Papers

Feedback oscillators, such as lasers and masers, serve as time references in modern computing, communication, and measurement. Quantum fluctuations ultimately limit their phase stability and ability to keep time precisely; in the absence of quantum engineering, their phase stability is bounded by a standard quantum limit (SQL). Techniques to improve the frequency stability of feedback oscillators beyond the SQL have been theorized, but have not yet been demonstrated. We demonstrate an opto-electronic oscillator (OEO), a type of feedback oscillator, with phase stability approaching the SQL. We then engineer the OEO's quantum state to improve its phase stability, thereby demonstrating the essential principle quantum-enhancement of feedback oscillators. Similar techniques may be employed to evade the SQL in other feedback oscillators such as masers and lasers.

Open-system descriptions are typically introduced by coupling a quantum system to an external environment. Here we show that a closed interacting many-body system can itself generate a controlled non-Markovian quantum channel acting on a reduced nonlinear qubit through finite-size corrections to a nonlinear mean-field limit. We demonstrate this using the Kitagawa-Ueda one-axis twisting model, $H=\chi J_z^2$, a paradigmatic model of collective spin dynamics, spin squeezing, and two-component Bose-Einstein condensates. Although the large-$N$ regime of this model has been extensively studied, the conventional fixed-$\chi$ scaling does not yield a nontrivial dynamical large-$N$ limit. In this paper, we investigate a complementary large-$N$ formulation obtained from the double limit $N\rightarrow\infty$ and $\chi\rightarrow O(g/N)$, where $g$ is a coupling constant. We derive the leading finite-$N$ corrections to this limit and show that they correspond to an emergent non-Markovian dephasing process, producing a Gaussian decay of the Bloch-vector coherence with characteristic timescale $t_\varphi\geq\sqrt{N}/(2g)$. Exact finite-$N$ calculations demonstrate that this effective open-system description becomes quantitatively accurate for systems containing on the order of one hundred qubits. The resulting framework provides a microscopic realization of non-Markovian dephasing generated intrinsically by a closed many-body system and enables efficient simulation of collective quantum dynamics beyond unitary mean-field theory. These results link the long-studied phenomenon of phase diffusion in atomic ensembles and Bose-Einstein condensates to the growing effort to characterize non-Markovian, beyond-Lindblad noise in quantum computing hardware, providing a rare case in which such a noise channel is derived from microscopic dynamics rather than fit phenomenologically.

Product formulas, also known as Trotter formulas, are among the most widely used and practical methods for simulating quantum systems on quantum computers. Here we introduce two new classes of randomized product formulas for simulating Hamiltonians with separated energy scales, $H=A+\alpha B$, where $\alpha$ is small. In the standard access model, where one can implement exponentials of $A$ and $B$ separately, our randomized formulas achieve $\mathcal O(\alpha^2)$ error scaling at the cost of only doubling the gate depth of the corresponding deterministic formula. We further prove an $\Omega(\alpha)$ lower bound for deterministic product formulas. In a stronger access model, allowing exponentials of $A+\alpha B_\ell$ for $B = \sum_{\ell}B_\ell$, our randomized formula, based on Trotter Heuristic Resource Improved Formulas for Time-dynamics (THRIFT)~[J. L. Bosse et al., Nat. Commun. 16, 2673 (2025)], achieves $\mathcal O(\alpha^3)$ error scaling with only constant-factor expected gate overhead. We also establish an $\Omega(\alpha^2)$ lower bound for deterministic product formulas in this access model. Numerical simulations confirm gate-count reductions for simulating physically motivated systems.

Quantum optimization has shown promising results for quadratic unconstrained binary optimization (QUBO) problems. Real-world applications, however, often involve polynomial coefficients that depend on tunable external factors - such as demand forecasts or risk preferences - giving rise to bilevel optimization structures. We show how variational quantum algorithms (VQAs) can efficiently handle such parametric problems, making three contributions. First, we propose a bilevel optimization model for diagonal cost Hamiltonians where coefficients depend on a tunable outer parameter: an outer loop adjusts this parameter - reshaping the cost landscape - while an inner VQA optimizes circuit variables. Second, since derivative-free probing methods incur a multiplicative overhead when each outer evaluation requires a complete inner solve, we develop correlator-reuse implicit differentiation (CR-ID), which obtains outer gradients by reusing quantum measurements already collected during inner energy estimation, requiring essentially no additional circuit executions. Experiments across three coefficient families show that CR-ID consistently improves budget-normalized efficiency by ~4% in 1D and over 14% in multi-dimensional settings, showing a significant performance advantage compared to finite-difference methods. Third, we show that this property is architecture-dependent: VQE admits exact reuse gradients, whereas QAOA introduces a state-dependent term that creates a cost-bias trade-off.

I give a non-technical presentation of the argument that quantum mechanics, in the form in which it is currently used, needs to be understood in many-worlds (Everettian) terms; the alternatives that have been discussed are at present not able to reproduce the full empirical content of the theory. This is a draft of a chapter for the forthcoming Blackwell Companion to Philosophy and the Multiverse (Klaas Kraay and Daniel Rubio, eds.)

Quantum relaxometry is one of the most successful applications of nitrogen-vacancy (NV) centers in diamond and, more broadly, solid-state spin qubits, enabling ultrasensitive detection of magnetic noise and paramagnetic species via measurements of the spin-lattice relaxation time $T_1$. Conventional pulsed protocols, however, probe $T_1$ efficiently only over a limited temporal range, which restricts the scope and throughput of the technique. Here we introduce a continuous-wave quantum relaxometry protocol that operates in the frequency domain. By measuring the frequency response of the optically detected magnetic resonance signal under low-frequency microwave amplitude modulation, we extract $T_1$ from the characteristic response time of the spin system. The method enables efficient $T_1$ measurements spanning more than three orders of magnitude – directly demonstrated from 60 $\mu$s to 200 ms in our experiments – across a broad temperature range and under substantial ensemble inhomogeneity. We further show that this protocol enables quantitative relaxometry-based sensing in nanodiamonds, achieving a substantial speed-up over the pulsed methods and offering a practical approach to optimizing nanodiamond size for enhanced sensitivity.

The phase space instruction set is a continuous-variable universal gate set involving single-qubit rotations and qubit-dependent displacements on a single boson. Using these gates, we prove that a circuit depth $\mathrm{\Omega}(\varphi(N))$ is necessary to approximately prepare a large $N$-fold rotationally invariant Schrödinger cat state; here $\varphi(N) \gtrsim N/\log\log N$ is the Euler totient function. A protocol saturating this asymptotic bound on circuit depth is obtained for every prime number $N$. This protocol has an asymptotically optimal runtime, when the gates are generated by Hamiltonian evolution. Our results provide a sharp example where a universal gate set is surprisingly inefficient at preparing a simple family of states, and further imply that converting bosonic circuits between different universal gate sets can be extremely inefficient.

Open quantum walks couple transitions on a graph to quantum operations on an internal degree of freedom. We use this structure to formulate protocols for quantum state preparation with nonunitary Kraus operators. We construct a ring-shaped OQW preparing an ensemble of Dicke states, with W states appearing as the single-excitation case, from which any individual Dicke state is recovered by postselecting the walker position; its convergence is governed by the spectral gap of the underlying Markov chain, for which we obtain a closed-form approximate expression. For GHZ states we present a two-node protocol using Kraus operators built from projective measurements that prepares them deterministically without requiring a measurement of the walker, and analyze how unsharp measurements affect the results and the convergence of the walk. We also show that the quantum trajectories method embeds naturally in the OQW framework as a graph-structured collision model.

In the Quantum Approximate Optimization Algorithm (QAOA), the entanglement topology, where qubit pairs are connected by two-qubit gates, is conventionally set equal to the edge set of the problem graph. This coupling ties circuit design to explicit problem knowledge and may not yield the most trainable circuit under limited optimization budgets. We investigate whether a reinforcement learning (RL) agent can discover more effective entanglement topologies for QAOA-based MaxCut optimization without direct access to the problem graph. A Masked Proximal Policy Optimization agent sequentially places IsingZZ gates to construct a circuit topology, while a variational inner loop optimizes the resulting QAOA parameters and returns the approximation ratio as a sparse terminal reward. The agent's observation contains only the edges placed so far and the current approximation ratio; graph structure can only be inferred indirectly through the optimization reward. On Erdős–Rényi instances with up to $10$~qubits, the agent consistently converges to topologies that are strict subsets of the problem graph, achieving overlap ratios approaching $1.0$, despite receiving no explicit information about the graph structure in its observations. These sparse, problem-aligned topologies outperform the full graph topology and several structural baselines when the optimization budget is limited ($50$~gradient steps), but are overtaken by denser topologies given sufficient optimization budget. Our results reveal a trainability–expressibility trade-off governed by topology density and suggest that the variational optimization landscape implicitly encodes structural information about the problem Hamiltonian.

The performance of a quantum reservoir computer in temporal processing tasks depends on how its driven quantum substrate retains information about past inputs, distributes it across physical degrees of freedom, and loses it through environmental dissipation and measurement feedback. We formulate these processes using a classical-quantum state obtained by restricting a reservoir process tensor to classical input encoding and single-time readout. Conditional subsystem Holevo quantities describe information about selected input histories and bound its accessibility to measurements on subsystems of the reservoir. In a six-qubit all-to-all transverse-field Ising reservoir, we find that the total stored information changes relatively little across Hamiltonian parameters, while its spatial distribution and temporal decay vary strongly. Effective diagnostics of these two behaviours identify different regions of high information-processing capacity for linear and higher-degree temporal tasks. Measurement-induced dephasing can improve noiseless task performance when it increases forgetting rates without strongly reducing information delocalisation. The framework separates storage from subsystem accessibility and provides a common description of information flow in driven quantum learning systems.

Deep parameterized quantum circuits may remain sensitive to a parameter change while the observables retained by a learning model barely respond. We study this separation for a fixed computational-basis measurement. For a pure-state tangent, we compare the quantum Fisher information $F_Q$, the Fisher information $F_{\rm full}$ in the complete bitstring distribution, and the largest variance-normalized response $\mathcal I_{\mathcal A}$ available to a diagonal readout space $\mathcal A$. If the joint state–tangent frame is Haar random, we prove that the two successive information fractions are independent Beta variables whose means are $1/2$ and $r/(2^n-1)$, where $r$ is the centered dimension of the readout. Consequently, even the joint span of all computational-basis Pauli strings through any fixed weight $k$ retain only $O(n^k2^{-n})$ of the full-record information. Exact-statevector experiments across six circuit families show increasing finite-size agreement with this hierarchy in five nonconserving ensembles as the circuit depth grows. A number-conserving family departs strongly from the isotropic prediction even after correcting the support and readout rank, showing that rank alone is insufficient without tangent isotropy.

Quantum Key Distribution (QKD) protocols provide information-theoretic security by using quantum mechanical principles. Yet QKD is fundamentally a hybrid protocol: its security depends on the correct integration of the quantum phase with classical post-processing. While ETSI and ITUT specifications standardize QKD architectures and interfaces, they evaluate protocol security in isolation, leaving cross-layer interactions as an underexplored attack surface. This paper introduces a formal verification framework that holistically models QKD protocols based on ETSI and ITUT QKD specifications. Our model is the first hybrid QKD protocol model that supports automated analysis of protocollevel security focusing on how classical operations influence the security guarantees provided by the quantum phase of the QKD protocol. We formalize a comprehensive symbolic model of QKD protocols, based on ETSI and ITU-T QKD specifications, in Tamarin, an automated protocol verifier. Applying this framework, we obtain formal evidence of three specification-level vulnerabilities in ETSI- and ITU-T-grounded protocol models under adversary Eve+: subverted entanglement injection, basis-deferred measurement, and message reflection. Each arises from a classical control-plane omission in the procedure text and is established under a symbolic abstraction rather than as a claim about all practical deployments. We introduce two protocol improvements: measurement commitment and identitybound message authentication codes (MACs). Tamarin verification confirms that these countermeasures eliminate the identified vulnerabilities under Eve+. We have communicated our results and recommendations to relevant standardization organizations.

We give a Lefschetz thimble definition of the Chern–Simons–Kodama wavefunctional in Lorentzian self-dual gravity with positive cosmological constant. By complexifying the connection and choosing the Lefschetz thimble attached to the self-dual de~Sitter saddle, Witten's analytic continuation of Chern–Simons theory replaces the real contour, on which the defining integral is at best conditionally convergent, by an absolutely convergent integration cycle and yields a controlled semiclassical expansion. The relevant integrand is the full holomorphic exponential $e^{I}$, with $I=\kappa Y_{\rm CS}+(\text{source})$, and the steepest descent flow is governed by the Morse function $h=\operatorname{Re} I$. In the homogeneous isotropic de Sitter reduction, the construction reproduces the Hartle–Hawking Airy wavefunction. In the Bianchi~IX truncation, we take the Lefschetz thimble attached to the expanding de~Sitter saddle (the contracting branch defines a conjugate Lefschetz thimble); within this sector, the symmetric configuration is the only critical point for $\Lambda>0$. The corresponding Lefschetz thimble contains one trace direction with the FRW Airy structure and two anisotropic shear directions that are real-Gaussian damped at leading quadratic order. This gives a finite Bianchi~IX wavefunction which, to leading order, is the FRW Airy factor multiplied by a real anisotropy Gaussian. Thus, the Airy behavior is not an artifact of the one-dimensional minisuperspace reduction, but the leading form of the wavefunction on the Lefschetz thimble. We also discuss how the Lefschetz thimble prescription interfaces with Lorentzian reality conditions.

Generating entanglement rapidly and reliably is essential for quantum information processing, communication, and metrology. Dissipative preparation is attractive because engineered reservoirs robustly drive a system toward an entangled target, yet relaxation can carry a substantial time cost. Here we formulate the entanglement Mpemba effect, whereby an initially less entangled state overtakes a more entangled state under the same open-system dynamics. This effect turns initial-state engineering into a route for faster preparation without altering the dissipative protocol. We derive a general criterion for the reversal from the relaxation spectrum, applicable even when entanglement evolves nonmonotonically. A reversal of deterministic local operations and classical communication (LOCC)-reachability preorder provides a measure-independent certificate of reversed entanglement order. Exactly solvable models show that initial-state selection can substantially shorten the time required to reach high entanglement. We further propose an experimentally relevant trapped-ion protocol that can realize the entanglement Mpemba effect.

We experimentally and theoretically study the origin of heating in optical lattices by disentangling the respective roles of intensity and phase noise depending on the lattice parameters. While intensity noise is widely identified as a major limiting factor, we show that phase noise can become the dominant heating source, especially for light atoms and deep optical lattices. We provide a simple theoretical framework to predict the phase-noise-induced heating from the power spectral density of the laser phase noise, which can be measured experimentally. We show that such predictions can accurately reproduce the measured heating rates of lithium-6 atoms in a triangular lattice. Our approach is readily generalized to other lattice geometries and atomic species.

Quantum natural language processing (QNLP) provides a grammar-aware framework for text modeling, and Distributional Compositional Categorical (DisCoCat) is one of its theoretically grounded formulations. Prior work on financial sentiment analysis has identified practical limitations of DisCoCat, including parser sensitivity, high simulation cost, and difficulty handling longer sentences. We study an LLM-assisted preprocessing workflow that uses controlled rewriting to compress, simplify, or decompose moderate-complexity financial sentiment sentences into parser-compatible, circuit-efficient variants while preserving sentiment-bearing meaning. We compare prompting strategies, language models, and filtering configurations with the low-complexity-only DisCoCat baseline of Stein et al. At the circuit level, the strongest compression variants reduce average qubit and gate counts by more than 70 percent relative to the raw moderate-complexity subset. Across repeated training runs, GPT-4.1-mini with Prompt B achieves the highest observed mean accuracy, $0.550 \pm 0.035$, compared with $0.521 \pm 0.050$ for the baseline. Larger training splits do not necessarily improve downstream performance; across evaluated configurations, training-split size has a moderately negative association with accuracy (Pearson $r=-0.446$). These results provide exploratory evidence that LLM-assisted rewriting can make some moderate-complexity inputs usable within the evaluated DisCoCat configuration, while highlighting prompt design, filtering, and circuit-aware preprocessing as considerations for more scalable QNLP-based financial sentiment analysis.

Achieving useful fault-tolerant applications requires co-designing the quantum error-correcting code for footprint, logical instruction set, and hardware compatibility simultaneously. Recent breakthroughs in ultra-high-rate codes have the potential to reduce footprint of large scale quantum applications but their practical utility is limited without an addressable logical instruction set and efficient implementation on near term hardware. Reconfigurable neutral atom arrays, for example, support only hundreds of qubits with constrained reconfigurability from a few crossed acousto-optic deflectors (AOD). We introduce the GALA codes, or Group-Action Lifts with Active orthogonality, that allows such co-design by construction. GALA lifts over a product group $G = H_k \times C_m$ (or $H_k \ltimes C_m^k$); the small non-abelian factor $H_k$ supplies active orthogonality that improves qubit overhead, reaching 1/2 encoding rate with above-weight distance, while the large abelian factor $C_m$ supplies symmetries that give code automorphisms and explicit, simple AOD move schedules. Logical addressibility and hardware compatibility follow directly from construction, rather than verified post-hoc. The GALA family contains several known rate-1/2 Kasai codes of Ref.[arXiv:2601.08824, arXiv:2604.16209] while exposing simpler parameter bounds, logical operations, and ZX-dual variants with AOD-compatible fold-transversal Clifford gates. In particular, we find a compact self-dual $[[132,30,12]]$ with $1.0^{+0.9}_{-0.6}\times 10^{-9}$ per-round per-qubit logical error rate at $10^{-3}$ physical error rate, equipped with 3.1 ms syndrome-extraction cycles and an addressable logical instruction set; a ZX-dual, girth-6, rate-1/2 $[[672,336,12]]$ with a 6.76 ms cycles; and barrier-breaking $[[1752,880,14]]$ and $[[2232,1120,16]]$ smaller than previously known hardware-compatible rate-1/2 codes.

This paper investigates a quantum extension of classical Multiple-Input Multiple-Output (MIMO) communication in which the conventional linear channel model is replaced by a parameterized multi-qubit unitary transformation. Within this framework, interference is represented through coherent quantum interactions rather than additive signal coupling. To recover transmitted information, a Variational Quantum Circuit (VQC) receiver is introduced that learns an approximate inverse channel transformation through supervised variational optimization. The proposed system is evaluated under realistic noisy intermediate-scale quantum (NISQ) conditions incorporating depolarizing noise, thermal relaxation, and measurement imperfections, and its performance is compared with that of standard classical detection methods. The results reveal a trade-off between the two approaches: classical detectors achieve substantially lower bit-error rates across much of the investigated parameter range but exhibit pronounced performance degradation for specific channel configurations, whereas the VQC receiver maintains a more uniform error profile as channel complexity increases, albeit at a higher average BER. These findings suggest that variational quantum receivers are not a direct replacement for classical detection methods, but rather a complementary approach that may offer increased performance stability in communication scenarios characterized by strong coupling and complex interference patterns.

In this work we theoretically and experimentally investigate bound states in the continuum (BICs) in a reconfigurable integrated photonic structure, focusing on spontaneous four-wave mixing. We consider a configuration in which only one mode, the idler, is tuned to the BIC condition, and show that suppressing the radiative loss of this single mode profoundly reshapes the overall nonlinear dynamics. In particularly, we realize electrically tunable Friedrich-Wintgen BICs with Q > 10^6 in an interferometrically coupled silicon-nitride microresonator. Although inaccessible through linear excitation, the BIC is populated by four-wave mixing and read out through its radiative photon partner. In the low-gain regime, we investigate the spectral, correlation, and coherence properties of the generated photon pairs, revealing distinctive signatures in the signal-idler correlations and an extracted signal whose coherence time approaches the intrinsic-loss-limited lifetime of the dark idler. In the high-gain regime, making one mode participating in optical parametric amplification a BIC enhances the parametric gain by 12 dB and lowers the oscillation threshold by 1.6 dB. These results establish BICs as a tool for mode-selective lifetime engineering, enabling control over both biphoton wavepackets and the threshold dynamics of integrated parametric devices.

Spread complexity has emerged as a useful probe of quantum chaos, yet the microscopic spectral origin of its characteristic finite-time peak remains incompletely understood. We develop an analytic framework that relates spread complexity directly to local spectral statistics. Starting from an energy-space representation of the Krylov kernel, we show that the kernel is approximately banded, leading to a rapidly convergent diagonal expansion dominated by nearby levels in the ordered spectrum. Motivated by this structure, we propose an approximate kernel-universality hypothesis: after unfolding, the Krylov kernel is well approximated by that of a uniform lattice. Combining this universal kernel with local spectral statistics yields a simple analytic expression for spread complexity in terms of the Fourier transforms of the $k$-th nearest-neighbour spacing distributions. In particular, at leading order, the finite-time peak is controlled by the Fourier transform of the nearest-neighbour spacing distribution. The resulting framework describes both chaotic random-matrix ensembles and the integrable Poisson limit, identifies the spectral origin of the complexity peak and its late-time behaviour, and provides a direct connection between Krylov dynamics and spectral statistics.

Flip-chip integration offers a promising route toward scalable superconducting quantum processors and hybrid semiconductor-superconductor quantum devices. We develop a three-dimensional transmon architecture using electroplated indium in which the qubit electric field is shared nearly equally between two bump-bonded substrates while maintaining low participation at the indium-bump interface. The resulting geometry is well suited for future hybrid qubits, enabling the integration of distinct material platforms while minimizing sensitivity to bump-interface loss. Using this platform, we evaluate electroplated indium interconnects for superconducting quantum circuits. Flip-chip transmons incorporating electroplated indium bumps exhibit qubit quality factors around $10^6$. In addition, a systematic study of coplanar-waveguide resonators is used to identify losses associated with the electroplating process. In particular, we find that surface losses associated with the gold-layer, used to enable good electric contact with the indium, is likely the primary contributor to the qubit decay rate. These results demonstrate the compatibility of electroplated indium technology with high-coherence superconducting circuits and establish a promising platform for three-dimensional hybrid quantum integration.

Continuous-variable quantum key distribution (CV-QKD) promises high rates and seamless integration with classical beams within a single optical fiber. Over the years, implementations have been performed by transmitting a local oscillator reference along with the quantum channel, opening security loopholes for eavesdroppers and limiting potential applications. Here, we report on a Gaussian CV-QKD implementation using fully independent transmitter and receiver lasers (local-oscillator sources) over a 12 km fiber spool. The system was experimentally evaluated using logical frames containing approximately $10^7$ coherent states, each composed of ten independently processed subframes of approximately $10^6$ states, and security was assessed in both asymptotic and finite-size regimes under a trusted-device model. The full-fledged classical post-processing is capable of recovering the channel parameters and extracting secret key rates of 5.11 Mbit/s in the asymptotic regime and 4.67 Mbit/s in the finite-size regime, showing good agreement with theoretical predictions. This work establishes the foundation for metropolitan fiber deployment of CV-QKD under strict security constraints.

We derive and investigate the reduced dynamics of a nonrelativistic quantum matter system interacting with quantized gravitational waves. Because gravitational radiation couples tidally to the mass quadrupole moment, we emphasize that the leading interaction is quadratic in the mechanical displacement. Rather than treating it as a complication to be removed by linearization, we retain this full quadratic dependence, which gives rise to two-phonon rather single-phonon processes typical in dipolar interactions. We clarify its relation to the effective linear coupling that often appears in optomechanical literature, but which conceals the delicate quantum signatures of the full quadratic coupling. Using the Born-Markov and secular approximations, we microscopically derive Lindblad master equations for the matter dynamics induced by graviton baths in multi-mode vacuum, coherent, number, thermal, and squeezed states. We treat the ultraviolet-divergent Lamb-shift Hamiltonian by an explicit renormalization procedure, with the mechanical frequency identified as the physical frequency. Remarkably, owing to the nature of the interaction, the matter Hilbert space decomposes into even- and odd-parity sectors for all bath states considered. For a coherent graviton bath, the decoherence is identical to that of the vacuum, while the bath one-point function produces a coherent-shift Hamiltonian that exactly reproduces the tidal interaction with a classical gravitational wave. For a vacuum graviton bath, we recover the coherence protection between the two lowest mechanical number states, while number and thermal graviton baths remove this protection and enhance decoherence, although the effect remains small for realistic parameters. By contrast, a squeezed graviton bath enlarges the coupled coherence structure, and gives rise to a novel, coherence-protected sector spanned by dressed dark states.

Quantum coherence, quantum decoherence, and photon number reduction are coexistent in linear lossy optical systems. However, how these three elements combine together to determine the evolution of the quantum light remains unclear. Here, based on singular value decomposition (SVD), we propose the theory of deterministic photon-loss subspace (DPLS) for quantum interferences in lossy systems. By performing an SVD of scattering matrices with singular values either 0 or 1, a series of completely lossy and lossless input modes are first defined. According to n_1,...,n_i photons in the first,..., i-th lossy modes, the Hilbert space of the input states can be decomposed into a set of orthogonal subspaces H_((n_1,...,n_i ))^in, i.e., deterministic photon-loss subspaces (DPLSs). When the concept of DPLS is established, the input state can be projected onto these DPLSs. In each DPLS, the photons in lossy modes will be completely dissipated, while those in lossless modes experience a unitary evolution. The output state is a statistical mixture of the evolved outcomes of all projections, since decoherence is a concurrent process. Then, based on the DPLS theory, we not only revisited Anti-HOM interference and the distillation of quantum states, but also demonstrate a robust W-state generation for various input states in a three-port lossy system with one-dimensional DPLSs. Through investigating the loss-induced subspace structure of the system, our general theory for analyzing quantum state evolution in lossy systems explicitly reveals the interplay among quantum coherence, quantum decoherence, and photon number reduction. By engineering the loss, the constructed DPLSs can be used to precisely control quantum interferences in dissipative systems, with potential applications in quantum state preparation, quantum logic operations, and other quantum information processes.

The quantum-mechanical two-sided Bogoliubov inequality provides upper and lower bounds for the free energy required to separate a system of interacting particles into independent subsystems. The bounds can be calculated straightforwardly from the ensemble average of the interface energy, bypassing the direct evaluation of the free energy. In this work, we generalize the two-sided Bogoliubov inequality to arbitrary von Neumann algebras by employing the Araki-Uhlmann relative entropy and the framework of unbounded perturbation theory of KMS states. Furthermore, we obtain variational expressions for the relative free energy that extend existing bounded-perturbation principles to the unbounded setting. Crucially, these mathematical developments yield a physically well-founded thermodynamic criterion for the quantification of entanglement in infinite-dimensional systems.

Hybrid classical-quantum approaches are instrumental in numerous fields, from condensed matter physics to quantum information science. We recently proposed to describe hybrid systems starting from a set of natural axioms for measurement probabilities without adding any underlying mathematical structure. The so defined probability measures fulfill a no-signaling condition that ensures that instantaneous communication is impossible. We formulate here a dynamical generalization of this condition. It means that, for two independent systems, the outcome probabilities of a measurement made on one of them are not affected by a measurement performed earlier on the other. Analogous requirements are satisfied for usual classical and quantum bipartite systems and violating them would make faster-than-light signaling possible. The dynamical no-signaling condition has important consequences for classical-quantum interactions that depend on the hybrid approach used. For no-signaling hybrid dynamics with classical trajectories, the classical degrees of freedom can influence the quantum ones but the latter cannot react on the former. If pure states of quantum systems remain pure then the dynamical no-signaling condition implies the absence of classical reaction. When all hybrid states are allowed, there are no genuine classical-quantum interactions for no-signaling hybrid dynamics that do not generate correlations between the classical and the quantum degrees of freedom. In all these cases, the proposed condition is equivalent to the convex-linearity of the probability measure transformations describing finite-time evolutions.

Delocalized long-lived states (LLSs) and collective zero-quantum long-lived coherences (LLCs) in aliphatic chains provide a promising route for preserving nuclear spin order with lifetimes that exceed the conventional $T_1$ and $T_2$ relaxation times, respectively. Their extended lifetimes make them attractive for applications including hyperpolarization storage, ligand-observed drug screening based on the loss of longevity upon binding to a target protein, and quantum information processing exploiting the collective properties of many-body spin systems. Although LLSs and LLCs have been observed experimentally in methylene networks, their origin and general structure in chains of arbitrary length have remained unclear. Here we show that these relaxation-protected modes follow directly from Redfield relaxation theory. Specifically, we construct the long-lived subspace, i.e., the zero-eigenvalue subspace of the relaxation superoperator associated with the dominant intra-pair dipole–dipole relaxation mechanism. The long-lived subspace contains $2^N-1$ independent non-trivial operators, which excludes the identity operator, where $N>1$ is the number of $-\mathrm{CH}_2-$ groups in the chain. In achiral molecules, conservation of the global intra-pair permutation parity restricts experimental access to at most $2^N-2$ of these operators, whereas in chiral molecules this parity is not conserved, making up to $2^N-1$ long-lived operators accessible. We further develop a general framework for constructing both LLSs and LLCs in aliphatic chains containing an arbitrary number of $-\mathrm{CH}_2-$ groups in achiral molecules, and illustrate the approach explicitly for chains with $N=2$, 3, and 4 methylene groups.

The transient regime of far-from-equilibrium quantum many-body dynamics lacks the established organizing principles that universality and scaling provide in equilibrium. It is least understood for two-dimensional short-range interacting systems, where mean-field arguments are not expected to hold, controlled theoretical descriptions are few, and fluctuations are strong. Here we investigate the quench dynamics of the transverse-field Ising model using programmable Rydberg-atom arrays realizing honeycomb, square, kagome, and triangular lattices. Starting from a fully magnetized state, we observe a pronounced softening of the dominant collective magnetization oscillation accompanied by a maximum in the damping rate, signaling a crossover between interaction- and field-dominated transient dynamics. Even though the microscopic lattice geometries are different, both the oscillation frequencies and the damping rates collapse onto common curves after being rescaled by the coordination-number-weighted interaction strength. Our findings show that a mean-field description effectively reproduces the magnetization oscillations. The importance of correlated quantum fluctuations is underlined by the failure of the discrete truncated Wigner approximation to predict the damping for strong interactions, while tree-tensor-network simulations reproduce the dynamics accurately. These results reveal a robust scaling regime governing the transient dynamics of short-range interacting two-dimensional quantum magnets. They reveal that the dominant transient dynamics is governed by a simple collective description despite the presence of strong quantum fluctuations — an important insight in the quest to uncover organizing principles in far-from-equilibrium quantum matter.

An algorithm is presented for Kraus decomposition of a completely positive operator over separable (countably-infinite-dimensional) Hilbert spaces, together with an elementary proof that the generated sum convergences in strong-operator topology. This improves on the standard, nonconstructive, proof by fusing the abstract problem with practical process tomography. Kraus operators are generated one-by-one, each having one more guaranteed zero matrix entry than the previous one. In this way, the stream of outputs of the algorithm provides a coherent family of Kraus decompositions of restrictions of the target CP map to ever-larger subspaces.

Collapse models introduce stochastic and nonlinear modifications in the quantum dynamics, predicting observable effects, such as spontaneous radiation from charged particles, which can be used to constrain their parameters. Recently, attention has focused on the 1-100 keV energy range, where the wavelength of the emitted photons becomes comparable to atomic dimensions, making the emission sensitive to atomic structure and leading to model-dependent behaviors that enable their discrimination. Here, we derive a general expression for the spontaneous emission rate for arbitrary noise, providing a framework that systematically incorporates the atomic structure through the radial distribution of the emitters, modulated by the specific collapse model. The formalism recovers previous results in the appropriate limits and naturally includes new low-energy effects, such as cancellation mechanisms arising from charge correlations. We evaluate the rates for germanium and xenon within the Diósi-Penrose and Continuous Spontaneous Localization models, showing how these correlations modify the predicted emission rates. This approach provides a unified framework to account for atomic effects and enables more robust, material-dependent experimental constraints on collapse model parameters.