP phases and introduce three progressively more general sparse ansatzes. To provide fine-grained control and identify the most suitable ansatz for a given target fidelity, we further employ a scalarized multi-objective optimization that trades off fidelity against either the number of phases or the duration of the ansatz. Numerical results for several target states and qudit dimensions up to $d=64$, evaluated through the hypervolume of the Pareto frontiers, show that these sparse ansatzes achieve favorable trade-offs over the fully parameterized SD protocol in both ideal and noisy settings. The advantage is strongest and most consistent when minimizing the number of phases, while improvements in ansatz duration are smaller and more dependent on the target-state family and noise level, suggesting a practical route to more efficient near- and medium-term bosonic state preparation.

We introduce an algebraic structure for studying state-independent contextuality arguments, a key form of quantum non-classicality exemplified by the well-known Peres-Mermin magic square, and used as a source of quantum advantage. We introduce commutation groups presented by generators and relations, and analyse them in terms of a string rewriting system. There is also a linear algebraic construction, a directed version of the Heisenberg group. We introduce contextual words as a general form of contextuality witness. We characterise when contextual words can arise in commutation groups, and explicitly construct non-contextual value assignments in other cases. We give unitary representations of commutation groups as subgroups of generalized Pauli $n$-groups.

Are Gaussian measurements enough to distinguish between Gaussian states? Here, we tackle this question by focusing on the max-relative entropy as an operational distinguishability metric. Given two general multimode Gaussian states, we derive a condition, based on their covariance matrices, that completely determines whether or not there exists an optimal Gaussian measurement achieving the max-relative entropy. When the condition is satisfied, we find this optimal measurement explicitly. When the condition is not met, there is a strict gap between the distinguishability achievable by Gaussian measurements and the unconstrained max-relative entropy in which all measurements are allowed. We illustrate our results in the single-mode setting, and show examples of states for which this gap can be made arbitrarily large, revealing novel instances of Gaussian data hiding.

Driven nonlinear oscillators constitute a universal paradigm for understanding synchronization, frequency pulling, and frequency comb formation in nonequilibrium systems. Here, we realize such an emergent nonlinear oscillator in strongly interacting cesium Rydberg vapor, where coherent optical excitation, dissipation, and long-range interactions give rise to a driven-dissipative time crystal phase with intrinsic oscillation frequencies. Applying a radio-frequency (RF) field allows controlled tuning of the intrinsic oscillation frequency. Under RF heterodyne conditions, we observe intermodulation, frequency pulling, and, at strong drive, the emergence of a comb-like spectrum in the atomic coherence. We quantitatively capture these observations using a four-level mean-field model and demonstrate a classical analogue with a driven Van der Pol oscillator. Our results establish interacting Rydberg ensembles as a tunable platform for exploring nonequilibrium time-crystalline order, nonlinear synchronization, and frequency comb generation in many-body atomic systems.

High-fidelity quantum operations are the cornerstone of fault-tolerant quantum computation. In open quantum systems, traditional optimal control only passively resists decoherence, leaving environment-induced uncertainty as a fundamental performance bottleneck. To overcome this, we propose a new optimal control framework with flag ancillas and the Flag-GRAPE algorithm, which can actively tailor the system's noise structure. Through embedding post-selection directly into the objective function, Flag-GRAPE correlates decoherence errors with the ancilla's unexpected state. Subsequent measurement and post-selection effectively expel this uncertainty, circumventing the fidelity bounds of traditional control. Numerical simulations in a superconducting quantum circuit demonstrate a $51\%$ reduction in infidelity compared to traditional closed-system pulses and also show that such enhancement is robust across broad noise regimes. Furthermore, by actively converting unstructured decoherence into heralded erasure errors, Flag-GRAPE is inherently compatible with quantum error correction. We demonstrate this by initializing a logical cat-code state, showing that the combination between Flag-GRAPE and QEC yields immediate state preparation enhancements. This new framework can reduce hardware overhead for fault-tolerant architectures and open up a practical path toward logical state preparation gain in near-term experiments.

Developing quantum algorithms to simulate fluid dynamics has become an active area of research, as accelerating fluid simulations could have significant impact in both industry and fundamental science. While many approaches have been proposed for simulating fluid dynamics on quantum computers, it is largely unclear whether these algorithms will provide speedup over existing classical approaches. In this paper we give evidence that quantum computers cannot significantly outperform classical simulations of fluid dynamics in general. We study two models of fluids: the Korteweg-de Vries (KdV) equation, which models shallow water waves, and the incompressible Euler equations, which model ideal, inviscid fluids. We show that any quantum algorithm simulating the KdV equation or the Euler equations for time $T$ requires $\Omega(T^2)$ and $e^{\Omega(T)}$ copies of the initial state in the worst case, respectively. These lower bounds hold for the task of preparing the final state, and similar bounds hold for history state preparation. We prove the lower bound for the KdV equation by investigating divergence of solitons. For the Euler equations, we show that instabilities enable fast state discrimination.

The coordination complexes of Yb(III) exhibit some of the longest spin coherence times among 4f compounds, making them a promising platform for molecular quantum technologies. While spin-phonon relaxation remains a limiting factor for coherence times even at low temperature, its control through chemical design has the potential to push these spin qubits prototypes beyond current limits. With the aim of providing insights on how to chemically control spin-phonon relaxation, we here present a full ab initio study of spin-phonon dynamics for three Yb(III) molecules exhibiting minimal chemical differences, yet quantitatively different spin relaxation times. Results show that low-temperature relaxation is governed by Raman processes triggered by a small group of largely delocalized low-energy phonons. The analysis of these contributions highlights that the modulation of spin-phonon coupling by molecular structure modifications beyond the first coordination shell are highly non-trivial in nature and hard to rationalize in simple chemical terms. These findings call for a conceptual step change from the attempt to use simple magneto-structural correlations to interpret the effect of molecular structural modifications on spin-phonon relaxation, and present predictive first-principles frameworks as a potential driving force of future chemical design strategies

In quantum theory, equilibrium statistical mechanics is usually formulated through the canonical ensemble, whose privileged status is tied to the Euclidean continuation of time evolution. The microcanonical ensemble, by contrast, is commonly introduced as a separate spectral construction. In this work we show that this asymmetry is representational rather than structural. We formulate the system in an extended Hilbert space in which time is promoted to an auxiliary clock degree of freedom and physical states are selected by a reparametrization-invariant constraint operator $\hat C = \hat P_T + \hat H$. The corresponding projector $\delta(\hat C)$ provides a single unified object from which both canonical and microcanonical ensembles emerge as complementary projections in the clock sector. In the clock-time representation, a purely imaginary clock separation yields the Euclidean kernel and the canonical partition function. In the conjugate clock-energy representation, the same projector reduces to the spectral operator $\delta(\hat H-E)$ and hence to the microcanonical density of states. The main consequence is structural: canonical and microcanonical statistics need not be introduced as independent constructions, since both are already encoded in the same constrained quantum dynamics.

We present a method for analyzing general time series by employing the history state formalism of quantum mechanics. This formalism allows us to describe a complete evolution based on a single quantum state, the history state, which simultaneously includes -also as a quantum system- the reference clock. It naturally leads to the concept of system-time entanglement, with the ensuing entanglement entropy constituting a measure of the effective number of distinguishable states visited in the history. Through a quantum coherent state embedding of the time series data, it is then possible to associate a quantum history state to the series. The gaussian overlap between these coherent states provides thus a smooth measure of distinguishability between the series data. The eigenvalues of the corresponding overlap matrix determine in fact the entanglement spectrum and entropy of the history state, which provide a rigorous characterization of the evolution. As illustration, the formalism is applied to typical financial time-series data. Through the entanglement entropy and spectrum, different evolution regimes can be identified. Entanglement based volatility indicators are also derived, and compared with standard volatility measures.

Quantum channel discrimination is a fundamental task in quantum information processing. In the one-shot regime, discrimination between two candidate channels is characterized by the diamond norm. Beyond this basic setting, however, many scenarios in distributed quantum information processing remain unresolved, motivating notions of distinguishability that capture the power of the available resources. In this work, we formulate a theory of testers for bipartite channel discrimination, leading to the concept of the entanglement cost of bipartite channel discrimination: the minimum Schmidt rank $k$ of a shared maximally entangled state required for local protocols to achieve the globally optimal success probability. We introduce $k$-injectable testers as a tester-based description of entanglement-assisted local discrimination and, in particular, study the class of $k$-injectable positive-partial-transpose (PPT) testers, which constitutes a numerically tractable relaxation of the practically relevant class of LOCC testers. For every $k$, we derive a semidefinite program (SDP) for the optimal success probability, which in turn yields an efficiently computable one-shot PPT entanglement cost. To render these optimization problems numerically feasible, we prove a symmetry-reduction principle for covariant channel pairs, thereby reducing the effective dimension of the associated SDPs. Finally, by dualizing the SDP, we derive bounds on the composite channel-discrimination problem and illustrate our framework with proof-of-principle examples based on the depolarizing channel, the depolarized SWAP channel, and the Werner–Holevo channels.

The Bernstein-Vazirani (BV) algorithm is frequently taught as a canonical example of quantum parallelism, yet the standard interference-based explanation often obscures its underlying simplicity. We present a geometric reframing in which the Hadamard gate "wrapping" acts as a global basis rotation rather than a generator of computational complexity. This perspective reveals that the algorithm is effectively a classical linear computation over GF(2) performed in the conjugate Fourier basis, with the apparent parallelism arising from coordinate transformation. Building on Mermin's earlier pedagogical shortcut, which presented a 'classical' circuit equivalent but stopped short of explicitly labeling it as such, we elevate this to a formal geometric framework. In the extension, we distinguish between globally rotated circuits – which we reveal as classical linear computations – and topologically twisted circuits that generate quantum entanglement. We introduce a pedagogical taxonomy distinguishing (1) pure computational-basis circuits, (2) globally rotated circuits (exemplified by Bernstein-Vazirani), and (3) topologically twisted circuits involving non-aligned subsystem bases. This framework allows viewing the Gottesman-Knill theorem from a new angle, extends students' understanding of phase kickback and the 'Ricochet Property'. Furthermore, it provides a more intuitive starting point for explaining Bell-pair extensions through concrete circuit derivations and Qiskit simulations suitable for undergraduate quantum information courses. The outlook explores how this geometric view paves the way for understanding entanglement as topological twists.

Fast and high-fidelity qubit measurement plays a key role in quantum error correction. In superconducting qubits, measurement is typically performed using a resonant microwave drive on a readout resonator dispersively coupled to the qubit. Shorter measurement times require larger numbers of photons populating the readout resonator, which ultimately leads to undesired measurementinduced state transitions (MIST) of the qubit. MIST can be particularly problematic because these transitions often leave the qubit in a high energy state, and the MIST locations in readout parameter space drift as a function of qubit offset charge. In transmon qubits, these drifts have been avoided using very large qubit-resonator detunings or dedicated offset charge biases. In this work, we take an alternative approach and add an inductive shunt to the transmon to eliminate the offset charge dependence and stabilize the MIST. We experimentally characterize MIST in several different inductively-shunted transmons, in agreement with quantum and semiclassical models for MIST. These results extend to other inductively-shunted qubits.

The Clifford Hierarchy has been a central topic in quantum computation due to its strong connections with fault-tolerant quantum computation, magic state distillation, and more. Nevertheless, only sections of the hierarchy are fully understood, such as diagonal gates and third level gates. The diagonal part of the hierarchy can be climbed by taking square roots and adding controls. Similarly, square roots of Pauli gates (first level) are Clifford gates (climb to the second level). Based on this theme, we study gates whose square roots climb to the next level. In particular, we fully characterize Clifford gates whose square roots climb to the third level.

This is a book about operational probabilistic theories. The standard approach in such theories is from a time forward perspective. In this book we mostly take a time symmetric perspective. This presents a branding problem. Is this a niche book merely about time symmetry? No. This is a comprehensive book about operational probabilistic theories, but mostly from a time symmetric perspective. In fact, this book consists of (1) a simple book about simple operations having simple causal structure (where all the inputs are before all the outputs), and (2) a complex book about complex operations that can have complicated causal structure (a complex operation is equipped with a causal diagram). For the simple case we are able to show that the time symmetric perspective is equivalent to the time forward perspective. In each book we set up (A) operational probabilistic theories (OPTs) in terms of operations, (B) Operational Quantum Theory (OQT) in terms of operator tensors which correspond to operations, and (C) the theory of Hilbert objects which can be doubled up to give operator tensors. Operations are required to be physical which guarantees that circuits built out of operations have probabilities between 0 and 1 and that certain causality conditions are met. We prove that when we wire together operations the resulting networks are also physical. We model Sorkin's impossible measurements with complex operations and show that physicality prevents anomalous signalling. We develop diagrammatic notation for Hilbert objects. This includes mirrors for doubling up and mirror theorems. We use this framework to prove time symmetric causal dilation theorems for various causal diagrams.

We study in detail the dynamics of unstable two-level quantum systems by adopting the Bloch-vector representation. We identify a novel class of critical scenarios in which the so-called energy-level and decay-width vectors, ${\bf E}$ and ${\bf\Gamma}$, are orthogonal to one another, and the parameter $r = |{\bf \Gamma}|/(2|{\bf E}|)$ is less than~1. Most remarkably, we find that critical unstable qubit systems exhibit atypical behaviours like coherence–decoherence oscillations when analysed in an appropriately defined co-decaying frame of the system. By making use of a Fourier series decomposition, we define anharmonicity observables that quantify the degree of non-sinusoidal oscillation of a CUQ. We apply the results of our formalism to the neutral-meson systems and derive generic upper limits on these new observables. In particular, we provide a compilation table of all well-explored meson–antimeson two-level systems in terms of Bloch-sphere parameters.

Randomized compiling (RC) is an established tool to tailor arbitrary quantum noise channels into Pauli errors. The effect of both spatial and temporal noise correlations in randomly compiled circuits, however, is not fully understood. Here, we show that for a broad class of correlated Gaussian noise, RC reduces both the strength and temporal range of correlations. For Clifford circuits, we derive a simple analytical expression for the circuit fidelity of randomly compiled circuits. Surprisingly, we show that this fidelity is always increased by the presence of correlations, suggesting that correlations are a resource in randomly compiled circuits. To leading order in system-bath coupling, we also show that RC suppresses the quantum component of bath correlations, implying that one can safely treat weak noise as being classical. Finally, through extensive numerical simulations, we show that our results remain valid for many relevant non-Clifford circuits. These results clarify how RC mitigates memory effects and enhances circuit robustness.

Valence-bond wavefunctions such as spin-coupled generalized valence bond (SCGVB) provide compact and chemically interpretable descriptions of strong correlation, but their nonorthogonal determinant structure makes quantum evaluation of overlaps and Hamiltonian matrix elements difficult. Here we introduce an ancilla-free, measurement-driven framework that reformulates these quantities as vacuum expectation values of Pauli-string operators, enabling evaluation with shallow circuits, local Clifford rotations, and computational-basis measurements, without controlled operations. We validate the method for H$_4$ along a dissociation pathway and for a 70-determinant C$_2$ active-valence benchmark. The reconstructed matrices agree with the classical Löwdin-based reference, while Chirgwin-Coulson weights remain chemically consistent. These results establish the proposed estimators as a low-depth, circuit-compatible formulation for evaluating SCGVB matrix elements, while making no claim of quantum computational advantage.

One-axis twisting (OAT) interaction is a pivotal resource for manipulating quantum states of atomic ensembles, enabling spin squeezing, atomic-cat-state generation, and weak-phase amplification. Current implementations of OAT dynamics predominantly rely on the Tavis-Cummings model of light-atoms coupling; however, this approach inevitably introduces an additional Stark term that entangles the light with the atoms, which compromises the unitarity of OAT evolution and thereby degrades the OAT-based control precision. Here we propose a scheme based on a driven Tavis-Cummings model to achieve near-unitary OAT evolution. We demonstrate that both constant and time-varying driving of an atoms-cavity hybrid system can realize near-unitary OAT evolution, albeit with distinct coupling strength. Furthermore, when atomic dissipation is taken into account, we find that the time-varying-driving scheme exhibits superior resistance to decoherence. Our approach is broadly applicable to a variety of atomic platforms, including cold atoms, trapped ions, and nitrogen-vacancy centers.

Certifying that quantum randomness generated by untrusted devices is unpredictable to an attacker (say, Eve) is crucial for device-independent security. Bipartite protocols where only one of the parties is trusted are termed one-sided device-independent (1SDI) or steering-based protocols, where the untrusted party (say, Alice) performs measurements on her part of a bipartite entangled state to steer the subsystem of the trusted party (say, Bob) into different ensembles (collectively, an assemblage) of quantum states. Recent work has shown that an assemblage has certified randomness if and only if its realization requires a set of measurements that are star-incompatible, i.e., the measurement setting of interest for the guessing probability of Eve is incompatible with at least one of the remaining measurement settings of Alice. However, can one always extract randomness from star-incompatible measurements? And if so, how much randomness can one extract from them? Here we demonstrate that one can extract steering-based randomness from any set of star-incompatible measurements, thereby establishing an equivalence between star-incompatibility and steering-based randomness. We then provide a lower bound on the minimum guessing probability for a given set of measurements that is computable via semidefinite programming. This bound is tight when the Hilbert space dimension of Bob's system is at least that of Alice's. Finally, to provide a quantitative handle on star-incompatibility and the randomness extractable from it, we introduce a weight-based measure of star-incompatibility and lower bound the amount of star-incompatibility required to certify a given amount of randomness.

We analyze propagation and detection of two-photon states expanded in Zernike modes through atmospheric turbulence using the extended Huygens-Fresnel formalism. For SPDC states prepared with a single Zernike pump mode, we analytically reduce the 8-dimensional continuous propagation integrals to an exact, discrete modal expansion. In the absence of turbulence, Zernike addition enforces conservation of azimuthal index and a strict radial-order bound. Turbulence relaxes these constraints, driving structured azimuthal and radial crosstalk dominated by low-order aberration modes.

This paper investigates quantum simulation algorithms for the Liouville equation in geometrical optics with partial transmission and reflection at sharp interfaces, based on the Schrödingerization method. By means of a warped phase transformation in one higher dimension, the Schrödingerization method converts linear partial differential equations into a system of Schrödinger-type equations with unitary evolution, thereby rendering them suitable for quantum simulation. In this work, the Schrödingerization method is combined with a Hamiltonian-preserving scheme that incorporates partial transmission and reflection into the numerical flux. A main difficulty is that the interface treatment in the classical scheme relies on threshold-dependent "if/else" procedures, making it highly nontrivial to reformulate the method in a matrix form suitable for quantum simulation. To overcome this difficulty, we encode the interface conditions into a partial transmission and reflection matrix prepared a priori, rather than during the time evolution. We present detailed constructions of the resulting quantum algorithms and show through complexity analysis that the proposed methods achieve polynomial quantum advantage in the precision parameter $\epsilon$ over their classical counterparts.

We present an algebraic framework for approximate model reduction of Markovian open quantum dynamics that guarantees complete positivity and trace preservation by construction. First, we show that projecting a Lindblad generator on its center manifold – the space spanned by eigenoperators with purely imaginary eigenvalue – yields an asymptotically exact reduced quantum dynamical semigroup whose dynamics is unitary, with exponentially decaying transient error controlled by the generator's spectral gap. Second, for analytic perturbations of a Lindblad generator with a tractable center manifold, we propose a perturbative reduction that keeps the reduced space fixed at the unperturbed center manifold. The resulting generator is shown to remain a valid Lindbladian; explicit finite-time error bounds that quantify leakage from the unperturbed center sector are provided. We further clarify the connection to adiabatic elimination methods, by both showing how the algebraic reduction can be directly related to a first-order adiabatic-elimination and by providing sufficient conditions under which the latter method can be applied while preserving complete positivity. We showcase the usefulness of our techniques in dissipative many-body quantum systems exhibiting non-stationary long-time dynamics.