Entanglement concentration is essential for quantum technologies yet, rigorous bounds on the success probability for universal protocols (those requiring no prior knowledge about the input state) have remained underexplored. We establish such fundamental limits for conclusive protocols distilling a perfect Bell state from pure two-qubit states by deriving the optimal success probability starting with two copies of a state with known Schmidt basis and four copies of a state with unknown Schmidt basis, using concatenated two-qubit operations. We prove that a known protocol achieves these bounds, confirming its optimality. Crucially, universality imposes an inherent efficiency trade-off, yielding an average success probability of just $2/105$ over Haar measure.

Quantum entanglement and coherence constitute fundamental resources for quantum information processing. Ultracold polar molecules, with their permanent electric dipole moments and tunable Stark levels, offer a promising platform for scalable quantum computing. In this work we propose qubit encoding in the pendular states of SrO molecules and employ the differential evolution (DE) algorithm, a global optimization strategy, to design microwave control fields for high-fidelity preparation of entangled states. In the absence of noise, fidelities above 0.9983 and concurrences above 0.9974 are achieved for Bell states and maximally coherent states. Under three representative Pauli noise channels, i.e., bit flip, dephasing, and isotropic noise, the DE-optimized control fields exhibit strong robustness, enabling reliable state preparation even in noisy environments. Furthermore, we extend this approach to prepare hybrid qutrit-qubit entangled states, demonstrating the scalability of the method. Our results provide a robust and experimentally feasible strategy for quantum state engineering with polar molecules, providing a practical link between theoretical control protocols and experimentally realistic noisy environments.

We present a framework for embedding arbitrary real linear generators into continuous-variable quantum systems through deterministic first-moment dynamics of a quadratic Hamiltonian. We show that any matrix $A\in {\mathbb{R}}^{N\times N}$ can be realized exactly on an invariant locking manifold, where the embedded dynamics evolves as $\langle \dot{\mathbf{x}}\rangle =A\langle \mathbf{x}\rangle$. Reversibility of the full symplectic evolution enforces a conjugate sector evolving under $-A^{\mathsf{T}}$, establishing a fundamental trade-off: Any contraction generated by $A$ must be compensated by expansion in the adjoint sector. For dissipative generators, this renders the locking manifold transversely unstable, requiring periodic resets. We derive resource bounds, including squeezing requirements that scale as $O\left(N^{2}t\right)$ for diffusive dynamics, and classify generators by their stability properties: Dissipative generators require active stabilization, conservative generators are marginally stable, and amplifying generators self-stabilize. Numerical validation of three discretized partial differential equations, including heat, advection, and backward heat, confirms the theoretical predictions with relative errors below ${10}^{-8}\%$.

Standard quantum speed limits presuppose exactly known parameters, overestimating operational speed under calibration uncertainty. We introduce a projected speed limit based on the quantum Fisher information that profiles out these nuisance parameters on a quotient manifold. We derive constructive bounds for general Markovian evolution using sensitivity equations. Applying this to Jaynes-Cummings sensors, we obtain explicit detuning tolerances and quantify speed limits arising from field-dependent Purcell loss. This framework turns geometric bounds into concrete design rules for calibration and interrogation time.

Certifying high-dimensional quantum channels is essential for ensuring the reliability of quantum communication protocols. Existing certification schemes often rely on fully trusted internal devices, which is difficult to achieve in realistic scenarios. Here, we propose a semi-device-independent framework for certifying channel properties directly from observed statistics, assuming only that the system dimension is known. By explicitly incorporating the full set of structural constraints inherent in Choi states, our approach exploits the Choi-Jamiołkowski isomorphism for rigorous certification of quantum channels. The entanglement dimensionality of quantum channels is first certified by introducing a witness and numerically determining its Schmidt-number-dependent bounds. This certification method reproduces known analytical benchmarks and is applied to dephasing and depolarizing noise channels, thereby confirming its validity. To provide a more complete assessment of channel performance, the entanglement fidelity of quantum channels is also certified using a hierarchy of semidefinite programming relaxations based on localizing matrices. Lower bounds on the entanglement fidelity are obtained that are compatible with either the full set of observed statistics or a single witness value.

Quantum learning from state samples is often benchmarked in a fixed-budget paradigm, relating error to a prescribed number of copies. We instead adopt a stopping-time viewpoint: in minimal-feedback learning, the learning completion can be defined by an online run-length certificate extracted from a one-bit-per-copy record. As an instantiation, we analyze the previously introduced single-shot measurement learning [Phys. Rev. A 98, 052302 (2018); Phys. Rev. Lett. 126, 170504 (2021)], which tunes a unitary and halts after $M_H$ consecutive successes. Viewing the halting as a sequential certification linking the observed counter to infidelity, we derive sample-complexity bounds that separate search (driving success probability toward unity) from certification (run statistics of consecutive successes). The resulting trade-off among $M_H$, dimension $d$, and one-bit reliability clarifies when performance is control-limited versus certificate-limited. With label-flip noise probability $q$, we find a sharp feasibility threshold: once $q{M}_H\gtrsim 1$, the expected halting time grows exponentially, making the learning completion impractical even under ideal control. More broadly, this shows that under severely constrained feedback, the certification can dominate sample complexity and small label noise becomes the information bottleneck. Finally, the near-optimal accuracy enabled by run-length certification aligns with the quantum-state-estimation (and equivalently, no-cloning) limits, expressed in the stopping-time terms.

Rydberg atom arrays are a front-running platform for quantum processors. A major challenge hindering the scalability of this platform is the limited qubit connectivity due to the finite range of interatomic interactions. We explore an approach to realize dynamical all-to-all connectivity with the use of moving “messenger” atomic qubits that couple distant “computational” qubits held in a static tweezer array. Our aim is to present a general framework and systematically compare several possible realizations of this concept within a unified perspective. To this end, we detail and compare five specific architectures based on this concept, each presenting distinct advantages and challenges tied to the efficacy of techniques used to couple, move, and measure atomic qubits. We demonstrate that, though technologically demanding, the messenger-qubit paradigm opens a promising avenue to a truly scalable quantum processor based on Rydberg atoms.

We theoretically investigate ground-state properties and collective excitations of one-dimensional quantum droplets in asymmetric Bose-Bose mixtures with unequal intraspin interactions. Using the extended Gross-Pitaevskii equation supported by variational, sum-rule, and linearization methods, we show that the intraspin interaction ratio substantially alters the droplet's density profile, driving a transition from Gaussian-like to flat-top shapes. By examining two experimentally relevant parameter regions, we analyze density profiles, radii, peak densities, and excitation spectra to distinguish quantum phases and to depict phase diagrams in the space of asymmetric interaction ratio and total atom number. We carefully study the frequencies of both well-known dipole and breathing modes and less-explored spin-dipole and spin-breathing modes. The breathing-mode frequency decreases monotonically with interaction ratio, approaching asymptotically the result of a conventional weakly interacting Bose gas. It varies nonmonotonically with total atom number, peaking at a critical point that highlights the crucial role of quantum fluctuations. In contrast, spin modes display distinct temporal spin density distributions and reveal in-phase and out-of-phase relative dynamics between components. Their frequencies depend instead monotonically on the interaction ratio and atom number. Our results provide a comprehensive understanding of asymmetric quantum droplets and link to experimentally accessible regimes in ultracold ${}^{39}\mathrm{K}$ atomic gases.

Utilizing ultracold spinor gases as large-scale, many-body quantum simulation platforms, we establish a toolbox for the precise control, characterization, and detection of nonequilibrium dynamics via internal spinor phases. We develop a method to extract the phase evolution from the observed spin population dynamics, allowing us to define an order parameter that sharply identifies dynamical phase transitions over a wide range of conditions. This work also demonstrates a technique for inferring spin-dependent interactions from a single experimental time trace, in contrast to the standard approach that requires mapping a cross section of the phase diagram, with immediate applications to systems experiencing complex time-dependent interactions. Additionally, we demonstrate experimental access to and control over nonergodic relaxation dynamics, where states of similar energy in the (nominally) thermal region of the energy spectrum retain a dependence on the initial state, via the manipulation of spinor phases, enabling the study of nonergodic thermalization dynamics connected to quantum scarring.

In static lattice systems, the Nielsen-Ninomiya theorem enforces the pairing of Weyl points with opposite chiralities, which precludes the chiral magnetic effect (CME) in equilibrium. Periodic driving provides a viable route to circumvent this no-go constraint. Here, we propose a scheme to realize and control unpaired Weyl points using ultracold atoms in a three-dimensional (3D) optical Raman lattice under continuous periodic driving. By engineering distinct relative symmetries between the lattice and multiple Raman potentials, the configuration generates an effective 3D spin-orbit coupling and yields a tunable topological-insulator phase. Through adiabatic periodic modulation of this system, we show that eight Weyl points emerge in the quasienergy spectrum of the low-energy sector, whose net chirality can be precisely tuned. A nonzero total chirality directly corresponds to the formation of unpaired Weyl points. Furthermore, by implementing a synthetic magnetic field via laser-assisted tunneling in this setup, we demonstrate that the chirality imbalance drives a quantized charge current in the weak-field regime, providing a direct signature of the CME. We verify that the adiabatic condition of the driving protocol, as well as the proposed experimental preparation and detection techniques, are within reach of current ultracold-atom experiments. This work establishes a realistic and controllable platform for exploring chiral-anomaly physics and nonequilibrium topological phenomena linked to Weyl fermions.

Quantum backflow refers to the appearance of negative probability current in a state whose momentum distribution is essentially positive. We propose a scheme to prepare such states in a noninteracting Bose-Einstein condensate using large-momentum-transfer (LMT) atom interferometry. Our approach extends the single-pulse proposal of Palmero et al. [Phys. Rev. A 87, 053618 (2013)] by allowing one interferometer arm to undergo a tunable sequence of momentum-transfer pulses before recombination with a freely propagating arm. For realistic parameters for ${}^{88}\mathrm{Sr}$, the protocol generates interference states with tunable probability current and negligible negative-momentum contamination. We evaluate both the probability current and the critical-density criterion introduced by Palmero et al. [Phys. Rev. A 87, 053618 (2013)], and identify parameter regimes in which the backflow signature is enhanced relative to the single-pulse scheme. These results present LMT interferometry as a flexible route for preparing candidate quantum-backflow states in cold-atom experiments.

Temporal soliton formation requires a precise balance between dispersion and nonlinearity, yet this balance is easily disrupted, driving pulses into broadened, breathing, or breakup states. In this work we propose a universal strategy for temporal soliton generation and stabilization based on a phase framework that simultaneously accounts for dispersion, second-order $\left(2^{\mathrm{nd}}\text{−}\mathrm{NL}\right)$ and third-order $\left(3^{\mathrm{rd}}\text{−}\mathrm{NL}\right)$ nonlinearities. In this framework, pump-parameter phase diagrams map regions of nonsolitonic distortion, breathing-type dynamics, and stable soliton propagation. By engineering competing or synergic interactions between $2^{\mathrm{nd}}\text{−}\mathrm{NL}$ and $3^{\mathrm{rd}}\text{−}\mathrm{NL}$, operating pump conditions can be steered from distorted or breathing regimes into the stable-soliton domain. Using intentionally detuned phase-matched conditions, second-harmonic generation induces a controllable temporal chirp that either compensates or reinforces $3^{\mathrm{rd}}\text{−}\mathrm{NL}$ effects, substantially expanding the soliton stability window by achieving robust balance with dispersion. Simulations show that such optimized periodically poled lithium niobate structures enable tunable competing or synergic nonlinearities supporting soliton propagation over pump-parameter space with a wavelength range of 1.1–5 µm and intensities of $3.5–175 \mathrm{GW}/{\mathrm{cm}}^2$, even with second-harmonic generation efficiencies below 1%, substantially extending the accessible regime for broadband, phase-coherent, ultrafast soliton control far beyond single-nonlinearity limits.

We investigate reentrant topological transitions in a one-dimensional Su-Schrieffer-Heeger chain with generalized Bernoulli disorder in the intradimer hopping amplitudes. Owing to its independently tunable values and probabilities, the multivalued disorder distribution provides a direct way to control the topological phase diagram. We show that increasing the disorder strength can split the nontrivial regime into multiple disconnected topological windows, whose number, widths, and locations are determined by the distribution parameters. The phase boundaries are derived analytically from the zero-mode inverse localization length and are governed by a weighted geometric mean of the disordered hopping amplitudes, in agreement with numerical results from the reflection-matrix topological quantum number and the real-space winding number. We also show that the mean chiral displacement dynamically identifies these reentrant windows. These results demonstrate how multivalued random disorder can organize and tune reentrant topological behavior in one-dimensional chiral lattices.

Here we report reconfigurable optical skyrmionic wave plates based on self-organized liquid crystal textures exploiting spin-orbit interactions, entirely avoiding lithography or microfabrication. Beyond polarization-driven reconfigurability, we achieve dynamic control of both skyrmion topology and operating wavelength using temperature and external fields. The concept is demonstrated analytically and experimentally with two complementary realizations: sessile droplets, where topology is set by droplet radius and tuned thermally or electrically, and thin films under applied fields, where defect-mediated textures enable simultaneous tuning of topology and wavelength. By combining self-organization, external-field control, and spin-orbit optics, these results establish liquid crystals as a compact, reconfigurable platform for skyrmionic photonics, bridging fundamental topology and practical optical functionality.

Bound states of solitons, alias soliton molecules, are of great interest as they are responsible not only for many new physical phenomena but also for being useful in various applications. In contrast with bright soliton molecules, the formation of stable dark-soliton molecules (DSMs) is more challenging because the interaction between dark solitons is inherently repulsive in a defocusing medium. Here we propose a practical scheme to create stable two-dimensional (2D) DSMs in a gas of Rydberg atoms, which renders not only a giant and nonlocal Kerr nonlinearity but also tunable parameters. We show that stable 2D DSMs can be produced due to the balance of the nonlocality-induced attractive force and the inherent repulsive interaction between 2D dark solitons. Further, they have more spatial configurations than the stable 1D DSMs. We also show that the DSM size can be actively controlled by changing the nonlocality degree of the nonlocal Kerr nonlinearity.

Shor's algorithm can factor large integers with a certain success probability in polynomial time, making it one of the most significant quantum algorithms. However, its practical implementation requires an impractically large number of qubits in the current noisy intermediate-scale quantum era, posing major technological challenges. In this work, we present a classical optical scheme for implementing Shor's factorization algorithm. In our approach, the two core components of the algorithm—modular exponentiation and the quantum Fourier transform—are realized using classical coherent optical circuits. The number of required optical elements remains polynomial, matching the resource scaling of the quantum version. Importantly, this scheme avoids the decoherence issues inherent to quantum systems and is readily implementable with existing optical technologies. Using this method, we successfully factored $N=15$ and 21, with experimental results in excellent agreement with theoretical predictions. This work provides a practical classical pathway for simulating quantum algorithms and highlights the potential of classical optical computation for tackling complex computational problems.

The saturation intensity, $I_{\text{s}}$, of alkali vapors is often quoted for their strongest closed, nondegenerate two-level transition. In realistic atomic systems, however, level degeneracy and optical pumping substantially modify the saturation behavior. This paper presents a robust technique for measuring the saturation intensity of alkali vapors under real experimental conditions. Central to this approach is the derivation of a generalized Maxwell-based Beer-Lambert equation and its implementation for a three-level system (an upper level, two lower levels). We apply this technique to natural rubidium vapor $(27.8\%{}^{87}\mathrm{Rb}+72.2\%{}^{85}\mathrm{Rb})$ and determine the saturation intensities of all Doppler-broadened ${\text{D}}_2$-line transitions, probed by a linearly polarized laser beam at vapor temperatures $25–33{}^{\circ }\text{C}$. We find that all transitions exhibit $I_{\text{s}}$ in the range $31–34\text{W}{\text{m}}^{-2}$, roughly twice the commonly cited value $16.70\text{W}{\text{m}}^{-2}$. This technique also yields the hyperfine optical pumping factor $\beta$, which ranges from 3.1 to 22 across the transitions and can depend on intensity, leading to accelerated saturation. Accurate determination of the $I_{\text{s}}$ and $\beta$ values under experimentally relevant conditions allows more precise modeling and quantitative exploitation of alkali-vapor nonlinearities.

Implementation of a two-level non-Hermitian qubit via postselection of a three-level system has been demonstrated. The postselection procedure, which discards quantum jumps to the ground-state manifold $|g\rangle$ while retaining excitations in the $|e\rangle$ and $|f\rangle$ manifolds, effectively generates a non-Hermitian qubit exhibiting $\mathcal{PT}$ symmetry. In this work, we perform continuous homodyne measurement of this non-Hermitian qubit and analyze the interplay between decay introduced by postselection and measurement backaction. We compare the ensemble-averaged dynamics obtained from measurement trajectories with the Liouvillian average, highlighting the deviations arising from measurement backaction and postselection. We formulate the no-jump stochastic differential equation describing the postselected non-Hermitian qubit and show that its ensemble-averaged dynamics agree with those of the jump-updated postselected evolution at drive strengths far from the Liouvillian exceptional point (EP). The degree of deviation near the EP depends sensitively on the nature of the drive. This discrepancy is attributed to the interplay between measurement backaction and the non-Hermitian decay introduced by postselection. Furthermore, we determine the optimal path of the non-Hermitian qubit by extremizing the action within the path-integral formulation of the quantum trajectory framework. Our results provide insights into how measurement backaction and non-Hermitian dynamics together shape the transient behavior of open quantum systems and enable controlled manipulation of qubits near exceptional points.

We theoretically study time-dependent correlations in a strongly driven array of $N$ two-level atoms collectively coupled to photons. We focus on the spectrum $\left\{\lambda \right\}$ of the Liouvillian superoperator. Our main finding is the suppression of subradiant oscillating correlations between atomic states by a strong coherent drive: The correlation decay rates $-\mathrm{Re}\lambda$ are lower bounded by thresholds proportional to their oscillation frequencies $\mathrm{Im}\lambda$ and are larger than half of the single-atom decay rate. We demonstrate this limit numerically for various one-, two-, and three-dimensional arrays. In the one-dimensional case of atoms coupled to the waveguide we also provide a rigorous proof based on the analytical decomposition of the Liouvillian using spectral theory of simplicial complexes and partially ordered sets. This limit is independent of the number of atoms $N$; it holds both for small arrays and in the macroscopic limit.

We develop an experimentally grounded theory for cooling a phonon-coupled microwave cavity far below its ambient bath using a resettable two-qubit reservoir. Motivated by cQED hardware that can operate at the 1–4 K stage, we model a high-$Q$ three-dimensional (3D) cavity repeatedly and weakly engaged by internally correlated two-level pairs that are reprepared and actively reset between interactions. From a Lindblad master equation for a cavity subject to both a phonon bath and a Poisson train of finite-duration ancilla interactions, we obtain closed-form steady states for the cavity photon number and effective temperature in two geometries: (i) only one atom of each pair couples to the cavity, and (ii) both atoms couple collectively. The one-atom geometry cools the cavity below the phonon bath but not below the pair's own temperature. In contrast, when both atoms couple, intrapair coherence renormalizes the upward and downward transition rates seen by the cavity, creating a quantum-enhanced refrigeration effect that can drive the cavity well below the reservoir temperature when phonon damping is weak. Our detuning-aware, time-window–aware collision model (including finite interaction time, arrival rate, and cavity damping) yields analytic lineshapes and identifies broad “cooling valleys” near resonance, together with the crossover between reservoir-dominated and phonon-dominated regimes. Guided by these results, we outline a concrete cQED implementation with two transmons in a 3D cavity using nanosecond flux tuning and fast dissipative or measurement-based resets. Under realistic parameters (MHz-rate cycles, small-angle exchanges, measured reset fidelities), the engineered reservoir reaches $\approx 50$ mK even when the ambient bath is 4 K. Together, these results provide a compact, analyzable route to sub-100-mK microwave modes within a multikelvin cryostat, opening a realistic avenue toward scalable, higher-temperature quantum hardware.