Papers

Vacuum Rabi oscillations between a single photon and a single spin demonstrate the capability of harnessing light-matter interaction at the level of a single quantum of energy. Since the observation of strong spin-photon coupling in gate-defined quantum dots, probing this interaction in the time-domain has been a major objective. Here, we carefully engineer a device composed of two spatially separated double quantum dots hosting single electron spin qubits and a superconducting cavity to accommodate microwave photons. We observe multiple vacuum Rabi oscillations between each spin qubit and the cavity. By concatenating vacuum Rabi oscillations involving the two spins, an energy excitation in one qubit can be emitted as a photon and then transferred to the other qubit. When a single photon is emitted, the cavity is prepared in a Fock state, leading to an accelerated vacuum Rabi frequency. These results serve as building blocks not only in exploring light-matter interactions, but also in interfacing semiconductor spin qubits to photonic links.

The simplex of complete graphs, also known as the first-order truncated simplex lattice, is a network of $M+1$ identical complete graphs, each with $M$ vertices, such that each clique contains an edge or bridge to every other clique. It contains $N = M(M+1)$ vertices, and previous asymptotic results using a continuous-time quantum walk to search this graph for a single marked vertex have either numerically demonstrated an optimal runtime of $O(\sqrt{N})$, or analytically proved a deterministic success probability of 1, but not both, even when the bridges are weighted. In this paper, we give the first analytical proof of optimal quantum search on this graph, proving that it occurs when the weight of the bridges equals $M$. In addition, we numerically show that the optimal runtime is achieved more broadly whenever the weight is at least $\sqrt{M}$. Furthermore, the algorithm is also deterministic when the weight scales between $\sqrt{M}$ and $M$, and this is the first example of quantum search on the simplex of complete graphs that is both asymptotically optimal and deterministic. In addition, for weights where the algorithm is nondeterministic, we give a way to find the marked vertex by inspecting neighboring vertices. Finally, while it is known that connectivity is not a reliable indicator of fast quantum search when comparing different graph families, we show that it is also unreliable within the graph family of weighted simplex of complete graphs.

Gaussian states are fundamental in continuous-variable quantum information, yet characterizing non-Gaussianity remains challenging due to the non-convexity of the Gaussian set. Existing witnesses typically rely on Wigner negativity or other information-theoretic quantities. In this work, we develop a group-theoretic, multi-copy approach to detect non-Gaussianity in bosonic systems. We study passive linear optical transformations that mix copies of a quantum state and analyze their commutation with identical Gaussian unitaries applied to each copy. Orthogonal copy-mixing transformations commute with the symplectic part of the Gaussian action, while the displacement part restricts the symmetry to the stabilizer of the collective mode. This structure yields a family of witnesses satisfied by all single-mode Gaussian states. Fixing the thermal reference parameter via the purity, violation of these identities certifies non-Gaussianity. We illustrate the method with several single-mode examples and present an experimental protocol based on passive interferometry and photon-number-resolved detection, showing that the relevant multi-copy expectation values can be estimated from bounded phase observables. Finally, we extend the construction to multi-mode systems and discuss how the same symmetry framework may lead to quantitative measures of non-Gaussianity.

Solids appear to have localised centres of mass, yet many-body quantum theory describes them using translationally symmetric models that preclude localisation. Conventionally, this is resolved through spontaneous symmetry breaking by introducing an interaction with a semiclassical environment that breaks the symmetry. In the thermodynamic limit, the interaction can be removed while leaving the state localised. This, however, raises the question of how localisation arises outside the thermodynamic limit, i.e., in finite quantum systems (Wallace, 2018). Here, we show that, by quantising the environment, the localisation of finite systems occurs within decoherent branches, while the state vector of the composite system remains translationally symmetric. Our approach is analogous to the Page-Wootters construction (Page & Wootters, 1983) and quantum reference frames; moreover, we recover the semiclassical description as a limiting case while predicting experimentally distinguishable corrections away from this limit.

Cavity quantum electrodynamics offers a route to control quantum phases by using vacuum fluctuations of confined electromagnetic fields. In particular, planar cavities based on polar van der Waals materials can generate strongly confined modes and are promising for controlling two-dimensional correlated materials. Recently, moiré materials have become central platforms for studying two-dimensional heavy-fermion systems and their quantum phase transitions. Kondo lattices provide a prototypical model for studying quantum phase boundaries, driven by competition between Kondo screening and the ordering of local magnetic moments. We show that a cavity-induced interaction can shift the quantum phase transitions between a heavy-fermion phase and an antiferromagnetic phase in a two-dimensional Kondo lattice through a momentum-dependent self-energy of the conduction bands. For the longitudinal projected field motivated by h-BN hyperbolic phonon polaritons, the self-energy favors Kondo hybridization and expands the heavy-fermion region. Transverse and circular in-plane model structures give distinct effects, with the transverse case relatively favoring the magnetically ordered phase and the circular case lying between the longitudinal and transverse cases. These results indicate that electromagnetic vacuum fluctuations can effectively modify the control parameters of strongly correlated two-dimensional Kondo materials.

Entanglement distillation is a fundamental task in quantum information processing. In this work, we investigate the distillability properties of a class of two-qutrit symmetric NPT states of rank five. We resolve the 1-distillability problem for this class by proving that the previously open interval of the eigenvalue parameter is 1-undistillable. For the 2-distillability, we uncover a structural obstruction showing that no Schmidt-rank-two vector has a negative expectation in the relevant subspace. We also perform numerical investigations to explore the 2-distillability beyond this obstruction.

Quantum optimal control is a key tool for steering quantum dynamics, but its computational cost grows rapidly with the Hilbert space dimension. Here, we introduce a Fourier Neural Operator (FNO)-based framework for learning high dimensional molecular quantum dynamics and accelerating the inverse design of control protocols. Given an initial molecular population distribution, laser frequency, and polarization, the FNO predicts molecular-motional population dynamics up to $10^7$ times faster than GPU-accelerated numerical propagation with CUDA-Q Dynamics. Using this fast and differentiable surrogate, we develop the FNO stochastic pulse-measurement planner (FNO-SPMP), which constructs pulse sequences to purify an initially mixed Boltzmann distribution. We demonstrate the protocol in an 888-dimensional subspace of the hydronium molecule at 20 K, achieving a target-state population of 0.98 with a sequence success rate of up to 86.2%. In a shared discrete control space, FNO-SPMP achieves nearly twice the success rate of a reinforcement-learning baseline while using roughly half as many quantum control pulses and reducing pulse-sequence generation time from approximately 10 hours to 10-20 minutes. These results show that operator-learning surrogates can enable inverse design in quantum systems whose Hilbert spaces are too large for conventional direct optimization.

We develop a structure-specific fidelity-threshold robustness margin for finite-dimensional closed quantum systems under piecewise-constant coherent control. A scalar physical parameter may perturb the drift, a control Hamiltonian, or another declared Hamiltonian component across the control horizon. A differential sensitivity bound for trace-amplitude gate fidelity yields a threshold-dependent Lipschitz constant on the connected safe parameter component and hence a certified finite perturbation radius. Recentering this certificate produces an iterative one-dimensional method that takes certified safe steps toward the first fidelity-threshold boundary in either parameter direction. A three-qubit gate-control example shows that these finite margins vary by up to a factor of three across controllers of comparable nominal fidelity and contain structure-dependent information not captured by nominal differential sensitivity alone.

DAMPyF is an open-source Python implementation of the dissipation-assisted matrix product factorization (DAMPF) method, a tensor-network-based approach for the numerically exact simulation of finite-dimensional quantum systems coupled to bosonic environments. The method relies on a pseudomode representation of structured reservoirs and a matrix-product-state representation of the density matrix of the extended system, comprising the system and the pseudomodes. DAMPyF currently provides two workflows. First, it supports excitation energy-transfer dynamics within the single-system-excitation manifold, in which a system excitation is propagated in time. Second, it provides a high-level workflow tailored to molecular spectroscopy, in which the system levels represent electronic states and optical coherences are propagated for the subsequent computation of linear spectra, including absorption and circular dichroism. This paper describes the physical model, the DAMPF algorithm, the user-facing code structure, installation and execution, input and output formats, and minimal examples.

Two-dimensional quantum gases provide a distinctive setting in which enhanced thermal fluctuations, finite-size effects, and two-body bound-state formation are intrinsically intertwined. In this work, we study a single attractive impurity immersed in a finite, weakly interacting two-dimensional Bose gas, where finite size stabilizes a nonzero condensate fraction by introducing an infrared momentum scale, thereby enabling a Bogoliubov description of the bath. Using a hybrid approach that combines finite-temperature many-body scattering theory with input from path-integral Monte Carlo, we analyze the impurity quasiparticle energy across the condensate and normal regimes. The infrared scale generates a phonon-activation temperature below which the impurity energy remains nearly temperature independent. Once the resolved phonon modes become thermally populated, their contribution competes with condensate depletion, producing a nonmonotonic temperature dependence of the polaron energy. These results suggest that attractive Bose polarons may serve as sensitive probes of finite-size thermal fluctuations, phonon dressing, and bound-state physics in low-dimensional Bose gases.

We investigate the generation of deterministic and heralded non-Gaussian states of light, using a single two-level system coupled to a chiral waveguide. We study the case of a single two level system driven by pulsed coherent and squeezed drive in a chiral waveguide. For coherent input pulses, we show that the emitter can deterministically generate Wigner-negative states, albeit of limited rank. Going beyond, using squeezed-vacuum inputs, we show that the interaction produces rich bimodal non-Gaussian states from which higher-stellar-rank states, including large squeezed cat states, can be experimentally extracted with a substantial success rate. For experimental feasibility and comparison, we analyze the effect of imperfect coupling and of the intrinsic $50\%$ collection limit of symmetric, non-chiral waveguides. Following that, we propose a simple interferometric scheme that recovers an effectively chiral interaction in an otherwise bidirectional waveguide.

In quantum optimal control theory, gradient-based trajectory optimization techniques have proven versatile in designing multi-qubit quantum gates. Furthermore, incorporating the underlying Lie-group structure can accelerate the optimization process. In this work, we adapt the Lie-group formulation of the iterative linear quadratic regulator (iLQR) to the special unitary group SU(N) and apply it to quantum gate synthesis, systematically comparing it against the standard Euclidean iLQR formulation across multiple two- to five-qubit gates. We find that in the idealized, unconstrained setting, where all Lie-algebra basis elements are available as drive Hamiltonian terms, the Lie-group formulation converges faster than the Euclidean iLQR formulation. If drive terms are constrained to 2-local Hamiltonian terms, the Lie-group variant converges faster in early optimization iterations, but exhibits greater sensitivity to initialization and a stronger tendency towards local minima. These results demonstrate that incorporating Lie-group geometry into iLQR substantially improves convergence and highlight important next steps for improvements in constrained control settings.

The quality of multi-scale modelling techniques in molecular electronic structure calculations, such as embedding and subspace methods, relies upon the chosen active space. The automation of active space selection is vital for ensuring the accuracy, reproducibility, and scalability in such calculations. In this work, we introduce Tensor Network Active Space Selection using the Entanglement Feature. Through the isolation of strongly correlated electrons, this method provides a scalable foundation for embedding methods in multi-scale modelling. By representing the purities of all possible orbital partitions as a Matrix Product State, our method isolates regions of strong electron correlation without requiring manual preselection of target atoms or the calculation of expensive high-order density matrices. The results demonstrate that this approach leads to lower ground state energies and more accurate dipole moments than other fully automated selection schemes such as those based solely on single-orbital entropy or the selection of spatial orbitals around the HOMO/LUMO gap.

An isolated occupied multiplet may admit local tensor-product descriptions without a globally consistent subsystem structure. We characterize the obstruction by comparing the transition functions of the occupied multiplet with those generated by independent basis changes in the two candidate subsystems. When a decomposition into rank-one sectors over a closed surface is specified, the resulting quotient removes row- and column-additive Chern data and yields mixed Chern classes. Momentum-dependent mixing of the sector labels adds the Gauss–Codazzi curvature of the moving lines, while in the label-conserving limit the mixed class is measured by a crossed Thouless pump. When only the factor dimensions $p$ and $q$ are specified, the comparison is made at the level of the clutching map of a rank-$pq$ bundle over $S^4$. Product frames generate winding numbers in $q\mathbb Z+p\mathbb Z$, so global factorization is possible exactly when $C_2$ is divisible by $\gcd(p,q)$; in particular, odd $C_2$ obstructs a $2\times2$ factorization. We illustrate the two settings with finite eight-level Hamiltonians and give pumping and occupied-projector tomography protocols for their readout.

Quantum technologies have been widely recognized as unprecedented opportunities for ultra-high precision metrology. As a celebrated example in modern quantum optics, the Hong-Ou-Mandel (HOM) interferometer is well-known for enabling temporal resolutions on the attosecond scale. However, the relatively low Fisher information per trial in ordinary HOM measurements typically necessitates tens of thousands of repetitions to achieve such precision. Here, we propose and demonstrate a sample-half-inserted HOM (SHOM) interferometer, which enhances the Fisher information by five orders of magnitude in a single interference event. By introducing an asymmetric photon-sample interaction, the SHOM configuration produces a distinctive dip-bump-dip interference structure, converting what was previously viewed as an artifact into a helpful metrological resource. Experimentally, we measured the optical path difference with an average precision of 4.09 nm (13.63 as) and an average accuracy of 1.22 nm (4.07 as) using $O(10^7)$ photons. Our results establish SHOM interferometry as an efficient phase-insensitive approach, not only paving the way toward practical quantum-enhanced thickness measurement for transparent materials, but also serving as an elegant strategy to improve the performance of various quantum devices.

This study investigates the generation and enhancement of quantum entanglement in an electro-optomechanical ring cavity system. The setup integrates two Coulomb-coupled mechanical resonators, which serve as the fundamental mechanism for the generation of bipartite and tripartite entanglement via charge mediated coupling. We then demonstrate the significant enhancement of this entanglement via a nonlinear parametric drive (an optical parametric amplifier, OPA), which injects a controllable nonlinearity into the cavity. We derive the system's Hamiltonian and the corresponding quantum Langevin equations, which are linearized around steady-state solutions to analyze Gaussian quantum fluctuations. Employing the covariance matrix formalism, we quantify bipartite entanglement via logarithmic negativity and tripartite entanglement via the minimum residual contangle. Our results unequivocally show that while the Coulomb interaction is indispensable for creating entanglement, the OPA acts as a powerful control tool, dramatically amplifying the degree of quantum correlations for all subsystems. We find that the strength of entanglement is highly sensitive to several parameters and can be optimized through the strategic selection of the OPA's gain and phase, the laser detuning, and the input power. A key finding is the existence of a trade-off, where parameters that maximize entanglement also constrain the stable operating regime of the system. Furthermore, thermal noise is shown to progressively degrade all quantum correlations, underscoring the necessity for low-temperature operation. These findings provide comprehensive guidance for parameter optimization, outlining a clear path from generation to enhancement, and highlight the potential of such hybrid systems as versatile platforms for controlling multipartite entanglement in quantum technologies.

Quantum causal networks enable tests of nonclassicality beyond Bell nonlocality while relaxing some physically unwarranted assumptions. By relaxing the freedom-of-choice and spacelike-separation assumptions, the unrelated-confounders causal networks provide a simple and robust route to certify quantum nonclassicality. Here, we implement the minimal three-node unrelated-confounders network in an optical experiment using two independent polarization-entangled photon sources and an intervention at the central node, experimentally achieved with a high-fidelity entangling measurement. We employ a causal data-fusion protocol that combines observational and interventional data to significantly improve the protocol's noise tolerance, and observe a violation of the corresponding hybrid causal inequality by more than three standard deviations. Our results provide deeper insights into quantum nonlocality in networks and highlight the UC network as a compact, experimentally accessible platform for device-independent quantum protocols that do not require actively chosen measurement settings.

The gravitational frequency shift of light is well understood in the theory of classical electromagnetism. Nevertheless, its description in quantum theory is not yet fully developed. Recent work pointed out inconsistencies in previously developed models aimed at describing the gravitational redshift as an effective multi-mode mixer (MMM) acting on modes of light, but so far a complete solution of these issues was not obtained. Here, we identify the root cause of the MMM model's inconsistency and provide two complementary approaches to correct it: a "natural" one from a field-theoretic perspective, and another adapted to the language of quantum mechanics of finite-dimensional systems. We show that the second approach allows for modeling of the redshift in a multi-mode transmission setup as a quantum channel that can be characterized using standard quantum information-theoretic techniques when restricting the input states to Gaussian states of light.

Classical simulation of quantum circuits is an essential tool in quantum information science, but its applicability is constrained by the exponential growth of the Hilbert space and the entanglement structure of quantum states. In this work, we introduce Matrix Product Evolution (MPE), a tensor-train representation of quantum circuits constructed along the circuit depth rather than along the qubit index. Within this formulation, the simulation of a quantum circuit is modeled as the contraction of multiple MPE tensors. We develop an efficient contraction strategy based on a zip-up procedure to carry out this contraction in practice. We investigate the numerical behavior of this MPE-based contraction framework through simulations of random quantum circuits and the time evolution of a quantum many-body state. Our results characterize the growth of temporal bond dimensions, clarify how post-selection modifies the contraction cost and approximation accuracy, and identify regimes in which depth-oriented tensor-network contractions provide a useful complement to standard MPS-based simulation approaches.

Resonance-frequency fluctuations can limit the sensitivity and stability of superconducting microwave cavities used for qubit readout, optomechanical displacement sensing, and magnetic flux detection. Here, we demonstrate the suppression of resonance-frequency fluctuations by locking a noisy nonlinear superconducting microwave cavity to a strong pump tone. The Kerr nonlinearity of this system, whereby the resonance frequency depends on the intracavity field amplitude, gives rise to an intrinsic feedback mechanism that enables passive stabilization without active external feedback. Using two-tone spectroscopy, we experimentally characterize the intrinsic nonlinear feedback mechanism and investigate its temporal stability through Allan deviation analysis. The frequency fluctuations of the locked cavity mode are reduced by nearly two orders of magnitude, reaching the $1/f$ noise floor, without continuous frequency tracking or active control. Kerr locking provides a general approach for self-stabilizing nonlinear microwave resonators by suppressing low-frequency cavity noise while preserving sensitivity to signals outside the locking bandwidth. This approach may benefit a broad range of systems, including SQUID-based resonators, optomechanical devices, and parametric amplifiers.

Mesoscopic optical states are a promising resource for quantum communication, combining robustness against losses with the preservation of genuine quantum features. Here, we propose a quantum communication protocol in which information is encoded in the first and second moments of the photon-number distributions of classical optical states, and then decoded by photon-number-resolving detectors. Security relies on the nonclassical photon-number correlations of a twin-beam state transmitted alongside the signal in the quantum channel, providing an experimentally accessible security witness against both intercept-resend and beam-splitter attacks investigated in this work. Numerical simulations performed in experimentally accessible parameter regimes support the feasibility and security of the proposed communication protocol, yielding nonzero key generation rates under the considered eavesdropping attacks, and motivating its future experimental implementation.

Integration of quantum optical technique on-chip is crucial for large scale applications of quantum technology, which were proven in a free space environment to be superior to the corresponding classical technology. Squeezed states of light can be used for enhancing the sensitivity of quantum sensors and for fault-tolerant quantum computing. Although chip-based squeezed light generation has advanced significantly, practical impact remains limited because coupling losses between the chip and off-chip detectors destroy delicate quantum correlations, restricting the amount of observed squeezing. Here, we overcome this limitation by implementing the idea of on-chip quantum measurement with the aid of a parametric amplifier and applying it to the squeezed state generated by a silicon nitride (SiN) microring resonator. In our scheme, two matched SiN micro-rings are sequentially constructed. The first ring generates a squeezed state, whereas the second ring acts as a high-gain parametric amplifier (PA) that measures the squeezed state before the light experiences significant off-chip loss. This architecture is inherently loss-tolerant: the amplifier elevates the quantum noise well above the vacuum level, making the measurement insensitive to downstream losses. We directly observe a quantum noise reduction of 4.6 dB from the first ring, despite a chip-to-fiber coupling loss exceeding 5 dB. This work also demonstrates the first monolithic SU(1,1) interferometer with an estimated 5 dB signal-to-noise enhancement compared to traditional linear interferometers, and thus establishes a practical pathway for chip-based quantum sensors.

We investigate the geometric structure of the set of spectra of bipartite absolute separable states ($\mathrm{ASEP}_{m,n}$) and absolute positive partial transpose states ($\mathrm{APPT}_{m,n}$), i.e., bipartite quantum states that remain separable or PPT, respectively, under all global unitary transformations. First, we establish general geometric properties of absolute convex sets of matrices, their spectra and extreme points. Regarding absolute separability, we present a permutation-symmetric reformulation of the absolute PPT criterion and use it to demonstrate that $\mathrm{APPT}_{m,n}$ is a spectrahedron for all $m\leq n$: in particular, all its faces are exposed. While $\mathrm{ASEP}_{2,n}$ is a spectrahedron, too, for $\mathrm{ASEP}_{m,n}$ we can in general only show that it is a semialgebraic set for all $m,n\geq 3$. Furthermore, we provide a complete characterization of the faces and extreme points of $\mathrm{APPT}_{m,n}$ and demonstrate that the dimension of a face is determined by the rank of a certain matrix, with maximal proper faces having dimension $mn-m-1$. In the quantitative setting, we provide a rigorous lower bound on the maximal attainable purity of $\mathrm{APPT}_{m,n}$ via an inscribed polytope $\mathcal{P}_{m,n}$ and conjecture that the maximal purity of $\mathrm{APPT}_{m,n}$ (along with its spectra) coincides with the polytope for arbitrary dimensions except when $m=n=2$. Additionally, we also provide a rigorous upper bound on the minimal von Neumann entropy of $\mathrm{APPT}_{m,n}$ and demonstrate numerically that the minimum entropy eventually coincides with the polytope $\mathcal{P}_{m,n}$ as the local system dimension $n$ increases. Finally, we show that the relative spectral volume of $\mathrm{APPT}_{m,n}$ decays exponentially in $n$ by a constant multiplicative factor of the relative volume of the inscribed polytope $\mathcal{P}_{m,n}$.

Protected superconducting qubits such as the $0$-$\pi$ qubit promise to substantially suppress error rates, facilitating fault-tolerant quantum computing with fewer qubits. Measuring these qubits is challenging due to their protected nature, and thus far no concrete proposal exists for how to measure them without breaking their protection. Here we show how to perform protected measurements of the $0$-$\pi$ qubit in two orthogonal bases. The protection of these measurements is facilitated by their quantum non-demolition nature, allowing faults on ancillary measurement qubits to be tolerated. As experimental progress pushes protected qubits further into the low error-rate regime, our techniques will be crucial for fault-tolerant universal control.

Fault-tolerant quantum processors based on topological codes execute programs through lattice surgery, where operations must be mapped, routed, and supplied with magic states across a 2D grid of physical patches. Non-Clifford operations require these magic states, produced either by distillation factories or by cultivation, each trading footprint against preparation latency, and delivering a magic state to the data patches that consume it requires routing through the same shared layout as every other operation. Yet placement, routing, scheduling, and magic-state supply cannot be optimized in isolation: two operations with no circuit-level dependency can still contend for the same ports, routes, or magic-state terminals once placed, so a compiler that decouples instruction scheduling from magic-state generation, or hard-codes a single generation protocol, is forced to trade execution time against layout footprint instead of co-optimizing both across protocols. We present Harvest, a resource-aware compilation approach for lattice-surgery that co-optimizes magic-state consumption with circuit-aware placement and congestion-aware routing under a protocol-agnostic resource model, then reclaims unused layout footprint after scheduling. Across standard benchmark suites (QAOA, QFT, QASMBench), Harvest achieves an average speedup of $4.83\times$ (up to $17.8\times$) over sequential execution, improves schedule length by up to $1.35\times$ through circuit-aware placement, and reclaims up to $72.0\%$ of unused magic-state patches and $33.9\%$ of unused routing patches.

We identify enhanced strong coherent Surface-Enhanced Raman Scattering (SERS) interactions facilitated by hybridized metallo-dielectric cavities with a resonant fluorescent molecule. By illuminating a detuned electronic transition near saturation via a narrowband hybrid plasmonic mode, we observe enhanced splittings in the Stokes and anti-Stokes spectra, revealing strong optomechanical coupling and nonlinear vibrational modifications at intensities far below irreversible SERS damage thresholds. We compute the second-order photon correlations that allows identifying the nonclassical character associated to these strong optomechanical interactions and SERS configurations that enables them to optically characterize the anharmonic character of the vibrational modes.

Recently, a DC magnetometry protocol utilizing $N$-spin-ensemble superradiance was proposed. This method physically amplifies the acquired signal, suppressing estimation errors from measurement noise and achieving $\mathcal{O}(1/N)$ precision scaling when measurement noise dominates quantum fluctuations. However, quantum metrology is generally vulnerable to independent Markovian pure dephasing. For instance, the scaling of Greenberger-Horne-Zeilinger (GHZ) state-based magnetometry deteriorates from $\mathcal{O}(1/N)$ to $\mathcal{O}(1/\sqrt{N})$. Although pure dephasing likely degrades superradiant sensing, its quantitative impact remains unclear. Here, we investigate the effect of independent Markovian pure dephasing on this protocol using numerical simulations and mean-field analysis. We demonstrate that, in the large-$N$ limit, the estimation error increase is limited to a constant factor. This sharply contrasts with GHZ-state-based sensing, where the error increases by a factor of $\sqrt{N}$. Our analytical solutions elucidate the physical origin of this robustness qualitatively. These findings establish the high robustness of superradiance-based DC magnetometry against independent Markovian pure dephasing.

The implementation of quantum circuits is currently very expensive, especially due to the usage of large Toffoli gates. Therefore, it is critical to optimize circuit costs by factoring expressions as they become more complex. In the proposed algorithms to factor ESOP expressions, each product term is converted into a cell in a 2D matrix, and optimal factored AND/EXOR solutions are determined using Disjoint and Even-Odd Rectangle covering methods. Two Python programs implementing these algorithms were tested and evaluated using well-known benchmarks. The results showed that both the literal counts used in classical logic circuits as well as the Maslov cost used in quantum circuits was reduced by 20%-95% depending on expression size.

We introduce a novel multipartite entanglement-assisted classical communication task, referred to as dense coding swapping, in which legitimate parties collaboratively swap the dense codeability from one communication channel to another through suitable joint unitary operations. Due to the dense coding (DC) exclusion principle, the scheme enhances the dense codeability of a target pair while simultaneously reducing it for a non-target branch in the network. This swapping capability has broader implications, as it may be viewed as a form of process swapping, distinct from resource swapping, while also providing a prevention measure when one of the receivers is compromised. We derive necessary and sufficient conditions, expressed in terms of the Schmidt coefficients, for three-qubit pure states to support DC swapping, while we obtain a sufficient criterion for mixed states using their Bloch correlation parameters. Furthermore, we identify the optimal two-qubit unitary operators capable of realizing the swapping of dense codeability between communication channels. We further examine the tolerance of these eligible states against both colored and white noise, demonstrating the resilience of the proposed task under environmental perturbations. We also show that multipartite states supporting DC swapping require only a small amount of genuine multipartite entanglement and that this requirement decreases with increasing system size.

Multi-phonon resonance conditions underpin kinetic theories of phonon transport and lattice thermalization. We show that exact resonance matching, nonzero interaction coefficients, and network connectivity do not guarantee persistent energy diffusion. Symmetry-enforced balance relations drive exact-resonant collision currents to nonthermal zero-flux states, producing kinetic arrest from individual resonant sets to connected networks. Complete energy spreading is sustained by quasi-resonances. The thermodynamic and weak-nonlinearity limits do not commute: the leading kinetic behavior is recovered in the former, whereas at fixed finite size the thermalization time diverges through higher-order crossovers as the nonlinearity vanishes. Exact-resonance existence and connectivity are therefore kinematic, not sufficient dynamical, criteria for phonon energy diffusion.