Papers

The interplay between many-body interactions and controlled dissipation provides a rich setting for nonequilibrium quantum phases. We explore the superradiant phase transitions in a Rydberg-interacting open Dicke model with cavity loss and local dissipation. We find that the nonlinear feedback from atomic interactions stabilizes the atomic collective excited state and induces resonant collective motion, which can be further converted into robust superradiant oscillations with the inclusion of local dissipation. Beyond the mean-field approximation, we prove this system can support the finite-size local dissipative temporal order, i.e., continuous time crystal, from evidences of the decreasing damping of a finite-frequency Liouvillian mode and the linear-size scaling of quantum fluctuations. The correlation between the atomic colletive dynamics and the cavity photon number makes our findings easy to detect from output optical signal. By bridging interacting atomic matter and driven-dissipative cavity QED, our Rydberg-interacting Dicke model provides a unique spin-1/2 platform for exploring dynamical phase transitions and macroscopic temporal order in open quantum matter.

Multiphoton entangled states are pivotal resources for implementing optical quantum information protocols. Recently, energy-time-entangled triphotons have been observed in hot atomic ensembles. However, in these protocols, the complex fifth-order nonlinear susceptibility entailed by four- or five-level systems limits our understanding of triphoton generation. Here, to directly capture the generation mechanism of triphotons and their associated optical properties, we investigate the generation of energy-time-entangled triphotons in a six-level cold atomic ensemble. The fifth-order nonlinear susceptibility indicates the existence of two sets of spontaneous six-wave mixing in the system. Notably, triphoton generation in this system is subject to stringent timing constraints. Collectively, these characteristics give rise to threefold coincidence counts, which – dominated by the fifth-order nonlinear susceptibility – exhibit asymmetrically damped Rabi oscillations in the two-dimensional time domain. Furthermore, we analytically derive that the temporal correlation properties of conditional two-photon states are preserved – a unique feature of $W$-class tripartite entanglement. These results not only lay the groundwork for the experimental preparation of triphotons using six-level systems but also provide key support for understanding the generation mechanism of triphotons involving more complex fifth-order nonlinear susceptibilities.

In this work, we investigate the reliability of information-theoretic measures based on the electron-density and shape-function, specifically Shannon and Rényi entropies, as descriptors of electronic correlation. By establishing a rigorous decomposition of these entropic measures into additive and nonadditive contributions, supported on a Mulliken-like atomic partition of molecules, we systematically analyze the asymptotic behavior of the entropies at the infinite-internuclear-distance limit to assess the problem of static correlation and extensivity. Our algebraic and numerical analysis reveals several flaws in the use of these density-based descriptors. We demonstrate that for minimal-basis and different theoretical levels, the Shannon and Rényi entropies fail to encode the amount of static correlation conveyed by the underlying wavefunction. Conversely, shape-function Shannon entropies and Rényi entropies (for $\alpha \neq 1$) violate extensivity. In larger basis sets, uncorrelated Hartree-Fock densities consistently overestimate entropy compared to sufficiently correlated (e.g., full-valence-CAS) densities. Moreover, the entropies for insufficiently correlated methods violate extensivity. These findings indicate that electron-density-based measures are insufficient for capturing static correlation, suggesting that robust entropic descriptors should be constructed from higher-dimensional Hilbert-space objects.

We present a matrix product state (MPS) method for including decoherence processes in calculations involving waveguide quantum electrodynamics (waveguide QED) using density matrices. The approach is based on collision quantum optics, where the many-body state of the waveguide is represented using discrete time bins, which are then efficiently encoded using an MPS chain. Our method is a generalization of previous MPS methods, and we demonstrate how one can efficiently extend the method to density matrices, allowing for the inclusion of various loss processes in the form of Lindblad terms in the Liouvillian superoperator responsible for the relevant dissipation dynamics. As an application of the theory, we study various waveguide QED systems and the influence of emitter pure dephasing (which is one of the most important processes in real systems) on the light-matter interactions, including a two-level system (TLS) in a semi-infinite waveguide with time-delayed feedback, two spatially separated TLSs with finite delays, and finally the scattering of few-photon Fock pulses on a TLS. In addition to emitter pure dephasing, we also show how to include off-chip radiative decay, and show how it differs qualitatively from pure dephasing.

Near-term quantum devices with limited qubits motivate the study of space-bounded quantum computation in the data stream model. We show that Shannon entropy estimation exhibits an exponential separation between quantum and classical space complexity in this setting. Technically, we develop a two-stage quantum streaming algorithm based on a quantum procedure with an explicitly constructed oracle derived from the streaming input. This algorithm achieves logarithmic space complexity in the accuracy parameter over the data stream, whereas any classical streaming algorithm under the same pass complexity requires polynomial space. In sharp contrast, existing results for Shannon entropy estimation in the quantum query model achieve only a quadratic speedup. Our work establishes a natural problem with practical applications in computer networking that admits an exponential quantum space advantage, revealing a fundamental gap between quantum query complexity and streaming space complexity.

Non-Hermitian dynamics in open systems can give rise to a variety of fascinating non-equilibrium phenomena, ranging from symmetry-breaking transitions to directional energy flow. Parity-time (PT) symmetry breaking determines the occurrence of dynamical instabilities, while non-reciprocal interactions enable asymmetric energy transfer between modes. Here, we present a versatile optomechanical platform based on a vacuum-levitated nanoparticle that allows full control over the coupling of its mechanical modes, including non-reciprocal and non-conservative interactions. By engineering the spatial ellipticity and polarization of the trapping beam, we continuously tune the system from a reciprocal to a strongly non-reciprocal regime. This allows us to observe PT-symmetry phase transitions and to isolate a unidirectional regime in which one mode remains effectively decoupled while driving the other. We demonstrate that elliptical polarisation of the trapping beam spanning unidirectional and reciprocal regimes induces asymmetric intermodal energy transfer. This results in the spontaneous cooling of one mechanical mode without external feedback. Both modes share identical mass, size, charge, and optical environment, providing a clean and robust setting for exploring non-Hermitian dynamics, exceptional-point physics, and energy redistribution in minimal systems. Combined with recent advances in ground-state cooling, our results provide a direct route to realising non-Hermitian phenomena in the quantum regime.

We show numerically that a repulsive Bose-Einstein condensate can be driven into implosive dynamics by a direct topological quench. We first realize giant vortices by quasi-adiabatic phase imprinting, and then perform a sudden anti-imprint that cancels the accumulated winding in a single step, abruptly switching the condensate from a highly charged vortex state to the trivial sector. The resulting phase-density mismatch launches a rapid inward radial flow and produces a strong central density buildup, despite the repulsive interactions. After the first implosion, the dynamics evolves into circular nonlinear wave fronts that subsequently undergo breaking of azimuthal symmetry (axisymmetry) down to a polygonal one, whose shape is determined by the way the giant vortex is built. These results establish topological engineering as a new tool for studying implosive dynamics and symmetry-breaking instabilities in quantum fluids.

Accurate modeling of surface catalytic processes often requires methods capable of describing strong correlation, charge transfer, and multiple closely lying electronic states. While density functional theory remains widely used, its limitations for localized electronic states motivate the use of wavefunction-based approaches and, more recently, quantum computing algorithms. However, the performance of quantum ansätze in chemically motivated, multistate settings remains largely unexplored. Here, we benchmark state-averaged factorized unitary coupled cluster with singles and doubles (SA-fUCCSD) and the adaptive, problem-tailored ansatz (SA-ADAPT) using an embedded cluster model of NO adsorption on Rh-doped TiO2(110). The system exhibits pronounced multiconfigurational character and multiple state crossings, providing a stringent test. State-averaged CASSCF serves as a reference, and the quantum ansätze are evaluated as solvers for the corresponding CASCI problem within a fixed orbital basis. We find that SA-fUCCSD improves with increasing circuit depth but requires many parameters and shows sensitivity to initialization. In contrast, SA-ADAPT achieves near-CASSCF accuracy with significantly fewer operators. A modified operator selection scheme, incorporating multiple operators per iteration, substantially accelerates convergence. Our results demonstrate the efficiency of adaptive ansätze for multistate problems and establish a controlled benchmark for quantum algorithms in chemically motivated systems beyond minimal models.

We introduce a traceable operator-algebraic framework for incompressible transport on M= T3 (and, more generally, compact Riemannian manifolds endowed with a smooth invariant probability measure). Given an autonomous divergence-free velocity field u, the time-1 map $\Phi$ induces the Koopman unitary U on L2(M) and the crossed-product finite von Neumann algebra Mu\,:= L$\infty$(M) ___$\alpha$ Z= W$\star$(L$\infty$(M),U), equipped with its canonical faithful normal trace $\tau$u. Within Mu we define tracial complexity functionals from commutators [U,Mf] (with Mf the multiplication operators) and associated positive elements, and we connect these quantities to Fuglede–Kadison determinants and entropy-like tracial functionals. In parallel, we introduce bounded regularized advection operators T(s) u\,:= KsTuKs as differential-level probes of transport oncommutativity, and we recall the Lie-bracket commutator identity at the formal generator level. This provides a natural algebraic setting in which tracial invariants are well posed and, in principle, computable on discretizations (e.g. cavity flow and vortex benchmarks).

We construct a family of positive but not completely positive linear maps acting on four dimensional space. We employ these maps to detect bound entanglement in high dimensional quantum systems.

Microwave photon detection is a key technology for low-temperature superconducting electronics and quantum information processing. A promising possibility is to use switching processes in parametric superconducting devices at criticality, which can be triggered by small perturbations. Here we demonstrate the unique sensing properties of the superconducting Kerr parametric resonator when operated in the proximity of the phase transition boundary. We utilize a semiclassical approximation to provide numerical and analytical results for the Heisenberg-Langevin and Fokker-Planck equations that describe the switching mechanism. We show that the probability of switching events is enhanced by probe input states with energies down to single quanta levels.

Molecular optomechanical cavities have recently emerged as a promising platform for frequency upconversion, enabling the quantum coherent conversion of infrared signal into the visible range. In a recent work [F. Zou et al., Phys. Rev. Lett. 132, 153602 (2024)], we proposed an amplification mechanism that can enhance the intensity of the upconverted infrared signals by a factor of 1000 or more within such a cavity under the ideal case without any noise. In this work, we employ the power spectrum method to investigate the noise added to the upconverted signal in a molecular optomechanical cavity along with the conversion efficiency from infrared signal into visible range. In the red-detuned regime, the anti-Stokes sideband achieves superior conversion efficiency relative to the Stokes sideband. Conversely, the Stokes sideband dominates under the blue-detuned condition, which amplifies the infrared signal. We further demonstrate the dependence of the added noise on the coupling strength and decay rates of the system. In particular, we find that when the infrared signal is amplified, the added noise approaches the quantum limit of one quantum.

In this paper, we apply the deterministic quantum imaginary time evolution (QITE) algorithm to obtain the ground state of a $2+1$-dimensional pure $\mathbb{Z}_2$ lattice gauge theory. We first construct the set of Pauli operators commuting with Gauss's law constraints, generalizing a previous result. This makes the deterministic QITE gauge-invariant and reduces both the measurement and gate costs significantly without adding extra algorithm errors in the QITE. Then, the classical numerical simulation of the deterministic QITE using tensor networks is performed, and the results are compared with the density matrix renormalization group (DMRG) to evaluate the accuracy of the algorithm. Specifically, we investigate the coupling and system size dependence, and find that the deterministic QITE can achieve a relative error of less than $0.1\%$ up to a twelve-plaquette system and coupling values in a regime that we study. Furthermore, the error dependence on the number of time steps is studied and discussed.

We derive a tight and saturable monogamy relation for three-qubit pure states that bounds the sum of concurrence and concurrence of assistance by the entanglement with an external qubit. The bound decreases strictly with increasing external entanglement, establishing a precise trade-off between internal and environment-induced entanglement. Equivalent formulations in terms of negativity and its convex-roof extensions follow. Our result provides a unified and quantitative constraint on entanglement distribution in open multipartite quantum systems.

We study resonances for the semiclassical magnetic Laplacian in the full plane with a compactly supported magnetic field in the framework of semiclassical complex scaling and black box scattering theory. Assuming that the magnetic field is locally constant, we prove the existence of semiclassical resonances near the Landau levels with exponentially small imaginary parts. We also prove that resonances emerge from a magnetic step discontinuity along a curved interface or a non-degenerate magnetic well, and in the vicinity of anharmonic Landau levels if the field has an isolated zero.

Recently, Hausmann and Renner have pointed out that several famous paradoxes relating to black holes have a similar character to various Extended Wigner's Friend paradoxes. In this paper I consider what the connection between these things could teach us about the Wigner's Friend scenarios. I argue that if we take the analogy between these cases seriously, the black hole paradoxes appear to favour a certain class of response to the Wigner's Friend scenario - specifically, those which posit intrinsic relationality, rather than effective and emergent relationality, and also those which posit some kind of retrocausality.

Classical opacity theory for discrete-event systems relies strictly on observable event sequences, fundamentally failing to capture security breaches in hybrid architectures where an attacker exploits both classical traces and localized quantum correlations. To address this gap, we formalize current-state opacity within the framework of safe partially observed quantum Petri nets by introducing a true-concurrency semantics that represents classical observations as partially ordered multisets via unfolding configurations. Building upon this, we define quantitative posterior-state leakage as the trace distance between the attacker's localized quantum states, evaluated conditionally on whether the underlying system has reached a secret or non-secret marking. This formulation strictly preserves classical opacity definitions. To achieve computational tractability, we apply the stabilizer formalism and develop an exact symbolic verification algorithm. By combining targeted unfolding exploration, state aggregation exclusively at maximal unobservable reach, and stabilizer-tableau propagation, this procedure circumvents both concurrent interleaving explosions and exponential density-matrix overhead. Finally, an entanglement-swapping case study validates the exact leakage evaluation, demonstrates substantial computational gains, and establishes a rigorous interface for counterexample-guided leakage enforcement.

Interference is conventionally attributed to path-accumulated phase differences, with measurement treated as a passive readout. Here we demonstrate that single-particle interference is governed by the relative phase between the prepared quantum state and the detector-defined measurement basis – a joint quantity that is operationally inaccessible in any conventional interferometer. Using coherently seeded entangled nonlinear biphoton sources, we show that independently scanning the pump phase difference, the seed phase difference, or the signal interferometric phase each produces identical sinusoidal fringes ($V\approx0.99$) – a three-scan equivalence impossible in any two-mode interferometer. The fringe visibility is continuously controlled through the idler-state overlap, directly encoding quantum distinguishability without idler detection. The same measurement-defined interference law persists from the single-photon to the high-flux regime. The bright-dark collective-state structure demonstrated here unifies coherent population trapping and electromagnetically induced transparency in atomic $\Lambda$-systems, discrete photonic interference, and single-slit diffraction within a common framework differing only in dark-subspace dimensionality, establishing measurement-defined photonic modes as a fundamental resource for quantum photonics.

Employing mutually-commuting von Neumann algebras to represent the algebra of observables on quantum systems provides a framework for studying quantum information theory in systems with infinite degrees of freedom and quantum field theory, yielding many profound results that differ from non-relativistic quantum systems. In this paper, we establish a mutually-commuting von Neumann algebra model of quantum networks with arbitrary structures. We derive Bell-type inequalities on this model, and determine various bounds for Bell-type inequalities based on the structure of underline von Neumann algebras, and identify the algebraic structural conditions required for their violation. The conditions on the algebraic structure of observables for maximal violation of Bell-type inequalities, which we discovered in the context of von Neumann algebra models, can in turn guide the search for measurements in the non-relativistic setting.

We establish a quantitative relation between local spin polarization and quantum entanglement in two-qubit systems by mathematically proving a closed-form upper bound on the concurrence at fixed local polarization magnitudes. The bound shows how the maximal concurrence is jointly constrained by the two local polarizations. We further demonstrate that this bound is saturated by pure states in certain cases with identical polarizations. As a concrete physical application, we consider the parity-violating process $e^+e^- \to Z^0 \to q\bar{q}$, which generates final-state spin polarization. We show that the maximal concurrence is attained in specific kinematic regions and is significantly reduced relative to the unpolarized case. These results establish a general, process-independent framework connecting local polarization, maximal entanglement, and pure states.

The long-range transmission of quantum information relies on multiple interfaces between photons, acting as flying qubits, and localized memories, serving as repeaters, to mitigate transmission losses. Efficient, long-range transmission necessitates the use of short, picosecond-scale photons, which are markedly different from the narrowband, nanosecond-scale photons optimal for absorption by memory elements, typically operating at wavelengths far from telecom. In this article, we point toward designs capable of bridging these regimes, leveraging the interplay between sum-frequency generation-based quantum frequency conversion and resonant confinement in an integrated ring resonator.

State-of-the-art photon sources based on spontaneous parametric down-conversion (SPDC) currently rely on artificial structuring of the material nonlinearity to satisfy phase-matching conditions. This technique, known as periodic poling, is available only in a limited number of material platforms and introduces additional fabrication steps and errors, which are detrimental to up-scaling efforts. Here, we present a device architecture that enables SPDC of a wide range of frequencies without the need for periodic poling. We present explicit designs and calculations for 4H Silicon Carbide on-insulator, in which SPDC photon generation is so far unavailable, and thin-film Lithium Niobate on-insulator, a state-of-the-art quantum photonics platform. Our design, based on mode conversion and subsequent modal phase-matched SPDC, facilitates a CMOS compatible $\chi^{(2)}$ platform, and simplifies photon sources by removing the requirement of periodic poling and the associated additional fabrication complexity.

Experimental access to many-body quantum systems is often limited by measurement backaction, and key dynamical properties are typically obtained by perturbing a system and measuring its response. Here we replace this active paradigm with a minimally invasive protocol based on a pair of weak quantum measurements that leverages measurement backaction as a strength. By correlating time-separated measurements with the first detecting fluctuations – of any sort – and the second tracking their time evolution, our method directly measures dynamical correlation functions without external perturbation. We demonstrate this technique in an atomic Bose-Einstein condensate using phase-contrast imaging to obtain the two-time density-density correlation function known as the Van Hove function and, through its Fourier transform, the dynamical structure factor. Due to the role of spatial correlations in scattering, these quantities underpin neutron and X-ray scattering and atomic Bragg spectroscopy. This approach is broadly applicable, providing access to correlation functions between any pair of observables amenable to weak measurement, thereby going beyond the capabilities of conventional strong measurements. We further isolate the role of quantum backaction through Aharonov's post-selection-based quantum weak values.

We investigate quantum spectroscopy with undetected photons for protein detection in the mid-infrared spectral region. Classical Fourier-transform infrared spectroscopy of protein samples (bovine serum albumin and N-terminal pro-brain natriuretic peptide) is used as reference to define the sample's mid-infrared absorption, which is then embedded in a numerical model of a double-pass quantum interferometer. We analyse parameters that influence visibility of the interference pattern formed by the signal beams, including the length of nonlinear crystal, sample length and mirror-sample distance. This leads us to a practical quantum spectrometer design with optimal image contrast at the specific amide I-II spectral bands. The simulated visibility spectra reproduce nearly identically the protein absorption features in the mid-IR and reveal temperature-induced changes to the protein secondary structure. Overall, this provides practical design rules for future quantum bio-spectroscopy applications that use only visible wavelength sources and detectors.

We investigate the effect of non-Hermitian Gamma interaction on the phase transitions and magnetic correlations for the transverse field Ising chain. We demonstrate that apart from the gapped antiferromagnetic and paramagnetic phases, there is a gapless phase induced by parity-time symmetry breaking, where the system exhibits long-range and short-range spin-nematic correlations in different regions divided by the quantum critical line determined from the correlation function and the subsystem entanglement entropy. Furthermore, we reveal that the parity-time symmetry breaking leads to the emergence of dynamical spin-nematic correlation, which also suggests a way of characterizing the spin-nematic map through non-equilibrium dynamics. Our findings show rich quantum phases stem from the competition among the Ising interaction, transverse field and non-Hermitian Gamma interaction, as well as providing a scheme for generating spin-nematic correlation in the spin chain.

The special unitary group SU(2) plays a fundamental role in the description of symmetries in quantum mechanics, theoretical physics, and spherical signal processing. In this paper, we address the computational challenges of performing spectral analysis on this non-abelian compact Lie group. We present the Fourier Transform (FT) on SU(2) and develop a Fast Fourier Transform (FFT) algorithm inspired by the classical Cooley-Tukey divide-and-conquer scheme. Our approach efficiently discretizes the group using Euler angles, applying a two-dimensional FFT on the angular variables and exploiting the recursive properties of Jacobi polynomials. We provide an analysis of the computational complexity, demonstrating that our FFT-based method significantly outperforms the direct computation of the FT. This algorithm serves as a foundational tool for understanding the implementation of the FFT on SU(2), a key component in numerical simulations and advanced data analysis for high-performance computing applications on curved manifolds and quantum systems.

This manuscript introduces a novel method to assess tissue oxygen concentration via the quantum entanglement (QE) of photons originating from positronium which is produced within the patient's body during positron emission tomography. We also investigate the possibility of assessing hypoxia by simultaneously detecting positronium lifetime and the positronium decay rate ratio. We introduce two distinct quantum sensing approaches. Method 1 utilizes the correlation between oxygen concentration and ortho-positronium (o-Ps) decay rates, relying on the simultaneous measurement of the mean o-Ps lifetime ($\tau_{\mathrm{oPs}}$) and the $3\gamma$-to-$2\gamma$ annihilation rate ratio of o-Ps ($R_{\mathrm{oPs-3\gamma/2\gamma}}$). Method 2 introduces a novel hypothesis: that the degree of QE is sensitive to the relative contribution of annihilation mechanisms (pick-off vs. conversion), which in turn depends on oxygen concentration. We derive a formula for partial pressure of oxygen ($p\mathrm{O}_2$) as a function of $R_{\mathrm{oPs-3\gamma/2\gamma}}$ and $\tau_{\mathrm{oPs}}$ and estimate the measurement accuracy required for these parameters - and for the degree of QE - to sense in-vivo oxygen pressure in the range between hypoxic and physoxic conditions. Theoretical models and quantitative estimates for $R_{\mathrm{oPs-3\gamma/2\gamma}}$, $\tau_{\mathrm{oPs}}$ and for the degree of QE ($C_{\mathrm{QE}}$ ) as a function of $p\mathrm{O}_2$ are provided for water, isopropanol, cyclohexane, isooctane, and adipose tissue. In particular, applying the formulas derived under the working hypothesis that in pick-off process the photons are not entangled, we estimated that for $p\mathrm{O}_2 = 0$, the degree of quantum entanglement $C_{\mathrm{QE}}$ is equal to 0.890 for adipose, 0.886 for isopropanol, 0.867 for water, 0.818 for cyclohexane, and 0.784 for isooctane.

This paper starts with surveying the evolution of quantum-like models of cognition and decision making, transitioning from static kinematic representations to a robust dynamical framework based on open quantum systems. We provide a comprehensive analysis of the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation's application in cognitive psychology and decision making, illustrating how it models mental state evolution as a dissipative process influenced by an informational environment. We categorize dynamical regimes into Passive and Active Hamiltonians, demonstrating how non-commutation with projections on decision basis serves as a mathematical signature of cognitive agency and Quantum Escape from classical equilibria. The utility of this framework is further explored through its ability to stabilize non-Nash outcomes in strategic games, such as the Prisoner's Dilemma. Building upon this dynamical foundation, we identify “cognitive beats” as a signature of the internal struggle between competing “flows of mind” deliberated at approximately equal frequencies. Distinct from the damped oscillations of simple interference, these beats emerge from a structural tension between Liouvillian channels that generates a secondary, slow-scale modulation of conviction. This beat envelope dictates the timing of peak readiness and hesitation, providing a mathematical map of the transition between conflicting cognitive states. By resolving these nested time scales, we provide a new spectral diagnostic for the depth of cognitive agency and the complexity of the underlying deliberation process. This paper develops a theoretical framework linking GKSL dynamics with quantum-like cognition and decision-making (QCDM), highlighting how dissipative quantum models can capture features of human thought and decision processes.

We derive strict quantitative conditions under which a collective quantum system of N~370 spins exhibits classically forbidden temporal correlations in a spinor Bose-Einstein condensate (BEC). The Lipkin-Meshkov-Glick (LMG) model near its Z_2-breaking quantum critical point supports a mesoscopic superposition a|P> + b|R> of two macroscopic ordered phases (|P>: m_z ~ +m_*; |R>: m_z ~ -m_*) at the Goldilocks crossover N ~ N_c, where the tunnel splitting equals k_B T and macroscopic susceptibility chi ~ N coexists with finite quantum coherence. We establish two quantum-discriminating predictions. P4 (Landau-Zener crossover, proposed discriminator): quantum tunnelling drives P_error -> 0 exponentially with quench time, while the classically non-ergodic system remains kinetically frozen at P_error -> 1 - a parametrically large, computable separation that rests on a specific kinetic foil. P5 (Leggett–Garg inequality violation, strictly model-independent): K_3 > 1 is forbidden by macrorealism for all classical models satisfying non-invasive measurability. A five-level Lindblad simulation yields K_3 ~ 1.32 and dephasing threshold gamma_phi < 0.289 s^{-1} at the BEC target (gamma_phi = 0.05 s^{-1}, N = 370, Gamma/J = 0.95) - a margin of 8.8x above the optimal measurement interval, well within current experimental reach. The threshold has a precise physical origin in the emergent collective Z_2 symmetry: exact parity eliminates the dominant dephasing cross-term and renders the LGI correlator immune to T_1 population mixing without requiring ground-state preparation (2.35x improvement over the naive mean-field estimate); constructive dynamical phase alignment of higher odd-parity states at the benchmark parameters contributes a further 2.47x. All results are reproducible from the provided self-tested Python code.

We propose a versatile and efficient algorithmic framework for optimizing fermion-to-qubit mappings by generalizing the idea of randomized block coordinate descent. Our greedy approach, termed Randomized Subsystem Descent, iteratively samples a tractable subsystem from the full Hamiltonian, performs optimization within the subsystem under a given metric, and then reintegrates the updated subsystem into the global operator. Restricting the optimization to a subsystem at each iteration ensures computational efficiency, bypassing the dimensional bottlenecks that usually hinder global search heuristics. We benchmark our algorithm on one- and two-dimensional lattice hopping models, the Hubbard model with up to $16 \times 16$ sites, alongside a collection of molecular electronic-structure Hamiltonians with up to $54$ modes and more than $180,000$ Pauli strings. Across all benchmarks, our method consistently provides appreciable reduction in (weighted) Pauli weight, suggesting that Randomized Subsystem Descent is a practical and scalable framework for lowering the resource overhead of finding hardware-efficient Hamiltonian encodings.